How do you use the remainder theorem to determine the remainder when the polynomial $2 x^{4} - 2 x^{3} + 5 x$ $2x^4-2x^3+5x$ is divided by $x + 2$ $x+2$ ?

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How do you use the remainder theorem to determine the remainder when the polynomial $2 x^{4} - 2 x^{3} + 5 x$ $2x^4-2x^3+5x$ is divided by $x + 2$ $x+2$ ?

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Answer 1 · 2017-02-28T13:17:19

The remainder is $= 38$ $=38$

Explanation:

We perform a synthetic division

$a a a a$ $color(white)(aaaa)$ $- 2$ $-2$ $a a a a$ $color(white)(aaaa)$ $∣$ $|$ $a a a a$ $color(white)(aaaa)$ $2$ $2$ $a a a a$ $color(white)(aaaa)$ $- 2$ $-2$ $a a a a a$ $color(white)(aaaaa)$ $0$ $0$ $a a a a a a$ $color(white)(aaaaaa)$ $5$ $5$ $a a a a a a$ $color(white)(aaaaaa)$ $0$ $0$

$a a a a a a$ $color(white)(aaaaaa)$ $a a a a a$ $color(white)(aaaaa)$ $∣$ $|$ $a a a$ $color(white)(aaa)$ $a a a a a a$ $color(white)(aaaaaa)$ $- 4$ $-4$ $a a a a$ $color(white)(aaaa)$ $12$ $12$ $a a a$ $color(white)(aaa)$ $- 24$ $-24$ $a a a a a a$ $color(white)(aaaaaa)$ $38$ $38$

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

$a a a a$ $color(white)(aaaa)$ $a a a a a a$ $color(white)(aaaaaa)$ $a a a a a a$ $color(white)(aaaaaa)$ $2$ $2$ $a a a a a$ $color(white)(aaaaa)$ $- 6$ $-6$ $a a a a$ $color(white)(aaaa)$ $12$ $12$ $a a a$ $color(white)(aaa)$ $- 19$ $-19$ $a a a a a a$ $color(white)(aaaaaa)$ $38$ $color(red)(38)$

The remainder is $= 38$ $=38$

The quotient is $= 2 x^{3} - 6 x^{2} + 12 x - 19$ $=2x^3-6x^2+12x-19$

Verification

Using the remainder theorem

$f (- 2) = 32 + 16 - 10 = 38$ $f(-2)=32+16-10=38$

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How do you use the remainder theorem to determine the remainder when the polynomial $2 x^{4} - 2 x^{3} + 5 x$ $2x^4-2x^3+5x$ is divided by $x + 2$ $x+2$ ?

1 Answer

Explanation:

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How do you use the remainder theorem to determine the remainder when the polynomial 2x^4-2x^3+5x2x4−2x3+5x2x^4-2x^3+5x is divided by x+2x+2x+2?

1 Answer

Explanation:

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How do you use the remainder theorem to determine the remainder when the polynomial $2 x^{4} - 2 x^{3} + 5 x$ $2x^4-2x^3+5x$ is divided by $x + 2$ $x+2$ ?