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Chapter 6: Q. 126E (page 590)

In the following exercises, factor using the 鈥榓c鈥� method30x2+105x鈭�60

Short Answer

Expert verified

The factors are152x-1x+4

Step by step solution

01

Step 1. Given Information

The trinomial is 30x2+105x-60

Find the factor using 'ac' method.

02

Step 2. Find GCF

Find GCF and factor it

GCF is 15

S0, 152x2+7x-4

03

Step 3. Find 'ac'

Compare the trinomial inside the parenthesis with ax2+bx+c

So, a=2,b=7,c=-4

so, ac=-8

Find two number such as their product is role="math" localid="1644581551461" ac=-8and their addition is b=7

So the numbers are 8 and -1.

04

Step 4. Split the middle and factor trinomial by grouping

Split the middle term

152x2+8x-x-4

Factor it by grouping

152xx+4-1x+4

15x+42x-1

05

Step 5. Check

To check multiply all factors,152x-1x+4

152x2+7x-430x2+105x-60

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