Question

Suppose the roots of a polynomial are 3 4 , − 7 8 , − 3 8 , and − 1 9 . Which choice is a factor of the polynomial?

A) (x +3/4)

B) (x + 3/8)

C) (x - 7/8)

D) (x - 1/9)

Answer 1

Answer: The factor of the polynomial is
`(x+(3)/(8))`

Explanation:

We are given:

4 roots of the polynomial

Root 1:
`(3)/(4)`

The factor for this root becomes:
`(x-(3)/(4))`

Root 2:
`(-7)/(8)`

The factor for this root becomes:
`(x+(7)/(8))`

Root 3:
`(-3)/(8)`

The factor for this root becomes:
`(x+(3)/(8))`

Root 4:
`(-1)/(9)`

The factor for this root becomes:
`(x+(1)/(9))`

Hence, the factor of the polynomial is
`(x+(3)/(8))`

Answer 2

x+7/8

Explanation:

A polynomial has roots at the points where the curve cuts the x axis.

This can also be said as values of x for which the polynomial is 0

Given that when x =a is root means, we have x-a is the factor.

Based on the above, we find when 3/4, -7/8, -3/8 and -1/9 are roots

factors are x-3/4, x+7/8, x+3/8, x+1/9

Hence answer is

B) (x + 3/8)

The other options do not match with the factors only option Bmatches.