Question

How do you find the quotient of `(4h^3+6h^2-3)div(2h+3)` using long division?

Answer 1

`(4h^3 +6h^2 - 3)div(2h+3) =2h^2 " remainder " -3`

Explanation:

Remember to leave a space for the `h` term in the dividend.

Divide: `4h^3 div 2h = 2h^2`

`color(white)(mmmmmm.m)2h^2`
`2h+3 |bar(4h^3 +6h^2 +" " - 3`

Multiply `2h^2` by both terms at the side (in the divisor)

`color(white)(mmmmmm.m)2h^2`
`2h+3 |bar(4h^3 +6h^2 +" " - 3`
`color(white)(xxxxxx)ul(4h^3 +6h^2)" "larr" "` subtract
`color(white)(xxxxxx)0h^3 +0h^2color(white)(mmmm)-3" "larr` remainder

`(4h^3 +6h^2 - 3)div(2h+3) =2h^2 " remainder " -3`