Factoring Using the Distributive Property

To factor a polynomial, undo the distributive property. Distribute: 3c(4c – 2) In this example, 12c2 – 6c, is the product. In this example, 3c and (4c-2) are the factors. 3c(4c-2) is the factored form of 12c2 – 6c. To factor a polynomial, undo the distributive property.

Factor the following polynomial using the distributive property. Step 1: Find the GCF for both terms. 9m3n2 = 3 • 3 • m • m • m • n • n 24mn4 = 2 • 2 • 2 • 3 • m • n • n • n • n The GCF is 3•m•n•n = 3mn2 .

Factor Step 2: Divide each term of the polynomial by the GCF.

Factor Step 3: Write the polynomial as the product of the GCF and the remaining factor of each term. The GCF First term ÷ GCF Second term ÷ GCF

Factor Step 4: Check the factors by multiplying (distributing). Notice that when the polynomial is factored, the terms inside the parentheses (3m2 + 8n2) have nothing in common. They share no variables and there is no number that can divide into both terms. This means that we have completely factored the polynomial.

You Try It. a. 4x2 + 6xy b. 60a2 + 30ab – 90ac c. 12b3d2 - 6b2d3 1. Find the GCF of the terms in each polynomial. 2. Divide each term by the GCF. 3. Factor the polynomial. a. 4x2 + 6xy b. 60a2 + 30ab – 90ac c. 12b3d2 - 6b2d3 d. 25x2 + 15x - 10

Answers 4x2 + 6xy = 2x(2x + 3y) a) 4x2 = 2 • 2 • x • x 6xy = 2 • 3 • x • y The GCF is 2x. 4x2 + 6xy = 2x(2x + 3y)

Answers 60a2 + 30ab - 90ac = 30a(2a + b - 3c) b) 60a2 = 2 • 2 • 3 • 5 • a • a 30ab = 2 • 3 • 5 • a • b 90ac = 2 • 3 • 3 • 5 • a • c The GCF is 30a. 60a2 + 30ab - 90ac = 30a(2a + b - 3c)

Answers 12b3d2 - 6b2d3 = 6b2d2(2b - d) c) 12b3d2 = 2 • 2 • 3 •b•b•b•d•d 6b2d3 = 2 • 3 •b•b•d•d•d The GCF is 6b2d2. 12b3d2 - 6b2d3 = 6b2d2(2b - d)

Answers 25x2 + 15x - 10 = 5(5x2 + 3x - 2) d) 25x2 = 5 • 5 • x • x 10 = 2 • 5 The GCF is 5. 25x2 + 15x - 10 = 5(5x2 + 3x - 2)