Question

2x3+x2-13x+6 factorize by remainder theorem

Answer 1

divide the term
$2 {x}^{3} + {x}^{2} - 13x + 6$
by x-2
then it will be
2x^2 + 5x -3
=2x^2 +6x-x-3
=2x(x+3)-1(x+3)
=(2x-1)(x+3)

so 2x^3+x^2-13x+6
=(x-2)(2x^2+5x-3)
=(x-2)(2x-1)(x+3)