Question

find p if (x-2) is a factor of the polynomial p(x) = x^3-px^2+12​

Answer 1

Hi there !

(x-2) is a factor of the polynomial of p(x)

It means 2 is a factor of p(x), So put 2 in p(x) to find p and it should be equal to 0.

$({2})^{3} - p( {2})^{2} + 12 = 0 \\ \\ 8 - 4p + 12 = 0 \\ \\ 20 - 4p = 0 \\ \\ 20 = 4p \\ \\ p = \frac{20}{4} \\ \\ p = 5$

Hence, p is 5.

Thankyou :)

Answer 2

Answer:-

Given,

(x-2) is the factor of P(x)

[ (x-2)=0 , x=2 ]

Therefore 2 is the factor of P(x)

To find p equate p(x) to 0 [zero]

${2}^{3} - p ({2})^{2} + 12 = 0$

$8 - p(4) + 12 = 0$

$8 - 4p + 12 = 0$

$- 4p + 12 = 0 - 8$

$- 4p + 12 = - 8$

$- 4p = - 8 - 12$

$- 4p = - 20$

[ "-" gets cancelled]

$p = \frac{20}{4}$

$p = 5$

Therefore the value of P=5