Question

find the value of p, if x-2 is a factor of polynomial x³ - px² + 12

Answer 1

( X-2) is a factor of the given polynomial x³-px²+12.



( X - 2 ) = 0


X = 2



P( X ) = X³ - PX² + 12


Substitute X = 2 in P(x).



P (2) = (2)³ - P × (2)² + 12




=> 8 - 4P + 12 = 0



=> -4P + 20 = 0



=> -4P = -20


=> P = 20/4


=> P = 5

Answer 2

Hello!

If $\bf{x-2}$ is factor of p(x)

Then, $\boxed{\sf x=2}$

$\sf p(x) = x^{3} - px^{2}+12 \\ \\ \implies \sf p(x) = (2)^{3} - p(2)^{2} + 12 = 0 \\ \\ \implies \sf 8 - 4p + 12 = 0 \\ \\ \implies \sf 20 - 4p = 0 \\ \\ \implies \sf 4p = 20 \\ \\ \implies \sf p = \dfrac{20}{4} \implies \boxed{\red{\bf{p = 5}}}$

Cheers!