Question

if x minus 3 is a factor of PX equal x cube minus x square + px+ q then ​

Answer 1

$\textbf{Given:}$

$\text{(x-3) is a factor of}$

$\mathrm{P(x)=x^3-x^2+px+q}$

$\textbf{To find:}$

$\text{The relation between p and q}$

$\textbf{Solution:}$

$\textbf{Factor theorem:}$

$\textbf{(x-a) is a factor of P(x) if and only if P(a)=0}$

$\text{Since (x-3) is a factor of P(x), we have P(3)=0}$

$\implies\mathrm{3^3-3^2+p(3)+q=0}$

$\implies\mathrm{27-9+3p+q=0}$

$\implies\mathrm{18+3p+q=0}$

$\implies\boxed{\bf\mathrm{3p+q=-18}}$

$\text{which is the required relation}$

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