Question

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

Answer 1

`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`

Answer 2

`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`