How do you divide #\frac { x ^ { 2} + 14x + 9} { x ^ { 2} + 2x + 3}#?

1 Answer
Jul 20, 2017

#1+(12x+6)/(x^2+2x+3)#

Explanation:

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

#"consider the numerator"#

#color(red)(1)(x^2+2x+3)color(magenta)(-2x-3)+14x+9#

#=color(red)(1)(x^2+2x+3)+12x+6#

#"quotient "=color(red)(1)," remainder "=12x+6#

#rArr(x^2+14x+9)/(x^2+2x+3)=1+(12x+6)/(x^2+2x+3)#