diff --git a/cpp/benchmarks/CMakeLists.txt b/cpp/benchmarks/CMakeLists.txt
index 03f11cc957b..549cb8e5d5d 100644
--- a/cpp/benchmarks/CMakeLists.txt
+++ b/cpp/benchmarks/CMakeLists.txt
@@ -344,11 +344,18 @@ ConfigureNVBench(CSV_WRITER_NVBENCH io/csv/csv_writer.cpp)
 
 # ##################################################################################################
 # * ast benchmark ---------------------------------------------------------------------------------
-ConfigureNVBench(AST_NVBENCH ast/transform.cpp)
+ConfigureNVBench(AST_NVBENCH ast/polynomials.cpp ast/transform.cpp)
 
 # ##################################################################################################
 # * binaryop benchmark ----------------------------------------------------------------------------
-ConfigureNVBench(BINARYOP_NVBENCH binaryop/binaryop.cpp binaryop/compiled_binaryop.cpp)
+ConfigureNVBench(
+  BINARYOP_NVBENCH binaryop/binaryop.cpp binaryop/compiled_binaryop.cpp binaryop/polynomials.cpp
+)
+
+# ##################################################################################################
+# * transform benchmark
+# ---------------------------------------------------------------------------------
+ConfigureNVBench(TRANSFORM_NVBENCH transform/polynomials.cpp)
 
 # ##################################################################################################
 # * nvtext benchmark -------------------------------------------------------------------
diff --git a/cpp/benchmarks/ast/polynomials.cpp b/cpp/benchmarks/ast/polynomials.cpp
new file mode 100644
index 00000000000..b8e4ca46b72
--- /dev/null
+++ b/cpp/benchmarks/ast/polynomials.cpp
@@ -0,0 +1,94 @@
+/*
+ * Copyright (c) 2025, NVIDIA CORPORATION.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#include <benchmarks/common/generate_input.hpp>
+
+#include <cudf/ast/expressions.hpp>
+#include <cudf/column/column.hpp>
+#include <cudf/detail/nvtx/ranges.hpp>
+#include <cudf/table/table.hpp>
+#include <cudf/transform.hpp>
+#include <cudf/utilities/error.hpp>
+
+#include <thrust/iterator/counting_iterator.h>
+
+#include <nvbench/nvbench.cuh>
+#include <nvbench/types.cuh>
+
+#include <random>
+
+template <typename key_type>
+static void BM_ast_polynomials(nvbench::state& state)
+{
+  auto const num_rows = static_cast<cudf::size_type>(state.get_int64("num_rows"));
+  auto const order    = static_cast<cudf::size_type>(state.get_int64("order"));
+
+  CUDF_EXPECTS(order > 0, "Polynomial order must be greater than 0");
+
+  data_profile profile;
+  profile.set_distribution_params(cudf::type_to_id<key_type>(),
+                                  distribution_id::NORMAL,
+                                  static_cast<key_type>(0),
+                                  static_cast<key_type>(1));
+  auto table = create_random_table({cudf::type_to_id<key_type>()}, row_count{num_rows}, profile);
+  auto column_view = table->get_column(0);
+
+  std::vector<cudf::numeric_scalar<key_type>> constants;
+  {
+    std::random_device random_device;
+    std::mt19937 generator;
+    std::uniform_real_distribution<key_type> distribution{0, 1};
+
+    std::transform(thrust::make_counting_iterator(0),
+                   thrust::make_counting_iterator(order + 1),
+                   std::back_inserter(constants),
+                   [&](int) { return distribution(generator); });
+  }
+
+  cudf::ast::tree tree{};
+
+  auto& column_ref = tree.push(cudf::ast::column_reference{0});
+
+  // computes polynomials: (((ax + b)x + c)x + d)x + e... = ax**4 + bx**3 + cx**2 + dx + e....
+  tree.push(cudf::ast::literal{constants[0]});
+
+  for (cudf::size_type i = 0; i < order; i++) {
+    auto& product =
+      tree.push(cudf::ast::operation{cudf::ast::ast_operator::MUL, tree.back(), column_ref});
+    auto& constant = tree.push(cudf::ast::literal{constants[i + 1]});
+    tree.push(cudf::ast::operation{cudf::ast::ast_operator::ADD, product, constant});
+  }
+
+  // Use the number of bytes read from global memory
+  state.add_global_memory_reads<key_type>(num_rows);
+  state.add_global_memory_writes<key_type>(num_rows);
+
+  state.exec(nvbench::exec_tag::sync, [&](nvbench::launch& launch) {
+    cudf::scoped_range range{"benchmark_iteration"};
+    cudf::compute_column(*table, tree.back(), launch.get_stream().get_stream());
+  });
+}
+
+#define AST_POLYNOMIAL_BENCHMARK_DEFINE(name, key_type)                          \
+  static void name(::nvbench::state& st) { ::BM_ast_polynomials<key_type>(st); } \
+  NVBENCH_BENCH(name)                                                            \
+    .set_name(#name)                                                             \
+    .add_int64_axis("num_rows", {100'000, 1'000'000, 10'000'000, 100'000'000})   \
+    .add_int64_axis("order", {1, 2, 4, 8, 16, 32})
+
+AST_POLYNOMIAL_BENCHMARK_DEFINE(ast_polynomials_float32, float);
+
+AST_POLYNOMIAL_BENCHMARK_DEFINE(ast_polynomials_float64, double);
diff --git a/cpp/benchmarks/binaryop/polynomials.cpp b/cpp/benchmarks/binaryop/polynomials.cpp
new file mode 100644
index 00000000000..782ae1db927
--- /dev/null
+++ b/cpp/benchmarks/binaryop/polynomials.cpp
@@ -0,0 +1,101 @@
+/*
+ * Copyright (c) 2025, NVIDIA CORPORATION.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#include <benchmarks/common/generate_input.hpp>
+
+#include <cudf/binaryop.hpp>
+#include <cudf/column/column.hpp>
+#include <cudf/column/column_factories.hpp>
+#include <cudf/detail/nvtx/ranges.hpp>
+#include <cudf/strings/strings_column_view.hpp>
+#include <cudf/types.hpp>
+
+#include <thrust/iterator/counting_iterator.h>
+
+#include <nvbench/nvbench.cuh>
+
+#include <algorithm>
+#include <random>
+
+template <typename key_type>
+static void BM_binaryop_polynomials(nvbench::state& state)
+{
+  auto const num_rows{static_cast<cudf::size_type>(state.get_int64("num_rows"))};
+  auto const order{static_cast<cudf::size_type>(state.get_int64("order"))};
+
+  CUDF_EXPECTS(order > 0, "Polynomial order must be greater than 0");
+
+  data_profile profile;
+  profile.set_distribution_params(cudf::type_to_id<key_type>(),
+                                  distribution_id::NORMAL,
+                                  static_cast<key_type>(0),
+                                  static_cast<key_type>(1));
+  auto table = create_random_table({cudf::type_to_id<key_type>()}, row_count{num_rows}, profile);
+  auto column_view = table->get_column(0);
+
+  std::vector<cudf::numeric_scalar<key_type>> constants;
+  {
+    std::random_device random_device;
+    std::mt19937 generator;
+    std::uniform_real_distribution<key_type> distribution{0, 1};
+
+    std::transform(thrust::make_counting_iterator(0),
+                   thrust::make_counting_iterator(order + 1),
+                   std::back_inserter(constants),
+                   [&](int) { return cudf::numeric_scalar<key_type>(distribution(generator)); });
+  }
+
+  // Use the number of bytes read from global memory
+  state.add_global_memory_reads<key_type>(num_rows);
+  state.add_global_memory_writes<key_type>(num_rows);
+
+  state.exec(nvbench::exec_tag::sync, [&](nvbench::launch& launch) {
+    // computes polynomials: (((ax + b)x + c)x + d)x + e... = ax**4 + bx**3 + cx**2 + dx + e....
+    cudf::scoped_range range{"benchmark_iteration"};
+    rmm::cuda_stream_view stream{launch.get_stream().get_stream()};
+    std::vector<std::unique_ptr<cudf::column>> intermediates;
+
+    auto result = cudf::make_column_from_scalar(constants[0], num_rows, stream);
+
+    for (cudf::size_type i = 0; i < order; i++) {
+      auto product = cudf::binary_operation(result->view(),
+                                            column_view,
+                                            cudf::binary_operator::MUL,
+                                            cudf::data_type{cudf::type_to_id<key_type>()},
+                                            stream);
+      auto sum     = cudf::binary_operation(product->view(),
+                                        constants[i + 1],
+                                        cudf::binary_operator::ADD,
+                                        cudf::data_type{cudf::type_to_id<key_type>()},
+                                        stream);
+      intermediates.push_back(std::move(product));
+      intermediates.push_back(std::move(result));
+      result = std::move(sum);
+    }
+  });
+}
+
+#define BINARYOP_POLYNOMIALS_BENCHMARK_DEFINE(name, key_type)                         \
+                                                                                      \
+  static void name(::nvbench::state& st) { ::BM_binaryop_polynomials<key_type>(st); } \
+  NVBENCH_BENCH(name)                                                                 \
+    .set_name(#name)                                                                  \
+    .add_int64_axis("num_rows", {100'000, 1'000'000, 10'000'000, 100'000'000})        \
+    .add_int64_axis("order", {1, 2, 4, 8, 16, 32})
+
+BINARYOP_POLYNOMIALS_BENCHMARK_DEFINE(binaryop_polynomials_float32, float);
+
+BINARYOP_POLYNOMIALS_BENCHMARK_DEFINE(binaryop_polynomials_float64, double);
diff --git a/cpp/benchmarks/transform/polynomials.cpp b/cpp/benchmarks/transform/polynomials.cpp
new file mode 100644
index 00000000000..f23789f5460
--- /dev/null
+++ b/cpp/benchmarks/transform/polynomials.cpp
@@ -0,0 +1,108 @@
+/*
+ * Copyright (c) 2025, NVIDIA CORPORATION.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#include <benchmarks/common/generate_input.hpp>
+
+#include <cudf/column/column.hpp>
+#include <cudf/column/column_factories.hpp>
+#include <cudf/detail/nvtx/ranges.hpp>
+#include <cudf/transform.hpp>
+#include <cudf/types.hpp>
+
+#include <thrust/iterator/counting_iterator.h>
+
+#include <nvbench/nvbench.cuh>
+
+#include <algorithm>
+#include <random>
+
+template <typename key_type>
+static void BM_transform_polynomials(nvbench::state& state)
+{
+  auto const num_rows{static_cast<cudf::size_type>(state.get_int64("num_rows"))};
+  auto const order{static_cast<cudf::size_type>(state.get_int64("order"))};
+
+  CUDF_EXPECTS(order > 0, "Polynomial order must be greater than 0");
+
+  data_profile profile;
+  profile.set_distribution_params(cudf::type_to_id<key_type>(),
+                                  distribution_id::NORMAL,
+                                  static_cast<key_type>(0),
+                                  static_cast<key_type>(1));
+  auto table = create_random_table({cudf::type_to_id<key_type>()}, row_count{num_rows}, profile);
+  auto column_view = table->get_column(0);
+
+  std::vector<key_type> constants;
+
+  {
+    std::random_device random_device;
+    std::mt19937 generator;
+    std::uniform_real_distribution<key_type> distribution{0, 1};
+
+    std::transform(thrust::make_counting_iterator(0),
+                   thrust::make_counting_iterator(order + 1),
+                   std::back_inserter(constants),
+                   [&](int) { return distribution(generator); });
+  }
+
+  // Use the number of bytes read from global memory
+  state.add_global_memory_reads<key_type>(num_rows);
+  state.add_global_memory_writes<key_type>(num_rows);
+
+  state.exec(nvbench::exec_tag::sync, [&](nvbench::launch& launch) {
+    // computes polynomials: (((ax + b)x + c)x + d)x + e... = ax**4 + bx**3 + cx**2 + dx + e....
+
+    cudf::scoped_range range{"benchmark_iteration"};
+
+    std::string expr = std::to_string(constants[0]);
+
+    for (cudf::size_type i = 0; i < order; i++) {
+      expr = "( " + expr + " ) * x + " + std::to_string(constants[i + 1]);
+    }
+
+    static_assert(std::is_same_v<key_type, float> || std::is_same_v<key_type, double>);
+    std::string type = std::is_same_v<key_type, float> ? "float" : "double";
+
+    std::string udf = R"***(
+__device__ inline void    compute_polynomial   (
+       )***" + type + R"***(* out,
+       )***" + type + R"***( x
+)
+{
+  *out = )***" + expr +
+                      R"***(;
+}
+)***";
+
+    cudf::transform(column_view,
+                    udf,
+                    cudf::data_type{cudf::type_to_id<key_type>()},
+                    false,
+                    launch.get_stream().get_stream());
+  });
+}
+
+#define TRANSFORM_POLYNOMIALS_BENCHMARK_DEFINE(name, key_type)                         \
+                                                                                       \
+  static void name(::nvbench::state& st) { ::BM_transform_polynomials<key_type>(st); } \
+  NVBENCH_BENCH(name)                                                                  \
+    .set_name(#name)                                                                   \
+    .add_int64_axis("num_rows", {100'000, 1'000'000, 10'000'000, 100'000'000})         \
+    .add_int64_axis("order", {1, 2, 4, 8, 16, 32})
+
+TRANSFORM_POLYNOMIALS_BENCHMARK_DEFINE(transform_polynomials_float32, float);
+
+TRANSFORM_POLYNOMIALS_BENCHMARK_DEFINE(transform_polynomials_float64, double);