Question

Given f(x)=2x^2+9x+k, and the remainder when f(x) is divided x+7 is 32, then what is the value of k?

Answer 1

Set up either long division or synthetic div. I'd do the latter.

Your divisor for synth. div. should be -7.

__________
Then -7 / 2 9 k
-14 +35
--------------------
2 -5 k+35 Rem is 32;
Let 32 = k + 5 and solve for k:

k = -3.

Let's check that. Is k correct?

Then -7 / 2 9 -3
-14 +35
--------------------
2 -5 -3+35 = 32

Since the rem is 32, we are correct; k = -3.