Question

The volume of the rectangular prism is 60x^3 + 145x^2 + 70x. Factor to find the possible expressions for length, width and height of the prism.

Answer 1

The volume of the rectangular prism:
$V=length\cdot width\cdot height=lwh$

$60x^3 + 145x^2 + 70x=5x(12x^2+29x+14)\\\\=5x(12x^2+21x+8x+14)=5x[3x(4x+7)+2(4x+7)]\\\\=5x(4x+7)(3x+2)\\\\Answer:\\length=5x\\width=4x+7\\height=3x+2$