Algebra 1 Common Core Student Edition, Grade 8-9

^ ^ a- What is the factored form of 6x2 + 13x + 5?

b. Reasoning In ax2 + bx + c, suppose ac is positive and b is negative. What

do you know about the factors of ac? Explain.

Pion

Can you apply th e

steps for Problem 1

to this problem?

Yes. Your g oal is s till to

find factors of ac that

have sum fa. Because

ac < 0 ,the factors must

have d iffe re n t signs.

How can you find the
dimensions o f the
rectangle?
Factor the rectangle's
area as th e p ro d u ct
of two binomials, one
o f w h ic h is th e w id th.
The o th e r m u st be
th e le n g th since
area = length • w id th.

Fact oring W hen ac Is N eg at ive

What is the factored form of 3 x 2 + 4x - 15?

Step 1 Find factors of ac that have sum b. Since ac = —45 and b — 4, find factors

of -4 5 that have sum 4.

Factors of - 45 1, - 4 5 -1,45 3, - 1 5 -3,15 5, - 9 -5,9

Su m o f Fa c t o r s - 4 4 4 4 -12 12 -4 4

Step 2 To factor the trinomial, use the factors you found to rewrite bx.

3x2 + 4x - 15 = 3x2 - 5x + 9x - 15 R e w rite fax: 4 x = - 5 x + 9x.

= x(3x - 5) + 3(3x - 5) Factor o ut the GCF o f each pair of terms.

= (3x - 5)(x + 3) Distributive Property

Go t I t? 2. What is the factored form of 10x2 + 31x — 14?

'*) Problem 3 Applying Trinomial Factoring

Geometry The area of a rectangle is 2 x 2 — 13x — 7. What are the possible

dimensions of the rectangle? Use factoring.

Step 1 Find factors of ac that have sum fa. Since ac= -1 4 and fa = -13, find factors of

-14 that have sum —13.

Factors of-14 1,-14 -1,14 2,-7 -2,7

Sum of Factors -13 13 - 5 5

Step 2 To factor the trinomial, use the factors you found to rewrite fax.

2x2 - 13x — 7 = 2x2 + x - 14x — 7 R e w rite fax: -13x = x - 1 4x.

= x(2x + 1) - 7(2x + 1) Factor o u t the GCF o f each pair o f terms.

= (2x + l)(x - 7) Distributive Property

The possible dimensions of the rectangle are 2x + 1 and x — 7.

J Got It? 3. The area of a rectangle is 8x2 + 22x + 15. What are the possible dimensions

of the rectangle? Use factoring.

c

PowerAlgebra.com Lesso n 8- 6 Fact o r i n g ax1 + fax + c 519