# Maths

If (x-k, where k is integral, is a factor of the polynomial P(X)=2x3-3x2-12x-7, what possible values may k have?
Working out please! I only have 7 as a possible answer need one more

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1. P(x) = 2x^3 - 3x^2 - 12x - 7 , (notice how we type exponents)

P(1) = 2-3-12-7 ≠0
P(-1) = -2 - 3 + 12 - 7 = 0
so x+1 is a factor

by either long division or synthetic division
2x^3 - 3x^2 - 12x - 7 = (x+1)(2x^2 - 5x - 7)
= (x+1)(x +1)(2x-7)
x = -1 or x = -1 or x = 7/2

so we have a double root at x= -1 and a single root at x = 7/2

but in x-k , k was supposed to be an integer, so the only value of k is
k = 1

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