How do you simplify and divide #(2b^3+b^2-2b+3)(b+1)^-1#?
1 Answer
Jul 5, 2017
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)#