How do you evaluate $f (x) = x^{3} + 3 x^{2} - 2 x + 5$ $f(x)=x^3+3x^2-2x+5$ at x=-3 using direct substitution and synthetic division?

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How do you evaluate $f (x) = x^{3} + 3 x^{2} - 2 x + 5$ $f(x)=x^3+3x^2-2x+5$ at x=-3 using direct substitution and synthetic division?

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Answer 1 · 2018-01-31T12:26:32

Quotient $Q = x^{2} - 2$ $color(blue)(Q = x^2 - 2)$ , Remainder $R = \frac{11}{x + 3}$ $color(blue)(R = 11 / (x + 3))$

Explanation:

Given equation is

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

Substitution

$f (x) = f (3) = - 3^{3} + (3 \cdot - 3^{2}) - (2 \cdot - 3) + 5 = 53$ $f(x) = f(3) = -3^3 + (3 * -3^2) - (2*-3) + 5 = 53$

Synthetic Division

$a a - 3 a a ∣ a a 1 a a a a 3 a a - 2 a a 5$ $color(white)(aa)-3color(white)(aa)|color(white)(aa)1color(white)(aaaa)3color(white)(aa)-2color(white)(aa)5$
$a a a a a a a ∣ a a ⏐ ↓ a - 3 a a a a 0 a a 6$ $color(white)(aaaaaaa)|color(white)(aa)darrcolor(white)(a)-3color(white)(aaaa)0color(white)(aa)6$
$a a a a a a a - - - - - - - - - -$ $color(white)(aaaaaaa)----------$
$a a a a a a a a a a a a 1 a a a 0 a a - 2 a a 11$ $color(white)(aaaaaaaaaaaa)1color(white)(aaa)0color(white)(aa)-2color(white)(aa)11$

Quotient $Q = x^{2} - 2$ $Q = x^2 - 2$ , Remainder $R = \frac{11}{x + 3}$ $R = 11 / (x + 3)$

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How do you evaluate $f (x) = x^{3} + 3 x^{2} - 2 x + 5$ $f(x)=x^3+3x^2-2x+5$ at x=-3 using direct substitution and synthetic division?

1 Answer

Explanation:

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Science

Math

Humanities

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How do you evaluate f(x)=x3+3x2−2x+5f(x)=x^3+3x^2-2x+5 at x=-3 using direct substitution and synthetic division?

1 Answer

Explanation:

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How do you evaluate $f (x) = x^{3} + 3 x^{2} - 2 x + 5$ $f(x)=x^3+3x^2-2x+5$ at x=-3 using direct substitution and synthetic division?