Find all rational zeros and factor f(x).
$f ( x ) = 8 x ^ { 3 } + 2 x ^ { 2 } - 5 x + 1$
A) $2,4 , - 1 ; f ( x ) = ( 2 x - 1 ) ( 4 x - 1 ) ( x + 1 )$
B) $\frac { 1 } { 8 } , 4 , - 1 ; f ( x ) = ( 8 x - 1 ) ( x - 4 ) ( x + 1 )$
C) $\frac { 1 } { 8 } , 1 , - 1 ; f ( x ) = ( 8 x - 1 ) ( x - 1 ) ( x + 1 )$
D) $\frac { 1 } { 2 } , \frac { 1 } { 4 } , - 1 ; f ( x ) = ( 2 x - 1 ) ( 4 x - 1 ) ( x + 1 )$

Question

Quizplus · Accepted Answer

The rational root theorem can be used to find the rational zeros of the polynomial. By testing the possible rational roots, we find that $ \frac{1}{2}, \frac{1}{4}, $ and $ -1 $ are indeed zeros of the polynomial. Factoring the polynomial using these zeros gives us $ f(x) = (2x - 1)(4x - 1)(x + 1) $.

Find All Rational Zeros and Factor F(x) f(x)=8x3+2x2−5x+1f ( x ) = 8 x ^ { 3 } + 2 x ^ { 2 } - 5 x + 1f(x)=8x3+2x2−5x+1

Find All Rational Zeros and Factor F(x) $f ( x ) = 8 x ^ { 3 } + 2 x ^ { 2 } - 5 x + 1$