Factor f(x) into linear factors given that k is a zero of f(x).
-$f ( x ) = x ^ { 4 } + 14 x ^ { 3 } + 44 x ^ { 2 } - 70 x - 245 ; k = - 7$ (multiplicity 2)
A) $f ( x ) = ( x - 7 ) ( x + 7 ) ( x - \sqrt { 5 } ) ( x + \sqrt { 5 } )$
B) $f ( x ) = ( x + 7 ) ^ { 2 } ( x - 5 ) ( x + 5 )$
C) $f ( x ) = ( x + 7 ) ^ { 2 } ( x - \sqrt { 5 } ) ( x + \sqrt { 5 } )$
D) $f ( x ) = ( x - 7 ) ^ { 2 } ( x - \sqrt { 5 } ) ( x + \sqrt { 5 } )$

Question

Quizplus · Accepted Answer

Since $k = -7$ is a zero of $f(x)$ with multiplicity 2, $f(x)$ must include the factor $(x + 7)^2$. Factoring $f(x)$ completely, we find that the remaining factors are $(x - \sqrt{5})(x + \sqrt{5})$, which gives us the linear factors of $f(x)$ including the given zero $k = -7$.

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