Question

if (x-3) is a factor of p(x) x^3 - kx^2 + ( k + 1 ) x-12 value of k

Answer 1

x-3=0
x=3

p(x)=x³-kx²+(k-1)x-12
p(3)=(3)³-k(3)²+(k-1)3-12
0=27-9k+3k-3-12
6k=12
k=12/6
k=2

The value of k is 2

Answer 2

$\fontsize{18}{10}{\textup{\textbf{The value of k is 3.}}}$

Step-by-step explanation:

We have the following theorem :

Factor theorem : If (x-a) is a factor of a polynomial f(x), then f(x)=0.

According to the given information, we have

$(x-3)~\textup{is a factor of the polynomial }p(x)=x^3-kx^2+(k+1)x-12.$

Therefore, we get

$p(3)=0\\\\\Rightarrow 3^3-k\times3^2+(k+1)\times3-12=0\\\\\Rightarrow 27-9k+3k+3-12=0\\\\\Rightarrow -6k+18=0\\\\\Rightarrow 6k=18\\\\\Rightarrow k=3.$

Thus, the required value of k is 3.

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