# The polynomial 3x^2 +18x has factors of 3x and which other?

Dec 28, 2016

color(green)(""(x+6))

#### Explanation:

color(white)("XX")underline(color(white)("XX")color(red)xcolor(white)("X")+color(white)("x")color(blue)6color(white)("X"))
$3 x \textcolor{w h i t e}{\text{x"))color(white)("x")3x^2color(white)("x}} + 18 x$
color(white)("XXxX")underline(color(red)(3x^2)color(white)("x"+18x))
$\textcolor{w h i t e}{\text{XXXXXXXX}} 18 x$
color(white)("XXxX")underline(color(white)(3x^2)color(white)("x"+)color(blue)(18x))
$\textcolor{w h i t e}{\text{XXXXXXXXX}} 0$

Jul 19, 2017

$3 {x}^{2} + 18 x = 3 x \left(x + 6\right)$

The factors of $\left(3 {x}^{2} + 18 x\right)$ are $3 x \mathmr{and} \left(x + 6\right)$

#### Explanation:

Factors of numbers or expressions are always in pairs.

For example: Consider $24$
Its factors are $1 , 2 , 3 , 4 , 6 , 8 , 12 , 24$

In pairs it means:

$24 = 1 \times 24 , \mathmr{and} 2 \times 12 , \mathmr{and} 3 \times 8 , \mathmr{and} 4 \times 6$

If we know a number is a FACTOR of another number, it means it can divide into exactly.

$50 \div 5 = 10 \text{ } \rightarrow$ 5 and 10 are factors.

$3 {x}^{2} + 18 x$ has a common factor of $3 x$ in both terms:

$3 {x}^{2} + 18 x = 3 x \left(x + 6\right)$

The factors of $3 {x}^{2} + 18 x$ are $3 x \mathmr{and} \left(x + 6\right)$