Question
. Let g(x)=-5x^4-2x^3+9x^2-8x+C for some constant C.Find the value of C so that x-1 is a factor of g.
Answer
4.2
(243 Votes)
Phillip
Master · Tutor for 5 years
Answer
If
is a factor of \(g(x)\), then \(g(1)\) must be equal to 0 (by the Factor Theorem). Substitute
into \(g(x)\):\(g(1) = -5(1)^4 - 2(1)^3 + 9(1)^2 - 8(1) + C = 0\)Solving this gives:
So,
.