How do you use synthetic division to divide $X^3 + 2x^2 - 5x - 6 div (x + 3)$ ?

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Answer 1 · 2018-07-05T16:29:43

The remainder is $0$ and the quotient is $=x^2-x-2$

$color(white)(aaaa)$ $-3$ $|$ $color(white)(aaaa)$ $1$ $color(white)(aaaaa)$ $2$ $color(white)(aaaaaa)$ $-5$ $color(white)(aaaaa)$ $-6$

$color(white)(aaaaaaa)$ $|$ $color(white)(aaaa)$ $color(white)(aaaa)$ $-3$ $color(white)(aaaaaaa)$ $3$ $color(white)(aaaaaaa)$ $6$

$color(white)(aaaaaaaaa)$ _________________________________________________________##

$color(white)(aaaaaaa)$ $|$ $color(white)(aaaa)$ $1$ $color(white)(aaa)$ $-1$ $color(white)(aaaaaa)$ $-2$ $color(white)(aaaaaa)$ $color(red)(0)$

The remainder is $0$ and the quotient is $=x^2-x-2$

Therefore,

$(x^3+2x^2-5x-6)/(x+3)=(x^2-x-2)$

Also,

If $f(x)=x^3+2x^2-5x-6$

$f(-3)=(-3)^3+2(-3)^2-5(-3)-6$

$=-27+18+15-6$

$=0$

How do you use synthetic division to divide X^3 + 2x^2 - 5x - 6 div (x + 3)X^3 + 2x^2 - 5x - 6 div (x + 3)?