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) $\frac { 1 } { 2 } , \frac { 1 } { 4 } , - 1 ; f ( x ) = ( 2 x - 1 ) ( 4 x - 1 ) ( x + 1 )$
C) $\frac { 1 } { 8 } , 4 , - 1 ; f ( x ) = ( 8 x - 1 ) ( x - 4 ) ( x + 1 )$
D) $\frac { 1 } { 8 } , 1 , - 1 ; f ( x ) = ( 8 x - 1 ) ( x - 1 ) ( x + 1 )$

Question

Quizplus · Accepted Answer

The rational root theorem suggests that the rational zeros of the polynomial $f(x) = 8x^3 + 2x^2 - 5x + 1$ can be found among the divisors of the constant term (1) divided by the divisors of the leading coefficient (8). The correct zeros are $\frac{1}{2}$, $\frac{1}{4}$, and $-1$, which correspond to the factors $(2x - 1)$, $(4x - 1)$, and $(x + 1)$ respectively, as shown in option B.

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) $f ( x ) = 8 x ^ { 3 } + 2 x ^ { 2 } - 5 x + 1$