Question

4x^2+28x+c
c=?

Answer 1

7?

Answer 2

i think it's 49

Answer 3

Is the question what is c for this trinomial to be the square of a binomial?

Answer 4

Yes.

Answer 5

So 49?

Answer 6

\(4x^2\) is the square of \(2x\)
For this to be the square of a binomial, you need:
\( (2x^2 + ...~)(2x^2 + ...~) = 4x^2 + 28x + c \)
Compare with:
\((a + b)(a + b) = a^2 + 2ab + b^2 \)
The middle term is 2ab
Your middle term is 28x, and you know a = 2x.
2ab = 28x, substitute 2x for a:
\(2 (2x) b = 28x \)
\(b = 7\)
Once you have \(b = 7\), then the last term of the trinomial is \(b^2\),
so it's \(7^2 = 49\).
\( 4x^2 + 28x + 49 \)
\(c = 49\)