Question

find the value of p such that (x-1)is Factor of the polynomial xcube +10x square +px​

Answer 1

SOLUTION

Given,

x-1 is a factor

So,

x-1 = 0

=) x= 1

Putting the value of x in this equation:

=) x^3 +10x^2 +px

=) (1)^3 +10(1)^2 +p(1)=0

=) 1 + 10 +p =0

=) 11 +p= 0

=) p= -11

hope it helps ☺️

Answer 2

$\huge\boxed{Solution}$

$\bold{\underline{x-1\:is\:a\:factor}}$

So x-1=0

x=1

Now,

${x}^{3} + 10 {x}^{2} + px = 0$

Substitute x=1 in the equation.

${1}^{3} + 10( {1})^{2} + p(1) = 0$

$1 + 10 + p = 0$

$11 + p = 0$

$p = - 11$