Question

Uestion to Answer:
1. What can you say about the value of a polynomial
when P(a)=0

Answer 1

The expression indicates that when polynomial P(x) is divided by divisor x - a, the remainder of the division is 0

Explanation:

The question would be better answered if you gave option. Since there is no option, I'll answer the question generally.

Given

`P(a) = 0`

The above expression indicates that when polynomial P(x) is divided by divisor x - a, the remainder of the division is 0

Take for instance, the polynomial is:

`P(x) = x^2 - x - 2`

And the divisor is x - 2, then P(2) = 0 because (x - 2) is a divisor of the equation.

`(P(x))/(x) =(x^2 - x - 2)/(x - 2)`

Factorize the numerator

`(P(x))/(x) =((x- 2)(x + 1))/(x - 2)`

`(P(x))/(x) =x + 1}`

See that x - 2 is a divisor

To check

Set x - 2 to 0

`x -2 = 0`

`x = 2`

So, we have:

`P(x) = x^2 - x - 2`

`P(2) = 2^2 - 2 - 2`

`P(2) = 4 - 2 - 2`

`P(2) = 0`