Factor f(x) into linear factors given that k is a zero of f(x).
-$$f ( x ) = x ^ { 3 } - 4 x ^ { 2 } - 25 x + 100 ; k = 5$$
A) $( x - 5 ) ( x + 4 ) ( x + 5 )$
B) $x ( x - 5 ) ( x - 4 )$
C) $( x - 5 ) ( x - 4 ) ( x + 5 )$
D) $( x - 5 ) ( x - 4 ) ( x + 4 )$

Question

Quizplus · Accepted Answer

Since k = 5 is a zero, (x - 5) is a factor. Using synthetic division or polynomial division, dividing $f(x)$ by $x - 5$ gives the quotient $(x^2 - 4x - 20)$. Factoring this quadratic gives $(x - 4)(x + 5)$. Thus, the complete factorization is $(x - 5)(x - 4)(x + 5)$.

Factor F(x) into Linear Factors Given That K Is a Zero