For what real values of c is 4x^2 + 14x - c - 3x^2 - 12x the square of a binomial?
+399 We start by simplifying
\(4x^2+14x-c-3x^2-12x\)
\(x^2+2x-c\)
To find all values of c, we take 2x the middle term, divide by 2, then x, which gives us 1,
So, a square root of some number should equal 1, which and that number is one, so -c = 1, c = - 1
This may sound complicated, dividing by so many numbers, but it's really not, the reason we do that
is because when (ax+b)2 is expanded, you get ax2+2abx+b2 so to get b when provided the first term and the middle term, we divide by 2ax, and square the result.
