Question

Find the value of p(x) for x=-b if (x+b) is a factor of p(x).

A. -2

B. 3

C. 0

D. None of these​

Answer 1

Concept Introduction:-

It might resemble a word or a number representation of the quantity's arithmetic value.

Given Information:-

We have been given that $p(x)$ for $x=-b$

To Find:-

We have to find that the value of $p(x)$ for $x=-b$ if $(x+b)$ is a factor of $p(x)$.

Solution:-

According to the problem

According to the remainder theorem, when $x=-b$ is a factor of $p(x)$, then

By putting the value of $x=-2$ in $p(x)=(x+b)$, we get

$p(-2)=(-2+b)$

Not satisfied

By putting the value of $x=-2$ in $p(x)=(x+b)$, we get

$p(3)=(3+b)$

Not satisfied

By putting the value of $x=0$ in $p(x)=(x+b)$, we get

$p(0)=(0+b)\\=b$

Not satisfied

Final Answer:-

The correct option is $D.$  None of these​.

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Answer 2

Answer:

Option (c) is the correct answer.

Step-by-step explanation:

Factor Theorem:-

• Let $p(x)$ be any polynomial of degree $\geq$ $1$ and $a$ be any real number such that $(x-a)$ is a factor of $p(x)$, then $p(a)=0$.

Step 1 of 1

According to the question,

It is given that (x + b) is a factor of p(x).

To find the value of p(x) for x = -b, i.e., p(-b) =?

Since (x + b) is a factor of p(x).

or we can write,

(x - (-b)) is a factor of $p(x)$.

Using the factor theorem, we get

p(-b) = 0

Therefore, the value of p(x) for x = -b is 0.

Hence, option (c) is correct.

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