Question

How do you divide `(4x^3 -12x^2+5x+3)/((x +3) )`?

Answer 1

`4x^2 - 24x + 77, R -228`

Explanation:

polynomial long division - yay!

Answer 2

`4x^2-24x+77-228/(x+3)`

Explanation:

`"one way is to use the divisor as a factor in the numerator"`

`"consider the numerator"`

`color(red)(4x^2)(x+3)color(magenta)(-12x^2)-12x^2+5x+3`

`=color(red)(4x^2)(x+3)color(red)(-24x)(x+3)color(magenta)(+72x)+5x+3`

`=color(red)(4x^2)(x+3)color(red)(-24x)(x+3)color(red)(+77)(x+3)color(magenta)(-231)+3`

`=color(red)(4x^2)(x+3)color(red)(-24x)(x+3)color(red)(+77)(x+3)-228`

`"quotient "=color(red)(4x^2-24x+77)," remainder "=-228`

`rArr(4x^3-12x^2+5x+3)/(x+3)`

`=4x^2-24x+77-228/(x+3)`