Question

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

Answer 1

`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"))`
`3xcolor(white)("x"))color(white)("x")3x^2color(white)("x")+18x`
`color(white)("XXxX")underline(color(red)(3x^2)color(white)("x"+18x))`
`color(white)("XXXXXXXX")18x`
`color(white)("XXxX")underline(color(white)(3x^2)color(white)("x"+)color(blue)(18x))`
`color(white)("XXXXXXXXX")0`

Answer 2

`3x^2 +18x = 3x(x+6)`

The factors of `(3x^2 +18x)` are `3x and (x+6)`

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 = 1xx24, or 2xx12, or 3xx8, or 4xx6`

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

`50 div 5 = 10 " " rarr` 5 and 10 are factors.

`3x^2 + 18x` has a common factor of `3x` in both terms:

`3x^2 +18x = 3x(x+6)`

The factors of `3x^2 +18x` are `3x and (x+6)`