Find all rational zeros and factor f(x).
-$$f ( x ) = 10 x ^ { 3 } + 43 x ^ { 2 } + 11 x - 4$$
A) $- 2,5 , - 4 ; f ( x ) = ( 2 x + 1 ) ( 5 x - 1 ) ( x + 4 )$
B) $- \frac { 1 } { 2 } , \frac { 1 } { 5 } , - 4 ; f ( x ) = ( 2 x + 1 ) ( 5 x - 1 ) ( x + 4 )$
C) $- 2,5 , - 4 ; f ( x ) = ( x + 2 ) ( x - 5 ) ( x + 4 )$
D) $- \frac { 1 } { 10 } , 1 , - 4 ; f ( x ) = ( 10 x + 1 ) ( x - 1 ) ( x + 4 )$

Question

Quizplus · Accepted Answer

The rational root theorem suggests that rational zeros of a polynomial are of the form ±(factor of constant term)/(factor of leading coefficient). For $f(x) = 10x^3 + 43x^2 + 11x - 4$, the factors of the constant term (-4) are ±1, ±2, ±4, and the factors of the leading coefficient (10) are ±1, ±2, ±5, ±10. The correct rational zeros are $-\frac{1}{2}$, $\frac{1}{5}$, and -4, which match option B. Factoring the polynomial using these zeros gives $f(x) = (2x + 1)(5x - 1)(x + 4)$, confirming B as the correct choice.

Find All Rational Zeros and Factor F(x) f(x)=10x3+43x2+11x−4f ( x ) = 10 x ^ { 3 } + 43 x ^ { 2 } + 11 x - 4f(x)=10x3+43x2+11x−4

Find All Rational Zeros and Factor F(x) $f ( x ) = 10 x ^ { 3 } + 43 x ^ { 2 } + 11 x - 4$