Answer:
The expression indicates that when polynomial P(x) is divided by divisor x - a, the remainder of the division is 0
Step-by-step explanation:
The question would be better answered if you gave option. Since there is no option, I'll answer the question generally.
Given
[tex]P(a) = 0[/tex]
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:
[tex]P(x) = x^2 - x - 2[/tex]
And the divisor is x - 2, then P(2) = 0 because (x - 2) is a divisor of the equation.
[tex]\frac{P(x)}{x} =\frac{x^2 - x - 2}{x - 2}[/tex]
Factorize the numerator
[tex]\frac{P(x)}{x} =\frac{(x- 2)(x + 1)}{x - 2}[/tex]
[tex]\frac{P(x)}{x} =x + 1}[/tex]
See that x - 2 is a divisor
To check
Set x - 2 to 0
[tex]x -2 = 0[/tex]
[tex]x = 2[/tex]
So, we have:
[tex]P(x) = x^2 - x - 2[/tex]
[tex]P(2) = 2^2 - 2 - 2[/tex]
[tex]P(2) = 4 - 2 - 2[/tex]
[tex]P(2) = 0[/tex]
