How do you evaluate #(10x ^ { 3} + 30x ^ { 2} + 60x - 106) \div ( 10x - 10)#?
1 Answer
Dec 31, 2017
Explanation:
#"one way is to use the divisor as a factor in the numerator"#
#"consider the numerator"#
#color(red)(x^2)(10x-10)color(magenta)(+10x^2)+30x^2+60x-106#
#=color(red)(x^2)(10x-10)color(red)(+4x)(10x-10)color(magenta)(+40x)+60x-106#
#=color(red)(x^2)(10x-10)color(red)(+4x)(10x-10)color(red)(+10)(10x-10)#
#color(white)(=)color(magenta)(+100)-106#
#=color(red)(x^2)(10x-10)color(red)(+4x)(10x-10)color(red)(+10)(10x-10)-6#
#"quotient "=color(red)(x^2+4x+10)," remainder "=-6#
#rArr(10x^3+30x^2+60x-106)/(10x-10)#
#=x^2+4x+10-6/(10x-10)#