Question

How do you find the quotient of (x^3-43x+42) divided by (x^2+6x-7)?

Answer 1

`x-6`

Explanation:

`"factorise numerator/denominator"`

`x^3-43x+42`

`=x^2(x-1)+x(x-1)-42(x-1)`

`=(x-1)(x^2+x-42)=(x-1)(x+7)(x-6)`

`x^2+6x+7=(x+7)(x-1)`

`rArr(x^3-43x+42)/(x^2+6x-7)`

`=(cancel((x-1))cancel((x+7))(x-6))/(cancel((x+7))cancel((x-1)))=x-6`