Question

If (x-2) is a factor of the polynomial p(x) then p(2)=

Answer 1

Answer:

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Answer 2

The value of p(2) is zero.

Given:

(x-2) is a factor of the polynomial p(x).

To Find:

The value of p(2).

Solution:

We know that a polynomial is an expression consisting of variables, exponents, and constants which is combined using mathematical expressions and is of the form:

p(x) = $x^{n}a_{n} + x^{n-1}a_{n-1}+...+xa_{1} + a_{0}$.

A factor of the polynomial is any polynomial that completely divides the given polynomial.

We are given that (x-2) is a factor of the polynomial p(x).

⇒ p(x) = (x-2)($x^{n-1}a_{n-1}+...+xa_{1} + a_{0}$)

We need to find the value of p(2).

p(2) = (2-2)($x^{n-1}a_{n-1}+...+xa_{1} + a_{0}$) = 0.($x^{n-1}a_{n-1}+...+xa_{1} + a_{0}$) = 0.

∴ The value of p(2) is zero.

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