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