Question

How do you factor `5x^2- 35x`?

Answer 1

`5x(x-7)`

Explanation:

take out common factors

`(1) " take " hcf(5,35) =color(red)(5)" out"`

`5x^2-35x= color(red)(5)(x^2-7x)`

`(2)" take "hcf(x^2,x)=color(blue)(x )" out"`

`5x^2-35x= color(red)(5)(x^2-7x)=color(red)(5)color(blue)(x)(x-7)`

Answer 2

`5x(x-7)`

Explanation:

We got:

`5x^2-35x`

Take the greatest common factor out, which is `5`.

`=5(x^2-7x)`

Notice how `x` still remains in both factors inside, and so we can take it out, and we get:

`=5x(x-7)`

Answer 3

`5x(x-7)`

Explanation:

Both terms are divisible by `5`, and `x`, so you factor those out of the polynomial. As for how this affects any solutions of this, because both factors equal `0` (or whatever is on the other side of the equation, but I'll use `0`), `5x=0`, so `x=0`, and `x-7=0`, so `x=7`