SOLUTION: If x+2 is a factor of 2x^3+kx^2+16x, what is the value of k?

SOLUTION: If x+2 is a factor of 2x^3+kx^2+16x, what is the value of k?

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Question 871946: If x+2 is a factor of 2x^3+kx^2+16x, what is the value of k?
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
If x+2 is a factor of 2x^3+kx^2+16x, what is the value of k?
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First we can factor out the x:
2x^3+kx^2+16x = x(2x^2 + kx + 16)
If x+2 is a factor, and the constant term=16, then we can write the quadratic as
(x+2)(2x+8) = 2x^2 + 12x + 16 = 2x^2 + kx + 16
Therefore k = 12

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