Question

How do you factor `40x^3 + 5`?

Answer 1

`5(8x^3+1)`

Explanation:

In the expression `40x^3+5` the only common factor is 5

So we have factored this expression as

`5(8x^3+1)`

Answer 2

`5(2x+1)(4x^2-2x+1)`

Explanation:

`"take out a "color(blue)"common factor of 5"`

`rArr40x^3+5`

`=5(8x^3+1)`

`8x^3+1" is a "color(blue)"sum of cubes"`

`•color(white)(x)a^3+b^3=(a+b)(a^2-ab+b^2)`

`"note that "8x^3=(2x)^3" and "1=1^3`

`"here "a=2x" and "b=1`

`rArr8x^3+1=(2x+1)((2x)^2-(2x.1)+1^2)`

`color(white)(rArr8x^3+1)=(2x+1)(4x^2-2x+1)`

`rArr40x^3+5=5(2x+1)(4x^2-2x+1)`