How do you divide #(b ^ { 3} + 8b ^ { 2} + 21b + 17) \div ( b + 4)#?

1 Answer
Jim G.
May 28, 2017

#b^2+4b+5-3/(b+4)#

Explanation:

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

#"consider the numerator"#

#color(red)(b^2)(b+4)color(magenta)(-4b^2)+8b^2+21b+17#

#=color(red)(b^2)(b+4)color(red)(+4b)(b+4)color(magenta)(-16b)+21b+17#

#=color(red)(b^2)(b+4)color(red)(+4b)(b+4)color(red)(+5)(b+4)color(magenta)(-20)+17#

#=color(red)(b^2)(b+4)color(red)(+4b)(b+4)color(red)(+5)(b+4)-3#

#"quotient "=color(red)(b^2+4b+5)," remainder "=-3#

#rArr(b^3+8b^2+21b+17)/(b+4)=b^2+4b+5-3/(b+4)#

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