Page 585 - Algebra 1

L E S S O N Factoring Polynomials by Grouping 87
Warm Up
1. Vocabulary For the terms in a polynomial, the product of the greatest
(38)
Factor each polynomial completely. 2.90k4 +15k3
(38)
4.4n2 +5n-21 (75)
integer that divides evenly into the coefficients and the greatest power of each variable that divides evenly into each term is the .
3.x2 -8x+15 (72)
5.81x2 -64y2 (83)
New Concepts Polynomials can be factored by grouping. When a polynomial has four terms, make two groups and factor out the greatest common factor from each
group.
Factoring Four-Term Polynomials
Factor 2x2 + 4xy + 7x + 14y. Check your answer. SOLUTION
Hint
Factoring is the opposite of multiplying. Check the answer by multiplying. The product should be the original polynomial.
Example
1
2x2 +4xy+7x+14y
= (2x2 + 4xy) + (7x + 14y) = 2x(x + 2y) + 7(x + 2y) = (x + 2y)(2x + 7)
Check
(x + 2y)(2x + 7)
2x2 + 7x + 4xy + 14y
= 2x2 + 4xy + 7x + 14y ✓
Group terms that have a common factor. Factor out the GCF of each binomial. Factor out (x + 2y).
Multiply using FOIL. Commutative Property
The product is the original polynomial.
Rearranging before Grouping
Factor 3y2 - 8y3 - 8y + 3. Check your answer.
SOLUTION
Use the Commutative and Associative Properties to rearrange terms to form two binomials with common factors.
Example
2
Hint
When rearranging terms, make sure the negative sign is distributed properly.
Online Connection www.SaxonMathResources.com
3y2 -8y3 -8y+3
= 3y2 + 3 - 8y3 - 8y
= (3y2 + 3) - (8y3 + 8y)
= 3(y2 + 1) - 8y(y2 + 1) = (y2 + 1)(3 - 8y)
Group terms that have a common factor. Group into two binomials.
Factor out the GCF of each binomial. Factor out (y2 + 1).
570 Saxon Algebra 1