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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)

Respuesta :

kudzordzifrancis

Answer:

(3x + 7)

(4x + 8)

Step-by-step explanation:

The given expresion that represents the area is

[tex]12 {x}^{2} + 52x + 56[/tex]

We factor 4 to get:

[tex]4(3 {x}^{2} + 13x + 14)[/tex]

Split the middle term now to get:

[tex]4(3 {x}^{2} + 6x + 7x + 14)[/tex]

We now factor by grouping to get:

[tex]4(3x(x + 2) + 7(x + 2))[/tex]

Factor further to get;

[tex]4(3x + 7)(x + 2)[/tex]

Or

[tex](3x + 7)(4x + 8)[/tex]

The factors are:

(4x + 8)

(3x+7)

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