Question

Factor 4x2 + 24x + 36.

A) 4(x + 3)(x + 3)
B) 4(x + 6)(x – 6)
C) (4x + 3)(x + 3)
D) (2x – 6)(2x – 6)

Answer 1

`\huge\boxed{\text{A) } 4(x+3)(x+3) }`

Explanation:

In order to factor this, we need to factor out a common term and then solve for x.

We can see that we can factor out a 4 from this entire equation as each term is a multiple of 4.

This leaves us with
`4(x^2+ 6x + 9)`.

We can now solve for x for the expression in the parentheses,
`x^2 +6x + 9`.

To solve for x, we can use the XBOX method. This tells us that:

• When the two roots are added, they will equal b (in this case, 6)
• When the two roots are multiplied, they will equal c (in this case 9)

Experimenting with some numbers gets us with 3 and 3 - 3+3 = 6 and 3*3 = 9.

Therefore, our roots will be
`(x+3)(x+3)`.

Putting that back into the factorization of our original expression, that leaves us with
`4(x+3)(x+3)`.

Hope this helped!