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Chapter 6: Q 115. (page 590)

Factor Trinomials of the Form ax2+bx+cusing the 鈥榓c鈥� Method.

6y2+y鈭�15

Short Answer

Expert verified

The solution is (3y+5)(2y-3).

Step by step solution

01

Step 1. Given information

The given trinomial is 6y2+y鈭�15.

02

Step 2. Find greatest common factor.

There is no greatest common factor.

03

Step 3. Compare the given trinomial to ax2+bx+c and then find the product of ac.

The values are as follows:

a=6b=1c=-15

The product is as follows:

role="math" localid="1644753373463" ac=6(-15)=-90

04

Step 4. Determine two numbers that multiply to ac and add to b.

Two numbers that multiply to acand add to bare as follows:

10(-9)=-90=ac10-9=1=b

So, two numbers are 10and localid="1644753833782" -9.

Now, split the middle term of the given trinomial 6y2+y-15as follows:

6y2+y-15=6y2+10y-9y-15

05

Step  5. Factor by grouping.

6y2+y-15=2y(3y+5)-3(3y+5)=(3y+5)(2y-3)

06

Step 6. Check by multiplying (3y+5)(2y-3).

(3y+5)(2y-3)=6y2+10y-9y-15=6y2+y-15

Hence, the factor is (3y+5)(2y-3).

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