Question

Find the value of p for which the polynomial 3x3 -x2 + px +1 is exactly divisible by
x-1, hence factorise the polynomial.

Answer 1

$since \: polynomial \: is \: exactly \: is \: divisible \: by \: x - 1 \\ it \: means \: 1 \: is \: factor \: of \: this \: polynomial - \\ \\ hence \: directly \: put \: value \: of \: x \: as \: 1 \: in \: given \: polynmial - \\ \\ 3 {x}^{3} - {x}^{2} + px + 1 = 0 \\ 3 {(1)}^{3} - {(1)}^{2} + p(1) + 1 = 0 \\ 3 - 1 + p + 1 = 0 \\ 3 + p = 0 \\ p = - 3$

Answer 2

hope it will helpful to you