Question

The area of a painting is given by the trinomial x^2+2x-8. What are the possible dimensions of the painting? Use factoring.

Answer 1

we have

x^2+2x-8

Complete the squares

x^2+2x-8=0

x^2+2x=8

(x^2+2x+1)=8+1

x^2+2x+1=9

Rewrite as pefect squares

(x+1)^2=9

take the square root both sides

(x+1)=(+/-)3

x=-1(+/-)3

the values of x are

x=2 and x=-4

therefore

x^2+2x-8=(x-2)(x+4)

the possible dimensions of the paint are

(x-2) and (x+4)