## Factor the trinomial below. 9×2 + 12x+4 A. (3x+2)(3x+2) B. (9x + 1)(x+4) C. (3x + 1)(3x + 4) D. (9x + 2)(x+2)<

Question

Factor the trinomial below.
9×2 + 12x+4
A. (3x+2)(3x+2)
B. (9x + 1)(x+4)
C. (3x + 1)(3x + 4)
D. (9x + 2)(x+2)

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2 weeks 2021-09-03T17:53:36+00:00 2 Answers 0 views 0

Explanation:

9x^2 + 12x + 4

= (3x)^2 + 2(3x)(2) + (2)^2

= (3x+2)(3x+2)

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

Step-by-step explanation:

The trinomial below is a quadratic which comes in the form of ax^2+bx+c

This is pretty self-explanatory when you factor a quadratic equation where a=1

However, in this case, a=9, b=12, and c=4

This is a special polynomial, but in case you can’t recognize that, here’s how you can factor it:

Now, there are many ways to solve this, I’m going to use a method known as Master Product.

First, we multiply a and c together.

ac=9*4=36

next, we find p and q so that ac = pq and p + q = b

Therefore we are trying to find 2 numbers that multiply to 36 and add to 12.

9 and 4 may be tempting, but it actually adds to 13.

The correct answer would be 6 and 6.

So p=6 and q=6

Next, we can use this to split our polynomial.

Rewrite it as ax^2+px+qx+c

Our new expression would then be

9x^2+6x+6x+4

Now, we just need to factor by grouping.

(9x^2+6x)+(6x+4)

Take GCF out

3x(3x+2)+2(3x+2)

You know this is factorable as the numbers within the parentheses is the same.

Hence you keep one as the numbers in the parentheses and use the numbers in front to get the other bracket.

So if it was ax(bx+c)+d(bx+c) it would become (ax+d)(bx+c)

Rewrite:

(3x+2)(3x+2)

This is a choice, so we can confidently choose A.

Hope that helps, let me know if you have any questions 🙂