Question

If x = 1 is a zero of the polynomial function f(x) = 3x3 − 8x2 + 3x + 2, which of the following is another zero of f(x)? 

Answer 1

Answer: x = 2

Step-by-step explanation:

Given polynomial function,

$f(x) = 3x^3-8x^2 + 3x + 2$,

According to question, If x = 1 is a zero of the polynomial function $f(x) = 3x^3-8x^2 + 3x + 2$

Therefore, (x - 1) is the factor of $f(x) = 3x^3 - 8x^2 + 3x + 2$

By dividing $3x^3- 8x^2 + 3x + 2$ by (x - 1)  (mentioned in below diagram)

We get, $3x^2-5x-2$.

Therefore, $3x^3 - 8x^2 + 3x + 2=(x - 1)(3x^2-5x-2)$

⇒$3x^3 - 8x^2 + 3x + 2=(x - 1)(3x^2-6x+x-2)$  (by grouping method)

⇒$3x^3- 8x^2 + 3x + 2=(x - 1)(3x+1)(x-2)$

Thus, x-2 is a factor of  $3x^3- 8x^2 + 3x + 2$,

Therefore, x=2 is a zero of $3x^3- 8x^2 + 3x + 2$

Answer 2

Divide 3x^3 -8x^2+3x  + 2 by (x - 1)

THis gives the quotient   3x^2 - 5x - 2

3x^2 - 5x -  2  = (3x + 1)(x  - 2 )


so x = 2 is another root  


Its  the first choice