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Chapter 6: Q 119. (page 590)

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

60y2+290y鈭�50

Short Answer

Expert verified

The solution is 10(y+5)(6y-1).

Step by step solution

01

Step 1. Given information

The given trinomial is 60y2+290y鈭�50.

02

Step 2. Find greatest common factor.

Factor the greatest common factor.

60y2+290y鈭�50=10(6y2+29y-5)

03

Step 3. Compare the trinomial 6y2+29y-5 to  ax2+bx+c and then find the product of ac.

The values are as follows:

a=6b=29c=-5

The product is as follows:

ac=6(-5)=-30

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:

30路(-1)=-30=ac30-1=29=b

So, two numbers are 30and localid="1645164583944" -1.

Now, split the middle term of the trinomial 6y2+29y-5as follows:

6y2+29y-5=6y2+30y-y-5

05

Step  5. Factor by grouping.

6y2+29y-5=6y(y+5)-1(y+5)=(y+5)(6y-1)

06

Step 6. Check by multiplying all the factors 10(y+5)(6y-1).

10(y+5)(6y-1)=10(6y2+30y-y-5)=10(6y2+29y-5)=60y2+290y-50

Hence, the factor is 10(y+5)(6y-1).

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