How do you evaluate $f (x) = - 3 x^{3} + 7 x^{2} - 4 x + 8$ $f(x)=-3x^3+7x^2-4x+8$ at x=3 using direct substitution and synthetic division?

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How do you evaluate $f (x) = - 3 x^{3} + 7 x^{2} - 4 x + 8$ $f(x)=-3x^3+7x^2-4x+8$ at x=3 using direct substitution and synthetic division?

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Answer 1 · 2017-08-10T12:58:28

The remainder is $- 22$ $color(red)(-22)$ and the quotient is $= - 3 x^{2} - 2 x - 10$ $=-3x^2-2x-10$

Explanation:

Let's perform the synthetic division

$a a a a$ $color(white)(aaaa)$ $3$ $3$ $a a a a a a$ $color(white)(aaaaaa)$ $∣$ $|$ $a a$ $color(white)(aa)$ $- 3$ $-3$ $a a a a a a a$ $color(white)(aaaaaaa)$ $7$ $7$ $a a a a a a$ $color(white)(aaaaaa)$ $- 4$ $-4$ $a a a a a a a$ $color(white)(aaaaaaa)$ $8$ $8$
$a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaa)$ $- - - - - - - - - - - -$ $------------$

$a a a a$ $color(white)(aaaa)$ $a a a a a a a$ $color(white)(aaaaaaa)$ $∣$ $|$ $a a a a$ $color(white)(aaaa)$ $a a a a a a$ $color(white)(aaaaaa)$ $- 9$ $-9$ $a a a a a a$ $color(white)(aaaaaa)$ $- 6$ $-6$ $a a a a a$ $color(white)(aaaaa)$ $- 30$ $-30$
$a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaa)$ $- - - - - - - - - - - -$ $------------$

$a a a a$ $color(white)(aaaa)$ $a a a a a a a$ $color(white)(aaaaaaa)$ $∣$ $|$ $a a a$ $color(white)(aaa)$ $- 3$ $-3$ $a a a a a$ $color(white)(aaaaa)$ $- 2$ $-2$ $a a a a a$ $color(white)(aaaaa)$ $- 10$ $-10$ $a a a a a$ $color(white)(aaaaa)$ $- 22$ $color(red)(-22)$

The remainder is $- 22$ $color(red)(-22)$ and the quotient is $= - 3 x^{2} - 2 x - 10$ $=-3x^2-2x-10$

Therefore,

$(- 3 x^{3} + 7 x^{2} - 4 x + 8) = (- 3 x^{2} - 2 x - 10) - \frac{22}{x - 3}$ $(-3x^3+7x^2-4x+8)=(-3x^2-2x-10)-22/(x-3)$

Also,

$f (3) = - 3 \cdot {(3)}^{3} + 7 \cdot {(3)}^{2} - 4 \cdot (3) \cdot 8 = - 81 + 63 - 12 + 8 = - 93 + 71 = - 22$ $f(3)=-3*(3)^3+7*(3)^2-4*(3)*8=-81+63-12+8=-93+71=-22$

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How do you evaluate $f (x) = - 3 x^{3} + 7 x^{2} - 4 x + 8$ $f(x)=-3x^3+7x^2-4x+8$ at x=3 using direct substitution and synthetic division?

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

How do you evaluate f(x)=−3x3+7x2−4x+8f(x)=-3x^3+7x^2-4x+8 at x=3 using direct substitution and synthetic division?

1 Answer

Explanation:

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How do you evaluate $f (x) = - 3 x^{3} + 7 x^{2} - 4 x + 8$ $f(x)=-3x^3+7x^2-4x+8$ at x=3 using direct substitution and synthetic division?