Question

Factor x^2+2x-63 completely if the polynomial is a prime, state so.

Answer 1

Hey there !

Check the attachment.
Hope it helps you :)

Answer 2

The only two usable numbers that make up 63 are 9 and 7 and 21 and 3 in some form. So that's how you start the question. 

(x   9)(x   7) is what you can get. The 2x is very small, so it suggests that 21 and 3  are not the right factors.

You have a plus 2 as the middle term. That is exactly the difference between 9 and 7. That tells you the sign on 9 because it is larger than 7.

(x + 9) ( x     7) is what you have so far. Since 63 is minus, the 7 must be minus. Now what you have is
(x + 9)(x - 7) and that is the final answer.