Question

Rewrite the expression 7x^2 + 14x - 56 as three factors where one of the factors is an integer value.

Choose three factors and write an equivalent expression.

options listed:
6

7

42

(x+1)

(x-1)

(x+2)

(x-2)

(x+3)

(x-3)

(x+4)

(x-4)

Answer 1

The factors are
`7,(x-2),(x+4)`

`7x^(2) +14x-56=7(x-2)(x+4)`

Explanation:

we have

`7x^(2) +14x-56`

equate the expression to zero

`7x^(2) +14x-56=0`

Group terms that contain the same variable, and move the constant to the opposite side of the equation

`7x^(2) +14x=56`

Factor the leading coefficient

`7(x^(2) +2x)=56`

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

Complete the square. Remember to balance the equation by adding the same constants to each side

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

`(x^(2) +2x+1)=9`

Rewrite as perfect squares

`(x+1)^(2)=9`

Take square root both sides

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

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

`x=-1(+)3=2`

`x=-1(-)3=-4`

therefore

`7x^(2) +14x-56=7(x-2)(x+4)`