Question

Find the value of p for which x-3 is a factor of polynomial p^2x^3-px^2+3px-p.

Answer 1

solution

p²x³-px²+3px-p the factor is x-3 ⇒x=3

⇒ p³(3)³-p(3)²+3p(3)-p=0

27p³-9p+9p-p=0

27p³-p=0

p(27p²-1)=0

⇒ p=0 or 27p²-1=0

p=0 or p²=1/27

p=0 or p=√1/27 ⇒p=1/√27 ⇒ p=√27/27

⇒ p=0 or p=√27/27