Factoring by Grouping Mrs. Book Liberty Hill Middle School Algebra.
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Transcript of Factoring by Grouping Mrs. Book Liberty Hill Middle School Algebra.
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.