Question

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

Answer 1

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

$P(a) = 0$

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.

$\frac{P(x)}{x} =\frac{x^2 - x - 2}{x - 2}$

Factorize the numerator

$\frac{P(x)}{x} =\frac{(x- 2)(x + 1)}{x - 2}$

$\frac{P(x)}{x} =x + 1}$

See that x - 2 is a divisor

To check

Set x - 2 to 0

$x -2 = 0$

$x = 2$

So, we have:

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

$P(2) = 2^2 - 2 - 2$

$P(2) = 4 - 2 - 2$

$P(2) = 0$