Iam having so much

1.)what values solve the polynomial equation?

0 = x2 – 12x – 64

choose all answers that are correct.

a.)–16 b.)–4 c.)4 d.)16

2.) one solution to the equation x2 – 8x = 48 is –4.

what is the other solution?

1) For a quadratic equation, we'll have two answers typically. We're looking for two numbers that when multiplied give -64, and when added give -12. This is a bit of trial and error, but you go about it by systematically factoring -64 in all possible combinations: 64=-2*32=2*-32=-4*16=4*-16=-8*8. Of these, I can 'see' that I can make -12 with 4 and -16. So the factorization of the equation becomes:

(x-16)(x+4)=0, so x=16 or x=-4.

Answers B and D are correct.

For (2), same trick applies. Rewrite as x²-8x-48=0. Factor as (x+4)(x-12)=0 because 4*-12=-48 and 4-12=-8. The other solution is x=12.