How do you evaluate $f (x) = - x^{4} + 8 x^{3} + 13 x - 4$ $f(x)=-x^4+8x^3+13x-4$ at x=-2 using direct substitution and synthetic division?

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How do you evaluate $f (x) = - x^{4} + 8 x^{3} + 13 x - 4$ $f(x)=-x^4+8x^3+13x-4$ at x=-2 using direct substitution and synthetic division?

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Answer 1 · 2017-02-24T09:43:46

The answer is $= - 110$ $=-110$

Explanation:

Direct substitution

$f (- 2) = - 16 - 64 - 26 - 4 = - 110$ $f(-2)=-16-64-26-4=-110$

The remainder is $= - 110$ $=-110$

We perform a synthetic division

$a a a a$ $color(white)(aaaa)$ $- 2$ $-2$ $a a a a$ $color(white)(aaaa)$ $∣$ $|$ $a a a a$ $color(white)(aaaa)$ $- 1$ $-1$ $a a a a$ $color(white)(aaaa)$ $8$ $8$ $a a a a a$ $color(white)(aaaaa)$ $0$ $0$ $a a a a a a$ $color(white)(aaaaaa)$ $13$ $13$ $a a a a$ $color(white)(aaaa)$ $- 4$ $-4$

$a a a a a a$ $color(white)(aaaaaa)$ $a a a a a$ $color(white)(aaaaa)$ $∣$ $|$ $a a a$ $color(white)(aaa)$ $a a a a a a a$ $color(white)(aaaaaaa)$ $2$ $2$ $a a a a a$ $color(white)(aaaaa)$ $- 20$ $-20$ $a a a a$ $color(white)(aaaa)$ $40$ $40$ $a a a a a$ $color(white)(aaaaa)$ $- 106$ $-106$

$a a a a a a a a a a$ $color(white)(aaaaaaaaaa)$ ------------------------------------------------------------

$a a a a$ $color(white)(aaaa)$ $a a a a a a$ $color(white)(aaaaaa)$ $a a a a a a$ $color(white)(aaaaaa)$ $- 1$ $-1$ $a a a$ $color(white)(aaa)$ $10$ $10$ $a a a a a$ $color(white)(aaaaa)$ $- 20$ $-20$ $a a a a a$ $color(white)(aaaaa)$ $53$ $53$ $a a a a a$ $color(white)(aaaaa)$ $- 110$ $color(red)(-110)$

The remainder is $= - 110$ $=-110$

The quotient is $= - x^{3} + 10 x^{2} - 20 x + 53$ $=-x^3+10x^2-20x+53$

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How do you evaluate $f (x) = - x^{4} + 8 x^{3} + 13 x - 4$ $f(x)=-x^4+8x^3+13x-4$ at x=-2 using direct substitution and synthetic division?

1 Answer

Explanation:

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Science

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Humanities

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How do you evaluate f(x)=−x4+8x3+13x−4f(x)=-x^4+8x^3+13x-4 at x=-2 using direct substitution and synthetic division?

1 Answer

Explanation:

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Impact of this question

How do you evaluate $f (x) = - x^{4} + 8 x^{3} + 13 x - 4$ $f(x)=-x^4+8x^3+13x-4$ at x=-2 using direct substitution and synthetic division?