Question

How do you divide `4x ^ { 3} + 6x ^ { 2} - 23x - 15\div ( 3+ x )`?

Answer 1

I a man assuming you mean to include brackets around the first four terms!

Answer 2

`4x^2-6x-5`

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)+6x^2-23x-15`

`=color(red)(4x^2)(x+3)color(red)(-6x)(x+3)color(magenta)(+18x)-23x-15`

`=color(red)(4x^2)(x+3)color(red)(-6x)(x+3)color(red)(-5)(x+3)color(magenta)(+15)-15`

`=color(red)(4x^2)(x+3)color(red)(-6x)(x+3)color(red)(-5)(x+3)+0`

`rArr(4x^3+6x^2-23x-15)/(x+3)=color(red)(4x^2-6x-5)`