Find all rational zeros and factor f(x).
-$$f ( x ) = 8 x ^ { 3 } + 34 x ^ { 2 } - 29 x + 5$$
A) $2,4 , - 5 ; f ( x ) = ( 2 x - 1 ) ( 4 x - 1 ) ( x + 5 )$
B) $\frac { 1 } { 8 } , 4 , - 5 ; f ( x ) = ( 8 x - 1 ) ( x - 4 ) ( x + 5 )$
C) $\frac { 1 } { 2 } , \frac { 1 } { 4 } , - 5 ; f ( x ) = ( 2 x - 1 ) ( 4 x - 1 ) ( x + 5 )$
D) $\frac { 1 } { 8 } , 1 , - 5 ; f ( x ) = ( 8 x - 1 ) ( x - 1 ) ( x + 5 )$

Question

Quizplus · Accepted Answer

The rational root theorem helps identify possible rational roots which are factors of the constant term divided by factors of the leading coefficient. Here, the possible rational roots are ±1, ±1/2, ±1/4, ±1/8, ±5, ±5/2, ±5/4, ±5/8. Testing these roots or using synthetic division, we find that 1/2, 1/4, and -5 are roots of the polynomial. Factoring the polynomial using these roots gives $f(x) = (2x - 1)(4x - 1)(x + 5)$.

Find All Rational Zeros and Factor F(x) f(x)=8x3+34x2−29x+5f ( x ) = 8 x ^ { 3 } + 34 x ^ { 2 } - 29 x + 5f(x)=8x3+34x2−29x+5

Find All Rational Zeros and Factor F(x) $f ( x ) = 8 x ^ { 3 } + 34 x ^ { 2 } - 29 x + 5$