Multiplying Polynomials Calculator

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The highest power of x in the first polynomial.
Coefficient of the highest power term.
Coefficient of the second-highest power term.
Coefficient of the constant or third-highest power term.
The highest power of x in the second polynomial.
Product P(x) x Q(x)
x^4 - x^3 - 5x^2 + 7x - -2

The fully expanded and simplified polynomial product.

Degree of product4
Number of terms5
Leading coefficient1
Constant term-2
P(x)x^2 - 3x + 2
Q(x)x^2 + 2x - -1
Degree of P(x)2
Degree of Q(x)2
Degree of product4
Degree of P(x)2
Degree of Q(x)2
Degree of product4

P(x) x Q(x) = x^4 - x^3 - 5x^2 + 7x - -2

  • The product is a quartic polynomial with 5 non-zero terms.
  • Its leading coefficient is 1, the product of the leading coefficients of P and Q.
  • The constant term is -2, which equals the product of the constant terms of P and Q. This is the value of P(0) x Q(0).
  • The degree of the product always equals the sum of the degrees of P and Q: 2 + 2 = 4.

Next stepTo factor the product back into its original polynomials, use a polynomial factoring tool. To evaluate the product at a specific x value, substitute that value into the result expression.

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