Question

How do you factor the expression `3x - 9x^2`?

Answer 1

`3x(1-3x)`

Explanation:

Recall that the greatest common factor is the largest number which two numbers can be divided by without producing a decimal . For example, the greatest common factor of `12` and `16` is `4`.

In addition, recall the distributive property: `a(b+c)=ab+ac`.

Factoring the Expression
`1`. Determine the greatest common factor for `color(red)3` and `color(blue)9`, which is `color(purple)3`. Using the distributive property, factor `color(purple)3` from the expression.

`color(red)3x-color(blue)9x^2`

`=color(purple)3(x-3x^2)`

`2`. Both terms, `color(orange)x` and `-3color(turquoise)(x^2)`, contain another common factor, `color(green)x`. Thus, factor out `color(green)x` from the expression.

`=3color(green)x(1-3x)`