Question

The total area, in square inches, of a picture in a picture frame is calculated by the expression of 12x^2 + 520x+ 56, where x is the width of the picture frame. Which of the following are factors of 12x^2 +52x +56?

is the width
Select all that apply.
(2x + 5)
(3x + 8)
(3x + 7)
(4x + 8)
(3x + 56)
(8x + 4)
(6x + 7)
(8x + 56)

Answer 1

(3x + 7)

(4x + 8)

Explanation:

The given expresion that represents the area is

`12 {x}^(2) + 52x + 56`

We factor 4 to get:

`4(3 {x}^(2) + 13x + 14)`

Split the middle term now to get:

`4(3 {x}^(2) + 6x + 7x + 14)`

We now factor by grouping to get:

`4(3x(x + 2) + 7(x + 2))`

Factor further to get;

`4(3x + 7)(x + 2)`

Or

`(3x + 7)(4x + 8)`

The factors are:

(4x + 8)

(3x+7)