Jcpenny wrote:

If b, c, and d are constants and x^2 + b^x + c = (x+d)^2 for all values of x, what is the value of c?

(1) d = 3

(2) b = 6

First, I'm absolutely certain that the question should read:

If b, c, and d are constants and x^2 + bx + c = (x+d)^2 for all values of x, what is the value of c?

(1) d = 3

(2) b = 6 because otherwise it's mathematically impossible that what is stated in the stem is true, unless b = 1, d = 0 and c = -1. Proceeding on that assumption:

We know that

\(x^2 + bx + c = (x+d)^2\)

for

all values of x. In particular, it's true for x=0:

\(0^2 + b*0 + c = (0+d)^2 \\

c = d^2\)

So you can find c if you know d, and Statement 1 is sufficient.

Further, knowing that \(c = d^2\), we have

\(x^2 + bx + d^2 = (x+d)^2 \\

x^2 + bx + d^2 = x^2 + 2dx + d^2 \\

bx = 2xd \\

b = 2d \\\)

so if you can find b, you can find d, and therefore you can find c. Statement 2 is sufficient.

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