Question

Which of the following is equivalent to the polynomial given below?

Answer 1

Answer:

$(x+(3+\sqrt{11}i)) (x+(3-\sqrt{11}i))$

Step-by-step explanation:

The first step to this problem is to look at the key features of the initial expression given to us. Namely, the middle term.

Notice that it is just $+6x$. This indicates that the square root terms cancel out, meaning that their signs need to be opposite, but the threes need to have the same, positive sign. This indicates that our answer is option C, but you should always double check by multiplying the expression out to confirm. Here are the steps:

$(x+(3+\sqrt{11}i)) (x+(3-\sqrt{11}i))$

$x^{2} +(3+\sqrt{11}i)x+(3-\sqrt{11}i)x+(3+\sqrt{11}i)(3-\sqrt{11}i)$$x^{2}+3x+\sqrt{11}ix+3x-\sqrt{11}ix+9+3\sqrt{11}i-3\sqrt{11}i-(\sqrt{11})^{2}(i^{2})$$x^{2}+6x+9-(11)(-1)$

$x^{2}+6x+9+11$

$x^{2}+6x+20$

Therefore as we suspected, the answer is C.