What is the first term of the quotient of the following division problem #(x^3-1)div(x+2)#?

2 Answers
Aug 20, 2017

#x^2#

Explanation:

Expression #=(x^3-1)/(x+2)#

By synthetic division of polynomials:

Expression #= x^2-2x+2 -(5/(x+2))#

Hence, the first term of the quotient is #x^2#

Aug 21, 2017

#x^2#

Explanation:

#"using the divisor as a factor in the numerator"#

#"consider the numerator"#

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

#=color(red)(x^2)(x+2)color(red)(-2x)(x+2)color(magenta)(+4x)-1#

#=color(red)(x^2)(x+2)color(red)(-2x)(x+2)color(red)(+4)(x+2)color(magenta)(-8)-1#

#=color(red)(x^2)(x+2)color(red)(-2x)(x+2)color(red)(+4)(x+2)-9#

#"quotient "=color(red)(x^2-2x+4)," remainder "=-9#

#"first term of the quotient "=x^2#