Prentice Hall Algebra 1

Chapter 8 Polynomials and Factoring > 8-6 Factoring ax2 + bx + c > Practice and Problem-Solving Exercises

To factor a polynomial completely, first factor out the GCF of the polynomial's terms. Then factor the remaining polynomial until it is written as the product of polynomials that cannot be factored further.

Problem 4 Factoring Out a Monomial First

What is the factored form of 18 x 2 − 33 x + 12 ? 18 , x squared , minus 33 x plus 12 question mark

Think

Write

Factor out the GCF.

18 x 2 − 33 x + 12 = 3 ( 6 x 2 − 11 x + 4 ) 18 , x squared , minus 33 x plus 12 equals 3 open 6 , x squared , minus 11 x plus 4 close

Factor 6 x 2 − 11 x + 4 . 6 , x squared , minus 11 x plus 4 . Since eh c equals 24 and b equals negative 11 comma find negative factors of 24 that have sum negative 11 .

Factors of 24	negative 1 comma negative 24	negative 2 comma negative 12	negative 3 comma negative 8	negative 4 comma negative 6
Sum of Factors	negative 25	negative 14	negative 11 ✓	negative 10

Rewrite the term bx. Then use the Distributive Property to finish factoring.

3 ( 6 x 2 − 3 x − 8 x + 4 ) 3 open 6 , x squared , minus 3 x minus 8 x plus 4 close
3 [ 3 x ( 2 x − 1 ) − 4 ( 2 x − 1 ) ] 3 left bracket 3 x open 2 x minus 1 close minus 4 open 2 x minus 1 close right bracket
3 ( 3 x − 4 ) ( 2 x − 1 ) 3 open 3 x minus 4 close open 2 x minus 1 close

✓ Got It?

What is the factored form of 8 x 2 − 36 x − 20 ? 8 , x squared , minus 36 x minus 20 question mark

✓ Lesson Check

Do you know HOW?

Factor each expression.

3 x 2 + 16 x + 5 3 , x squared , plus 16 x plus 5
10 q 2 + 9 q + 2 10 , q squared , plus 9 q plus 2
4 w 2 + 4 w − 3 4 , w squared , plus 4 w minus 3
The area of a rectangle is 6 x 2 − 11 x − 72 . 6 , x squared , minus 11 x minus 72 . What are the possible dimensions of the rectangle? Use factoring.

Do you UNDERSTAND?

Reasoning Explain why you cannot factor the trinomial 2 x 2 + 7 x + 10 . 2 , x squared , plus 7 x plus 10 .
Reasoning To factor 8 x 2 + b x + 3 , 8 , x squared , plus b x plus 3 comma a student correctly rewrites the trinomial as 8 x 2 + p x + q x + 3 . 8 , x squared , plus p x plus q x plus 3 . What is the value of pq?
Compare and Contrast How is factoring a trinomial a x 2 + b x + c eh x squared , plus b x plus c when eh not equal to 1 different from factoring a trinomial when eh equals 1? How is it similar?

Practice and Problem-Solving Exercises

A Practice

See Problem 1.