Question

What is the factorization of the polynomial below?

3x2 + 33x + 54


A. 3(x + 2)(x + 9)

B. (x + 2)(x + 27)

C. (3x + 2)(x + 9)

D. (x + 3)(x + 9)

Answer 1

3x^2 + 33x + 54 =
3(x^2 + 11x + 18) =
3(x + 2)(x + 9) <==

Answer 2

Answer:

A. 3(x+2)(x+9)

Step-by-step explanation:

We have the expression $3x^2+33x+54$, we can rewrite the expression as:

$3x^2+33x+54=3.(1x^2)+3.(11x)+3.(18)$

Then we can apply common factor 3:

$3.(1x^2)+3.(11x)+3.(18)=3(x^2+11x+18)$

Now we are going to factor: $x^2+11x+18$

We can rewrite it as: $x^2+2x+9x+18$, then we are going to use grouping, because we have 4 terms:

In

$x^2+2x=x.x+2.x=x(x+2)$

we use common factor x.

In

$9x+18=9.x+9.2=9(x+2)$

we use common factor 9.

Then we can express,

$x^2+11x+18=x(x+2)+9(x+2)\\=(x+9)(x+2)$

Now replacing:

$3(x^2+11x+18)=3(x+9)(x+2)=3(x+2)(x+9)$

Then the correct answer is option A. 3(x+2)(x+9)