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Chapter 6: Q 117. (page 590)

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

2n2鈭�27n鈭�45

Short Answer

Expert verified

The solution is (n-15)(2n+3).

Step by step solution

01

Step 1. Given information

The given trinomial is 2n2鈭�27n鈭�45.

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=2b=-27c=-45

The product is as follows:

ac=2(-45)=-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:

3(-30)=-90=ac3-30=-27=b

So, two numbers are 3and -30.

Now, split the middle term of the given trinomial 2n2-27n-45as follows:

localid="1644755588337" 2n2-27n-45=2n2-30n+3n-45

05

Step  5. Factor by grouping.

2n2-27n-45=2n(n-15)+3(n-15)=(n-15)(2n+3)

06

Step 6. Check by multiplying (n-15)(2n+3).

(n-15)(2n+3)=2n2-30n+3n-45=2n2-27n-45

Hence, the factor is (n-15)(2n+3).

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