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

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

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Answer 1 · 2018-07-05T16:29:43

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

Explanation:

Let's perform the synthetic division

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

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

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

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

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

Therefore,

$\frac{x^{3} + 2 x^{2} - 5 x - 6}{x + 3} = (x^{2} - x - 2)$ $(x^3+2x^2-5x-6)/(x+3)=(x^2-x-2)$

Also,

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

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

$= - 27 + 18 + 15 - 6$ $=-27+18+15-6$

$= 0$ $=0$

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

1 Answer

Explanation:

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Science

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How do you use synthetic division to divide X3+2x2−5x−6÷(x+3)X^3 + 2x^2 - 5x - 6 div (x + 3)?

1 Answer

Explanation:

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