Question

How do you factor completely `16y^3 - 14y^2 - 12y`?

Answer 1

`16y^3-14y^2-12y = 16y(y-7/16-sqrt(241)/16)(y-7/16+sqrt(241)/16)`

Explanation:

Complete the square then use the difference of squares identity:

`a^2-b^2 = (a-b)(a+b)`

with `a=(16y-7)` and `b=sqrt(241)` as follows:

`16y^3-14y^2-12y = 1/16y(256y^2-224y-192)`

`color(white)(16y^3-14y^2-12y) = 1/16y((16y)^2-2(16y)(7)+(7)^2-241)`

`color(white)(16y^3-14y^2-12y) = 1/16y((16y-7)^2-(sqrt(241))^2)`

`color(white)(16y^3-14y^2-12y) = 1/16y(16y-7-sqrt(241))(16y-7+sqrt(241))`

`color(white)(16y^3-14y^2-12y) = 16y(y-7/16-sqrt(241)/16)(y-7/16+sqrt(241)/16)`