How do you factor the expression $3 x - 9 x^{2}$ $3x - 9x^2$ ?

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How do you factor the expression $3 x - 9 x^{2}$ $3x - 9x^2$ ?

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Answer 1 · 2016-02-28T03:01:54

$3 x (1 - 3 x)$ $3x(1-3x)$

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 $12$ $12$ and $16$ $16$ is $4$ $4$ .

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

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

$3 x - 9 x^{2}$ $color(red)3x-color(blue)9x^2$

$= 3 (x - 3 x^{2})$ $=color(purple)3(x-3x^2)$

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

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

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How do you factor the expression $3 x - 9 x^{2}$ $3x - 9x^2$ ?

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