Question

Can the polynomial below be factored into a perfect square? If not, select the answer that best describes why not.

Answer 1

Option B;
A suitable x-coefficient for a quadratic function that factors into a perfect square has to be even.

Answer 2

Answer:

Option B is correct.

Step-by-step explanation:

We will work with the formula : $(a+b)^{2}$

= $a^{2}+2ab+b^{2}$

Given polynomial is :

$64x^{2} +49x+8$

here a = $\sqrt{64x^{2} } =8x$

b = $\sqrt{8}= 2\sqrt{2}$

2ab = $2*8x*2\sqrt{2} =32\sqrt{2}x$

Now, we can see that the middle term should be $32\sqrt{2} x$ but in the question, it is given 49x

So, option B is true that - The x^2 coefficient does permit the factoring, but the x coefficient does not permit the factoring.