SOLUTION: Determine the value of k in f(x) = 5x^3+kx^2-4x+4 so that x+2 is a factor

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Question 1047655: Determine the value of k in f(x) = 5x^3+kx^2-4x+4 so that x+2 is a factor
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Determine the value of k in f%28x%29+=+5x%5E3%2Bkx%5E2-4x%2B4 so that x%2B2 is a factor

That %28x%2B2%29 is a factor of f%28x%29=5x%5E3%2Bkx%5E2-4x%2B4 means exactly that
f%28-2%29=0.
That is you want to solve the equation:
5%28-2%29%5E3%2Bk%28-2%29%5E2-4%28-2%29%2B4+=0 for k
5%28-8%29%2B4k%2B8%2B4+=0
-40%2B4k%2B12+=0
-28%2B4k+=0
4k+=28
k+=28%2F4
k+=7
so, we have
f%28x%29=5x%5E3%2B7x%5E2-4x%2B4
check if x%2B2 is factor
f%28x%29=5x%5E3%2B7x%5E2-4x%2B4....write 7x%5E2 as 10x%5E2-3x%5E2 and -4x as -6x%2B2x
f%28x%29=5x%5E3%2B10x%5E2-3x%5E2-6x%2B2x%2B4...group
f%28x%29=%285x%5E3%2B10x%5E2%29-%283x%5E2%2B6x%29%2B%282x%2B4%29
f%28x%29=5x%5E2%28x%2B2%29-3x%28x%2B2%29%2B2%28x%2B2%29
f%28x%29=%28x%2B2%29+%285x%5E2-3x%2B2%29......so,x%2B2 is factor