Factoring by Grouping

Mrs. Book

Liberty Hill Middle School

Algebra

Bellwork• Find the GCF of the terms of each

polynomial30h2 – 25h2 – 40h16m3 – 12m2 – 36m

• Find each product.(2t – 5)(3t + 4)(4x – 1)(x2 + 2x + 3)

Schmoop Video

• http://www.shmoop.com/video/factoring-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.

y3 + 3y2 + 4y + 12• To factor by grouping look for a common

binomial factor of two pairs of terms.

y2(y + 3) + 4(y + 3)

Factoring Polynomials with Four Terms by Grouping

y2(y + 3) + 4(y + 3) • Factor out the common binomial

(y + 3)(y2 + 4)

Factoring Polynomials with Four Terms by Grouping

• Factor each expression. Check your answer.5t4 + 20t3 + 6t + 242w3 + w2 – 14w – 7

Factoring Completely

• 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.

Factoring Completely• Factor 12p4 + 10p3 – 36p2 – 30p• Factor out the GCF• = 2p(6p3 + 5p2 – 18p – 15)• Factor by grouping• = 2p[p2(6p + 5) – 3(6p + 5)]• Factor out the common binomial• 2p(6p + 5)(p2 – 3)

Factoring Completely

• Factor 45m4 – 9m3 + 30m2 – 6m

Factoring Trinomials by Grouping

• Factor 24q2 + 25q – 25• Step 1: Find the product of ac

(24)(-25) = -600• Step 2 Find the factors of ac that have

sum b.(-12)(50) -12 + 50 = 38(-15)(40) -15 + 40 = 25

Factoring Trinomials by Grouping

• Factor 24q2 + 25q – 25• Step 3: Rewrite the trinomial

24q2 -15q + 40q – 25• Step 4: Factor by grouping

3q(8q – 5) + 5(8q – 5)(3q + 5)(8q – 5)

Factor each trinomial by grouping

• 63d2 + 44d + 5• 4y2 + 33y - 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.