Question

How do you divide #(x^2 + 7x – 6) / (x-6) # using polynomial long division?

Answer 1

`(x^2+7x-6)=(x-6)(x+13)+72`

Explanation:

Here ,

Dividend `:color(blue)(x^2+7x-6) and` divisor `: color(red)(x-6`

So ,
`color(white)(..................................)ul(x+13color(white)(.........))larrquotient`
`color(white)(..................)(x-6)` `|` `x^2+7x-6`
`color(white)(......)color(violet)((x-6)*xtocolor(white)(......)ul(x^2-6x)` `color(white)(.......)lArr"subtract"`
`color(white)(........................................0)13x-6`
`color(white)(..........)color(violet)((x-6)*13tocolor(white)(.......)ul(13x-78)` `color(white)(.......)lArr"subtract"`
`color(white)(....................................................)color(green)(72` `color(white)(.........)larr"Remainder"`
Hence ,

`(x^2+7x-6)=(x-6)(x+13)+72`

`Quotient :q(x)=x+13` `"and Remainder " :r(x)=72`