Answer
a) $(3x+2)(x+5)$
b) $3x(2y-1)(y+6)$
Work Step by Step
a)
$3x^3+17x^2+10x$
$x*(3x^2+17x+10)$
Factors of 10: 1 and 10, -1 and -10, 2 and 5, -2 and -5
$(3x+1)(x+10)$
$3x*x+3x*10+1*x+10$
$3x^2+30x+x+10$
$3x^2+31x+10$ (wrong middle term)
$(3x+2)(x+5)$
$3x*x+3x*5+2*x+2*5$
$3x^2+15x+2x+10$
$3x^2+17x+10$
b)
$6xy^2+33xy-18x$
$3x*(2y^2+11y-6)$
Factors of 6: 1 and -6, 2 and -3, -1 and 6, -2 and 3
$2y^2+11y-6$
$(2y+1)(y-6)$
$2y*y+2y*-6+1*y+1*-6$
$2y^2-12y+y-6$
$2y^2-11y-6$ (right number, wrong sign for middle term)
$2y^2+11y-6$
$(2y-1)(y+6)$
$2y*y+2y*6+(-1)*y+6*-1$
$2y^2+12y-y-6$
$2y^2+11y-6$
$3x(2y-1)(y+6)$