Question

How do you find the quotient of 3x^3 - 2x^2 +5 / x - 4?

Answer 1

`3x^2+10x+40`

Explanation:

divide the term `3x^3-2x^2+5` traditionally by `x-4`
so you have `3x^3-2x^2+5` = `x-4 *` quotient + remainder

1. `x-4 * 3x^2 = 3x^3-12x^2`
2. Subtract this with the polynomial you get `10x^2+5`
3. `x-4 * 10x = 10x^2-40x`
4. Subtract this from the polynomial in step 2 to get `40x+5`
5. `x-4 * 40 = 40x-160`
6. Subtract this from the polynomial in step 4 to get `165`

now the number cannot be divided further hence 165 is remainder
and `3x^2+10x+40` is the quotient (sum of terms we used in steps 1, 3 and 5)

`3x^3-2x^2+5 = (x-4) * (3x^2+10x+40) +165`