How do you simplify and divide #(2b^3+b^2-2b+3)(b+1)^-1#?

1 Answer
Jim G.
Jul 5, 2017

#2b^2-b-1+4/(b+1)#

Explanation:

#(2b^3+b^2-2b+3)(b+1)^-1#

#=(2b^3+b^2-2b+3)/(b+1)#

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

#"consider the numerator"#

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

#=color(red)(2b^2)(b+1)color(red)(-b)(b+1)color(magenta)(+b)-2b+3#

#=color(red)(2b^2)(b+1)color(red)(-b)(b+1)color(red)(-1)(b+1)color(magenta)(+1)+3#

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

#"quotient "=color(red)(2b^2-b-1)," remainder "=4#

#rArr(2b^3+b^2-2b+3)/(b+1)#

#=2b^2-b-1+4/(b+1)#

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