Question

Rewrite the rational expression x^3+5x^2+3x-10/x+4 in the form q(x)+r(x)/b(x).

Answer 1

I have attached an image of a long division method that can be used to find the quotient and remainder.

Hope I helped :)

Answer 2

`x^2+x-1-(6)/(x+4)`

Explanation:

Rational expression form :
`(a(x))/(b(x))=q(x)+(r(x))/(b(x))`

a(x) = dividend

b(x) = divisor

q(x) = quotient

r(x) = remainder

Given expression :
`(x^3+5x^2+3x-10)/(x+4)`

We know that
`Dividend = Divisor * Quotient+Remainder`

So,
`x^3+5x^2+3x-10 =x+4 * (x^2+x-1)-6`

Thus a(x) = dividend =
`x^3+5x^2+3x-10`

b(x) = divisor=
`x+4`

q(x) = quotient=
`x^2+x-1`

r(x) = remainder=-6

Substitute the value in the rational form.

`(x^3+5x^2+3x-10)/(x+4)=x^2+x-1-(6)/(x+4)`

Hence the rational expression
`(x^3+5x^2+3x-10)/(x+4)` in the form of
`q(x)+(r(x))/(b(x))` is
`x^2+x-1-(6)/(x+4)`