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# 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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Mathematics
1 year
2021-09-03T17:53:36+00:00
2021-09-03T17:53:36+00:00 2 Answers
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Answers ( )

The answer is A.

Explanation:

9x^2 + 12x + 4

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

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

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

Step-by-step explanation:The trinomial below is a quadratic which comes in the form of

ax^2+bx+cThis is pretty self-explanatory when you factor a quadratic equation where a=1

However, in this case,

a=9, b=12, and c=4This 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 = bTherefore 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=6Next, we can use this to split our polynomial.

Rewrite it as

ax^2+px+qx+cOur new expression would then be

9x^2+6x+6x+4Now, 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 🙂