(-18x^3+17x+6)÷(3x+2) Need help please?

1 Answer
May 24, 2018

#-6x^2+4x+3#

Explanation:

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

#"consider the numerator"#

#color(red)(-6x^2)(3x+2)color(magenta)(+12x^2)+17x+6#

#=color(red)(-6x^2)(3x+2)color(red)(+4x)(3x+2)color(magenta)(-8x)+17x+6#

#=color(red)(-6x^2)(3x+2)color(red)(+4x)(3x+2)color(red)(+3)(3x+2)cancel(color(magenta)(-6))cancel(+6)#

#"quotient "=color(red)(-6x^2+4x+3)," remainder "=0#

#(-18x^3+17x+6)/(3x+2)=-6x^2+4x+3#