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lily
12-27-2013, 05:47 AM
Factor theorem

Which of the following is equal to the value of k given that the polynomial P(x)=2x^4-4x^3+(k+1)x^2-kx+8 is exactly divisible by the linear polynomial x-4?

(A) 10
(B) 11
(C) 12
(D) 13
(E) 14

Thanks!

miranda
12-27-2013, 05:49 AM
The Factor Theorem states that a polynomial p(x) has a factor x-r if and only if f(r)=0.
From Factor theorem we have that P(4)=0.

So, P(4)=2(4)^4-4(4)^3+(k+1)(4)^2-k(4)+8=0 \Rightarrow

512-256+16k+16-4k+8=0 \Rightarrow 20k=280 \Rightarrow k=14 .

Therefore the correct answer is (E).

lily
12-27-2013, 05:49 AM
Thank you!