# How do you divide #(x^3+3x^2-2x+5) div(x+1)# and identify any restrictions on the variable?

##### 2 Answers

Long division

#### Explanation:

(I am using the square root function to format it as close as possible to a long division sign, but it is not a square root.)

We cannot divide by *not* equal

The first step to long division is to fill in any terms of

Next, you divide the first term in the dividend by the first term in the divisor, in this case

The quotient of this division is multiplied by all terms in divisor, and this product is then subtracted from original dividend. Then drop down the rest of the original function.

The first term of the new function

One more division, in the same fashion as the 2 previous ones.

When the remaining difference is a term with no

This is the final answer.

#### Explanation:

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

#"consider the numerator"#

#color(red)(x^2)(x+1)color(magenta)(-x^2)+3x^2-2x+5#

#=color(red)(x^2)(x+1)color(red)(+2x)(x+1)color(magenta)(-2x)-2x+5#

#=color(red)(x^2)(x+1)color(red)(+2x)(x+1)color(red)(-4)(x+1)color(magenta)(+4)+5#

#=color(red)(x^2)(x+1)color(red)(+2x)(x+1)color(red)(-4)(x+1)+9#

#"quotient "=color(red)(x^2+2x-4)," remainder "=+9#

#rArr(x^3+3x^2-2x+5)/(x+1)#

#=x^2+2x-4+9/(x+1)to(x!=-1)#