How do you divide #(6b ^ { 3} + 28b ^ { 2} + 20b + 19) \div ( b + 4)#?

1 Answer
Jim G.
Jul 15, 2017

#6b^2+4b+4+3/(b+4)#

Explanation:

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

#"consider the numerator"#

#color(red)(6b^2)(b+4)color(magenta)(-24b^2)+28b^2+20b+19#

#=color(red)(6b^2)(b+4)color(red)(+4b)(b+4)color(magenta)(-16b)+20b+19#

#=color(red)(6b^2)(b+4)color(red)(+4b)(b+4)color(red)(+4)(b+4)color(magenta)(-16)+19#

#=color(red)(6b^2)(b+4)color(red)(+4b)(b+4)color(red)(+4)(b+4)+3#

#"quotient "=color(red)(6b^2+4b+4)," remainder "=3#

#rArr(6b^3+28b^2+20b+19)/(b+4)#

#=6b^2+4b+4+3/(b+4)#

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