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Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Objectives
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Factoring Trinomials
Factor trinomials when the coefficient of the quadratic term is 1.
Factor trinomials when the coefficient of the quadratic term is not 1.
Use an alternative method for factoring trinomials.
Factor by substitution.
6.2
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Factor trinomials when the coefficient of the quadratic term is 1.
Objective 1
Slide 6.2- 2
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Factoring x2 + bx + c
Step 1 Find pairs whose product is c. Find all pairs of integers whose product is c, the third term of the trinomial.
Step 2 Find pairs whose sum is b. Choose the pair whose sum is b, the coefficient of the middle term.
If there are no such integers, the polynomials cannot be factored.
A polynomial that cannot be factored with integer coefficient is a prime polynomial.
Slide 6.2- 3
Factor trinomials when the coefficient of the quadratic term is 1.
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Slide 6.2- 4
Factor trinomials when the coefficient of the quadratic term is 1.
Understanding PALOMINO’S “X”
a2 + 7a + 12
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Factor the trinomial.
a2 + 9a + 20
Slide 6.2- 5
CLASSROOM EXAMPLE 1
Factoring Trinomials in x2 + bx + c Form
x2 - 7x + 10
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Factor the trinomial
Slide 6.2- 6
CLASSROOM EXAMPLE 2
Recognizing a Prime Polynomial
y2 + 4y –21. t2 + 3t – 5.
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Factor.
Slide 6.2- 7
CLASSROOM EXAMPLE 3
Factoring a Trinomial in Two Variables
p2 – 5pq + 6q2
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Factor.
Slide 6.2- 8
CLASSROOM EXAMPLE 4
Factoring a Trinomial with a Common Factor
3a3 + 12a2 – 15a
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Factor trinomials when the coefficient of the quadratic term is not 1.
Objective 2
Slide 6.2- 9
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Factor trinomials when the coefficient of the quadratic term is not 1.
Understanding PALOMINO’S “X”
2x² + 9x − 5
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Factor.
CLASSROOM EXAMPLE 5
Factoring a Trinomial in ax2 + bx + c Form
Slide 6.2- 11
6k2 – 19k + 10 2x² − 11x + 5
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Factor.
CLASSROOM EXAMPLE 5b
Factoring a Trinomial in ax2 + bx + c Form
Slide 6.2- 12
2x² + 5x − 3 5x² − 7x − 6
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Use an alternative method for factoring trinomials.
Objective 3
Slide 6.2- 13
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Factor each trinomial.
10x2 + 17x + 3 6r2 + 13r – 5
CLASSROOM EXAMPLE 6
Factoring Trinomials in ax2 + bx + c Form
Slide 6.2- 14
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Factoring ax2 + bx + c (GCF of a, b, c is 1)
Step 1 Find pairs whose product is a. Write all pairs of integer factors of a, the coefficient of the second-degree term.
Step 2 Find pairs whose product is c. Write all pairs of integer factors of c, the last term.
Step 3 Choose inner and outer terms. Use FOIL and various combinations of the factors from Steps 1 and 2 until the necessary middle term is found.
If no such combinations exist, the trinomial is prime.
Slide 6.2- 15
Use an alternative method for factoring trinomials.
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Factor.
Slide 6.2- 16
CLASSROOM EXAMPLE 7
Factoring a Trinomial in Two Variables
6m2 + 7mn – 5n2
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Factor.
Slide 6.2- 17
CLASSROOM EXAMPLE 8
Factoring a Trinomial in ax2 + bx + c Form (a < 0)
–2p2 – 5p + 12
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Factor.
Slide 6.2- 18
CLASSROOM EXAMPLE 9
Factoring a Trinomial with a Common Factor
4m3 + 2m2 – 6m
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Factor.
Slide 6.2- 19
CLASSROOM EXAMPLE 9
Factoring a Trinomial with a Common Factor
12x10 + 42x9 + 18x8
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Factor by substitution.
Objective 4
Slide 6.2- 20
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Factor.
Slide 6.2- 21
CLASSROOM EXAMPLE 10
Factoring a Polynomial by Substitution
8(z + 5)2 – 2(z + 5) – 3
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Factor.
Slide 6.2- 22
CLASSROOM EXAMPLE 11
Factoring a Trinomial in ax4 + bx2 + c Form
6r4 – 13r2 + 5
