14)
$x^5 - 5x^4 - 2x^3 + 17x^2 - 13x + 2$
$=x^5 + 2x^4 - 7x^4 - 14x^3 + 12x^3 + 24x^2 - 7x^2 - 14x + x + 2$
$=x^4(x + 2) - 7x^3(x + 2) + 12x^2(x + 2) - 7x(x + 2) + (x + 2)$
$=(x + 2)(x^4 - 7x^3 + 12x^2 - 7x + 1)$
$=(x+2)(x^4 - 2x^3 + x^2 - 5x^3 + 10x^2 - 5x + x^2 - 2x + 1)$
$=(x+2)[x^2(x^2 - 2x + 1) - 5x(x^2 - 2x + 1) + (x^2 - 2x + 1)]$
$=(x+2)(x - 1)^2(x^2 - 5x + 1)$
16)
$3x^3 -5x^2 + 5x - 2$
$=3x^3 - 2x^2 - 3x^2 + 2x + 3x - 2$
$=x^2(3x - 2) - x(3x - 2) + (3x - 2)$
$=(3x - 2)(x^2 - x + 1)$
18)
$3x^3 + 5x^2 - x - 2$
$=3x^3 + 2x^2 + 3x^2 + 2x - 3x - 2$
$=x^2(3x + 2) + x(3x + 2) - (3x + 2)$
$=(3x + 2)(x^2 + x - 1)$
20)
$4x^3 - x^2 + x + 3$
$=4x^3 + 3x^2 - 4x^2 - 3x + 4x + 3$
$=x^2(4x + 3) - x(4x + 3) + (4x + 3)$
$=(4x + 3)(x^2 - x + 1)$
22)
$6x^3 - 7x^2 + 5x - 2$
$=6x^3 - 4x^2 - 3x^2 + 2x + 3x - 2$
$=2x^2(3x - 2) - x(3x - 2) + (3x - 2)$
$=(3x - 2)(2x^2 - x + 1)$
24)
$4x^3 + 5x^2 + 10x - 12$
$=4x^3 - 3x^2 + 8x^2 - 6x + 16x - 12$
$=x^2(4x - 3) + 2x(4x - 3) + 4(4x - 3)$
$=(4x - 3)(x^2 + 2x + 4)$
