Objectives I will use the distributive property to factor a polynomial.

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Presentation transcript:

Objectives I will use the distributive property to factor a polynomial.

Finding the Greatest Common Factor Factor the greatest common factor out of 14x x 3 SOLUTION First find the greatest common factor. It is the product of all the common factors. 14x 5 = 2 7 x x x x x 21x 3 = 3 7 x x x GCF = 7 x x x = 7x 3 Use the distributive property to factor the greatest common factor out of the polynomial. 14x x 3 = 7x 3 (2x 2 - 3)

Factoring Completely Factor 5x x x completely. SOLUTION 5x x x = 5x(x 2 + 7x + 10) = 5x(x + 2)(x + 5) Monomial Factor Prime Factors

Factoring Completely Factor 63x x 2 completely. SOLUTION 63x x 2 = 7x 2 (9x )Factor out GCF = 7x 2 (3x + 4)(3x - 4)Factor difference of squares

Guided Practice 1.Factor 2y y y completely. 2.Factor 4t t completely.

Factoring by Grouping When there are four terms in a polynomial, you can factor the polynomial by grouping into two groups of terms and factoring out the greatest common factor out of each term Factor x 3 + 2x 2 + 3x + 6 completely. x 3 + 2x 2 + 3x + 6 = (x 3 + 2x 2 ) + (3x + 6)Group terms = x 2 (x + 2) + 3(x + 2)Factor each group = (x 2 + 3)(x + 2) Use distributive property

Guided Practice 1.Factor t 3 - t t + 16 completely.

Writing and Using a Polynomial Model The width of a box is 1 inch less than the length. The height is 4 inches greater than the length. The box has a volume of 12 cubic inches. What are the dimensions of the box?

Independent Practice Factor each polynomial completely. 1.10x x x 2.5x x 2 3.3m m 2 - 6m + 30