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.How can you simplify
this problem?
Factor o u t th e GCF o f
th e trin o m ia l's term s. The
trinom ial th a t remains
is s im ila r to those in
Problems 1-3.Pr o b l em 4 JFa ct o r i n g O u t a M o n o m i a l Fi r st
What is the factored form of 18x2 - 33x + 12?^T hink
Factor ou t the GCF.Factor 6 x 2 - 1 1x + 4. Since
ac = 24 and b = -11, find
ne g a tive fa cto rs o f 2 4 th a t
have sum - 11.,/Write
18x2 - 33x + 12 = 3(6x2 - llx + 4)Factors of 24 -1 ,-2 4 -2 ,-1 2 -3 ,-8 -4 ,-6
Sum of F actors - 2 5 -14 -11 -10Rewrite the term bx. Then
use th e D istribu tive Property
to finish factoring.3(6x2 - 3x - 8x + 4)
3[3x(2x - 1) - 4(2x - 1)]
3(3x - 4)(2x - 1)J
. Got It? 4. What is the factored form of 8x2 - 36x - 20?
Lesso n Ch eck
Do y o u k n o w H OW?
Factor each expression.- 3 x2+ 16x + 5
- 10<72 + 9q + 2
- 4 w2 + 4w -3
- The area of a rectangle is 6x2 — llx — 72. What
are the possible dimensions of the rectangle?
Use factoring.
MATHEMATICAL
Do y o u UN DERSTAN D? { g g } PRACTICES- Reasoning Explain why you cannot factor the
trinomial 2x2 + 7x + 10.
6. R e a s o n i n g To factor 8x2 + bx + 3, a
student correctly rewrites the trinomial as
8x2 + px + qx + 3. What is the value of pql- Compare and Contrast How is factoring a trinomial
ax2 + bx + c when a + 1 different from factoring a
trinomial when a — 1? How is it similar?
J
Pr act i ce an d Pr o b l em - So l v i n g Ex er ci ses
Q Practice Factor each expression.- 2x2 + 13x + 6
- 4p2 + 7p + 3
- 3d2 + 23d + 14
- 6r2 - 23r + 20
MATHEMATICAL
PRACTICESSee Problem- 4n2 — 8 n + 3
- 8g2 - 14g+ 3
1.520 Ch ap t er 8 Po l yn o m i al s an d Fact o r i n g