Question

If the polynomial x 3 -3x 2 +kx+42 is divisible by x+3, then find the value of k.

Answer 1

given remainder = 0
so first lets divide the equation 

Answer 2

Answer:

The value of k is $-4$.

Step-by-step explanation:

Factor theorem:-

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

Given:-

The polynomial $x^3-3x^2+kx+42$ is divisible by $x+3$.

To find:-

The value of k.

Since $x+3$ divides the the polynomial $x^3-3x^2+kx+42$.

This means $x+3$ is $1$ of the factor of the polynomial $x^3-3x^2+kx+42$.

Consider the given polynomial as follows:

$p(x)=x^3-3x^2+kx+42$ . . . . . (1)

And $x-(-3)$

Here, $a=-3$

By using the Factor theorem,

Substitute the value -3 for $x$ in equation (1) as follows:

$p(-3)=(-3)^3-3(-3)^2+k(-3)+42$

$0=-27-27-3k+42$

0 = -12 - 3k

3k = -12

k = -12/3

k = -4

Therefore, the value of k is -4.

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