How do you find f(-3) given $f (x) = x^{3} - 2 x^{2} + 4 x + 6$ $f(x)=x^3-2x^2+4x+6$ using synthetic division?

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How do you find f(-3) given $f (x) = x^{3} - 2 x^{2} + 4 x + 6$ $f(x)=x^3-2x^2+4x+6$ using synthetic division?

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Answer 1 · 2017-08-05T14:29:56

The remainder is $- 51$ $color(red)(-51)$ and the quotient is $= x^{2} - 5 x + 19$ $=x^2-5x+19$

Explanation:

Let's perform the synthetic division

$a a a a$ $color(white)(aaaa)$ $- 3$ $-3$ $a a a a a a$ $color(white)(aaaaaa)$ $∣$ $|$ $a a$ $color(white)(aa)$ $1$ $1$ $a a a a$ $color(white)(aaaa)$ $- 2$ $-2$ $a a a a a a$ $color(white)(aaaaaa)$ $4$ $4$ $a a a a a a a$ $color(white)(aaaaaaa)$ $6$ $6$
$a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaa)$ _________

$a a a a$ $color(white)(aaaa)$ $a a a a a a a$ $color(white)(aaaaaaa)$ $∣$ $|$ $a a a a$ $color(white)(aaaa)$ $a a a a a$ $color(white)(aaaaa)$ $- 3$ $-3$ $a a A a a$ $color(white)(aaAaa)$ $15$ $15$ $a a a a a$ $color(white)(aaaaa)$ $- 57$ $-57$
$a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaa)$ ________

$a a a a$ $color(white)(aaaa)$ $a a a a a a a$ $color(white)(aaaaaaa)$ $∣$ $|$ $a a a$ $color(white)(aaa)$ $1$ $1$ $a a a a a$ $color(white)(aaaaa)$ $- 5$ $-5$ $a a a a a a$ $color(white)(aaaaaa)$ $19$ $19$ $a a a a$ $color(white)(aaaa)$ $- 51$ $color(red)(-51)$

The remainder is $- 51$ $color(red)(-51)$ and the quotient is $= x^{2} - 5 x + 19$ $=x^2-5x+19$

Therefore,

$\frac{x^{3} - 2 x^{2} + 4 x + 6}{x + 3} = x^{2} - 5 x + 19 - \frac{51}{x + 3}$ $(x^3-2x^2+4x+6)/(x+3)=x^2-5x+19-51/(x+3)$

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How do you find f(-3) given $f (x) = x^{3} - 2 x^{2} + 4 x + 6$ $f(x)=x^3-2x^2+4x+6$ using synthetic division?

1 Answer

Explanation:

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How do you find f(-3) given f(x)=x^3-2x^2+4x+6f(x)=x3−2x2+4x+6f(x)=x^3-2x^2+4x+6 using synthetic division?

1 Answer

Explanation:

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How do you find f(-3) given $f (x) = x^{3} - 2 x^{2} + 4 x + 6$ $f(x)=x^3-2x^2+4x+6$ using synthetic division?