diff --git a/UPolynomial.pas b/UPolynomial.pas
index 5d33937..f4cec85 100644
--- a/UPolynomial.pas
+++ b/UPolynomial.pas
@@ -46,6 +46,9 @@ type
     // Returns f(s * x), given a polynomial f(x) and scale factor s.
     function ScaleVariable(const AScaleFactor: TBigInt): TBigIntPolynomial;
 
+    // Returns f(2^n * x), given a polynomial f(x) and an exponent n.
+    function ScaleVariableByPowerOfTwo(const AExponent: Cardinal): TBigIntPolynomial;
+
     // Returns f(x / 2), given a polynomial f(x).
     function ScaleVariableByHalf: TBigIntPolynomial;
 
@@ -144,6 +147,21 @@ begin
   end;
 end;
 
+function TBigIntPolynomial.ScaleVariableByPowerOfTwo(const AExponent: Cardinal): TBigIntPolynomial;
+var
+  len, i: Integer;
+  shift: Cardinal;
+begin
+  len := Length(FCoefficients);
+  SetLength(Result.FCoefficients, len);
+  Result.FCoefficients[0] := FCoefficients[0];
+  shift := AExponent;
+  for i := 1 to len - 1 do begin
+    Result.FCoefficients[i] := FCoefficients[i] << shift;
+    Inc(shift, AExponent);
+  end;
+end;
+
 function TBigIntPolynomial.ScaleVariableByHalf: TBigIntPolynomial;
 var
   len, i: Integer;
diff --git a/tests/UPolynomialTestCases.pas b/tests/UPolynomialTestCases.pas
index e260f97..28c92dc 100644
--- a/tests/UPolynomialTestCases.pas
+++ b/tests/UPolynomialTestCases.pas
@@ -42,6 +42,7 @@ type
     procedure TestSignVariations;
     procedure TestScaleByPowerOfTwo;
     procedure TestScaleVariable;
+    procedure TestScaleVariableByPowerOfTwo;
     procedure TestTranslateVariableByOne;
     procedure TestRevertOrderOfCoefficients;
     procedure TestDivideByVariable;
@@ -143,6 +144,15 @@ begin
   AssertTrue('Polynomials are not equal.', a = b);
 end;
 
+procedure TBigIntPolynomialTestCase.TestScaleVariableByPowerOfTwo;
+var
+  a, b: TBigIntPolynomial;
+begin
+  a := TBigIntPolynomial.Create([10, 7, 5, 1034]).ScaleVariableByPowerOfTwo(5);
+  b := TBigIntPolynomial.Create([10, 7 * 32, 5 * 32 * 32, 1034 * 32 * 32 * 32]);
+  AssertTrue('Polynomials are not equal.', a = b);
+end;
+
 procedure TBigIntPolynomialTestCase.TestTranslateVariableByOne;
 var
   a, b: TBigIntPolynomial;