John M. answered • 04/28/16
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Certified Math Teacher with Statistics Masters
First, you should simplify the function expression.
3(x2 + 10x + 5) - 5(x-k) = 3x2 + 30x + 15 - 5x + 5k = 3x2 +15x +15 +5k
In order for the polynomial to be divisible by x, all terms need to divide by x with no remainder. The first two terms clearly divide by x. However, the last two do not. In order for this to work out where k is constant, 5k would have to cancel out the +15 term, leaving nothing to divide by x.
So: 15 + 5k = 0
5k = -15
k = -3
Sring P.
Choice A is the correct answer. If polynomial p(x) is divisible by x, then x must be a factor of the polynomial, or equivalently, the constant term of the polynomial must be zero. Multiplying out on the right side of the equation gives p(x) = 3x2 + 30x + 15 − 5x + 5k, which can be rewritten as p(x) = 3x2 + 25x + (5k + 15). Hence, 5k + 15 = 0, and so k = −3. Choices B, C, and D are the not correct answers because if the value of k were as indicated in those choices, then x would not be a factor of the polynomial p(x), and so p(x) would not be divisible by x.04/09/19