How do you divide #x^3+7x^2-3x+4) div(x+2)# and identify any restrictions on the variable?

1 Answer
Dec 20, 2017

Answer:

#x^2+5x-13+30/(x+2)to(x!=-2)#

Explanation:

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

#"consider the numerator"#

#color(red)(x^2)(x+2)color(magenta)(-2x^2)+7x^2-3x+4#

#=color(red)(x^2)(x+2)color(red)(+5x)(x+2)color(magenta)(-10x)-3x+4#

#=color(red)(x^2)(x+2)color(red)(+5x)(x+2)color(red)(-13)(x+2)color(magenta)(+26)+4#

#=color(red)(x^2)(x+2)color(red)(+5x)(x+2)color(red)(-13)(x+2)+30#

#"quotient "=color(red)(x^2+5x-13)," remainder "=30#

#rArr(x^3+7x^2-3x+4)/(x+2)#

#=x^2+5x-13+30/(x+2)to(x!=-2)#