Factoring by Grouping Mrs. Book Liberty Hill Middle School Algebra

Bellwork Find the GCF of the terms of each polynomialFind the GCF of the terms of each polynomial 30h 2 – 25h 2 – 40h 30h 2 – 25h 2 – 40h 16m 3 – 12m 2 – 36m 16m 3 – 12m 2 – 36m Find each product. Find each product. (2t – 5)(3t + 4) (2t – 5)(3t + 4) (4x – 1)(x 2 + 2x + 3) (4x – 1)(x 2 + 2x + 3)

Schmoop Video polynomials-by-groupinghttp:// polynomials-by-groupinghttp:// polynomials-by-groupinghttp:// polynomials-by-grouping

Factoring by Grouping You can use the Distributive Property to factor by grouping if two groups of terms have the same factor.You can use the Distributive Property to factor by grouping if two groups of terms have the same factor. y 3 + 3y 2 + 4y + 12 To factor by grouping look for a common binomial factor of two pairs of terms.To factor by grouping look for a common binomial factor of two pairs of terms. y 2 (y + 3) + 4(y + 3)

Factoring Polynomials with Four Terms by Grouping y 2 (y + 3) + 4(y + 3) Factor out the common binomialFactor out the common binomial (y + 3)(y 2 + 4)

Factoring Polynomials with Four Terms by Grouping Factor each expression. Check your answer.Factor each expression. Check your answer. 5t t 3 + 6t t t 3 + 6t w 3 + w 2 – 14w – 7 2w 3 + w 2 – 14w – 7

Factoring Completely Before you factor by grouping, you may need to factor the GCF of all the terms of a polynomial.Before you factor by grouping, you may need to factor the GCF of all the terms of a polynomial. Remember, a polynomial is not completely factored until there are no common factors other than 1.Remember, a polynomial is not completely factored until there are no common factors other than 1.

Factoring Completely Factor 12p p 3 – 36p 2 – 30pFactor 12p p 3 – 36p 2 – 30p Factor out the GCFFactor out the GCF = 2p(6p 3 + 5p 2 – 18p – 15)= 2p(6p 3 + 5p 2 – 18p – 15) Factor by groupingFactor by grouping = 2p[p 2 (6p + 5) – 3(6p + 5)]= 2p[p 2 (6p + 5) – 3(6p + 5)] Factor out the common binomialFactor out the common binomial 2p(6p + 5)(p 2 – 3)2p(6p + 5)(p 2 – 3)

Factoring Completely Factor 45m 4 – 9m m 2 – 6mFactor 45m 4 – 9m m 2 – 6m

Factoring Trinomials by Grouping Factor 24q q – 25Factor 24q q – 25 Step 1: Find the product of acStep 1: Find the product of ac (24)(-25) = -600 (24)(-25) = -600 Step 2 Find the factors of ac that have sum b. Step 2 Find the factors of ac that have sum b. (-12)(50)  = 38 (-12)(50)  = 38 (-15)(40)  = 25 (-15)(40)  = 25

Factoring Trinomials by Grouping Factor 24q q – 25Factor 24q q – 25 Step 3: Rewrite the trinomialStep 3: Rewrite the trinomial 24q 2 -15q + 40q – 25 24q 2 -15q + 40q – 25 Step 4: Factor by grouping Step 4: Factor by grouping 3q(8q – 5) + 5(8q – 5) 3q(8q – 5) + 5(8q – 5) (3q + 5)(8q – 5) (3q + 5)(8q – 5)

Factor each trinomial by grouping 63d d + 563d d + 5 4y y - 704y y - 70

Summary 1.Factor out the greatest common factor (GCF) 2.If the polynomial has two terms or three terms, look for a difference of two squares, a product of two squares, or a pair of binomial factors.

Summary 3.If there are four or more terms, group terms and factor to find common binomial factors. 4. As a final check, make sure there are no common factors other than 1.

Exit Ticket Find the expressions for the possible dimensions of rectangular prism.Find the expressions for the possible dimensions of rectangular prism.