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)? 

x = 2
x = −2
x = −1
x = 3

Answer 1

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

Answer 2

Answer: x = 2

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`