Write a polynomial from factored form to standard form

Learn how to write a polynomial from factored form to standard form with a couple of good examples.

Example #1

Write the expression (x + 2)(x + 3)(x + 4) as a polynomial in standard form

Multiply (x + 3) and (x + 4)

(x + 2)(x + 3)(x + 4) = (x + 2)(x² + 4x + 3x + 12)

Simplify

(x + 2)(x + 3)(x + 4) = (x + 2)(x² + 7x + 12)

Use the distributive property

(x + 2)(x + 3)(x + 4) = x(x² + 7x + 12) + 2(x² + 7x + 12)

Multiply

(x + 2)(x + 3)(x + 4) = x³ + 7x² + 12x + 2x² + 14x + 24

Combine like terms

(x + 2)(x + 3)(x + 4) = x³ + 7x² + 2x² + 12x + 14x + 24

Simplify

(x + 2)(x + 3)(x + 4) = x³ + 9x² + 26x + 24

The expression (x + 2)(x + 3)(x + 4) is the factored form of x³ + 9x² + 26x + 24

Example #2

Write the expression (x - 5)(x + 1)(x + 1) as a polynomial in standard form

Multiply (x + 1) and (x + 1)

(x - 5)(x + 1)(x + 1) = (x - 5)(x² + x + x + 1)

Simplify

(x - 5)(x + 1)(x + 1) = (x - 5)(x² + 2x + 1)

Use the distributive property

(x - 5)(x + 1)(x + 1) = x(x² + 2x + 1) + -5(x² + 2x + 1)

Multiply

(x - 5)(x + 1)(x + 1) = x³ + 2x² + x + -5x² + -10x + -5

Combine like terms

(x - 5)(x + 1)(x + 1) = x³ + 2x² + -5x² + x + -10x + -5

Simplify

(x - 5)(x + 1)(x + 1) = x³ + -3x² + -9x + -5

The expression (x - 5)(x + 1)(x + 1) is the factored form of x³ + -3x² + -9x + -5