Respuesta :

The answer is C.  Factor the equation: 2x^2 + 10x + 12 which gives you............. 2(x + 2) (x + 3), and then cancel out (x + 3) because dividing (x + 3) by itself gives you one and the remaining term is 2(x +2) which is the same as 2x +4.

Answer: Option 'C' is correct.

Step-by-step explanation:

Since we have given that

[tex]f(x)=2x^2+10x+12\\\\and\\\\g(x)=x+3\\\\\frac{2x^2+10x+12}{x+3}[/tex]

Now, we need to find the quotient of the given polynomial by dividing with g(x).

So, here we go:

Take out the common factor 2 from the numerator i.e. f(x), it becomes,

[tex]2\left(x^2+5x+6\right)[/tex]

Now, we will apply the "Split the middle term", we get,

[tex]\left(x^2+5x+6\right)\\\\=\left(x^2+2x\right)+\left(3x+6\right)\\\\=x\left(x+2\right)+3\left(x+2\right)\\\\=\left(x+2\right)\left(x+3\right)[/tex]

So, we will divide f(x) with g(x) :

[tex]\frac{2\left(x+2\right)\left(x+3\right)}{x+3}[/tex]

Now, Cancel out the like term :

So, we get

[tex]2\left(x+2\right)\\\\=2x+4[/tex]

Hence, Option 'C' is correct.

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