The question is ax^2+bx+c=(2x-7)(x-3) for all values of x, What is the value of b?

Question

The teacher went over and said the answer is -13, but I am not sure how she got that.
Can you please explain.
Thank you!

I did the first part
(2x-7)(x-3)
2x^2-6x-7x+21
2x^2-13x+21
here x=-13 but how do you find out the value of b?

Answer 1

Your teacher wanted you to match up the corresponding terms.

compare
ax^2 + bx + c with
2x^2 - 13x + 21 , and it says they are equal

so 2 matches with a, -13 matches with b, and
21 matches with c

Answer 2

If two polynomials are identical, all the coefficients must match. So,

a = 2
b = -13
c = 21

Answer 3

Thank you.
I was getting thrown off since the bx is +bx and since x=-13 I wasn't sure if you would change the sign to +13 since the bx was positive.