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Chapter 11: Q 114. (page 1069)

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

5s2鈭�9s+4

Short Answer

Expert verified

The solution is (s-1)(5s-4).

Step by step solution

01

Step 1. Given information

The given trinomial is 5s2鈭�9s+4.

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=5b=-9c=4

The product is as follows:

ac=5路4=20

04

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

Since the middle term in the given polynomial is negative, both factors will be negative.

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

(-5)(-4)=20=ac-5-4=-9=b

So, two numbers are -5and -4.

Now, split the middle term of the given trinomial 5s2鈭�9s+4as follows:

5s2鈭�9s+4=5s2鈭�5s-4s+4

05

Step  5. Factor by grouping.

5s2鈭�9s+4=5s(s鈭�1)-4(s-1)=(s-1)(5s-4)

06

Step 6. Check by multiplying (s-1)(5s-4).

(s-1)(5s-4)=5s2-5s-4s+4=5s2-9s+4

Hence, the factor is (s-1)(5s-4).

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