How do you use the remainder theorem and Synthetic Division to find the remainders in the following division problems $x^{5} + 2 x^{4} - 3 x + 3$ $x^5 + 2x^4 - 3x + 3$ divided by x - 1?

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How do you use the remainder theorem and Synthetic Division to find the remainders in the following division problems $x^{5} + 2 x^{4} - 3 x + 3$ $x^5 + 2x^4 - 3x + 3$ divided by x - 1?

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Answer 1 · 2017-02-19T19:31:15

The remainder is $= 3$ $=3$

Explanation:

The remainder theorem states that when a polynomial $f (x)$ $f(x)$ is divided by $x - c$ $x-c$

$f (x) = (x - c) q (x) + r (x)$ $f(x)=(x-c)q(x)+r(x)$

$f (c) = 0 + r$ $f(c)=0+r$

Here,

$f (x) = x^{5} + 2 x^{4} - 3 x + 3$ $f(x)=x^5+2x^4-3x+3$

and $(x - 1)$ $(x-1)$

$f (1) = 1 + 2 - 3 + 3 = 3$ $f(1)=1+2-3+3=3$

The remainder is $= 3$ $=3$

We now perform the synthetic division

$a a a a$ $color(white)(aaaa)$ $1$ $1$ $a a a a$ $color(white)(aaaa)$ $∣$ $|$ $a a a a$ $color(white)(aaaa)$ $1$ $1$ $a a a a$ $color(white)(aaaa)$ $2$ $2$ $a a a a$ $color(white)(aaaa)$ $0$ $0$ $a a a a$ $color(white)(aaaa)$ $0$ $0$ $a a a a$ $color(white)(aaaa)$ $- 3$ $-3$ $a a a a$ $color(white)(aaaa)$ $3$ $3$

$a a a a$ $color(white)(aaaa)$ #color(white)(aaaaa)|# $a a a a a$ $color(white)(aaaaa)$ #color(white)(aaaa)1# $a a a a$ $color(white)(aaaa)$ $3$ $3$ $a a a a$ $color(white)(aaaa)$ $3$ $3$ $a a a a$ $color(white)(aaaa)$ $3$ $3$ $a a a a a$ $color(white)(aaaaa)$ $0$ $0$

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

$a a a a$ $color(white)(aaaa)$ #color(white)(aaaaa)# $a a a a a a$ $color(white)(aaaaaa)$ $1$ $1$ $a a a a$ $color(white)(aaaa)$ $3$ $3$ $a a a a$ $color(white)(aaaa)$ $3$ $3$ $a a a a$ $color(white)(aaaa)$ $3$ $3$ $a a a a$ $color(white)(aaaa)$ $0$ $0$ $a a a a a$ $color(white)(aaaaa)$ $3$ $color(red)(3)$

The remainder is also $= 3$ $=3$

The quotient is $= x^{4} + 3 x^{3} + 3 x^{2} + 3 x$ $=x^4+3x^3+3x^2+3x$

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How do you use the remainder theorem and Synthetic Division to find the remainders in the following division problems $x^{5} + 2 x^{4} - 3 x + 3$ $x^5 + 2x^4 - 3x + 3$ divided by x - 1?

1 Answer

Explanation:

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How do you use the remainder theorem and Synthetic Division to find the remainders in the following division problems x5+2x4−3x+3x^5 + 2x^4 - 3x + 3 divided by x - 1?

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Explanation:

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How do you use the remainder theorem and Synthetic Division to find the remainders in the following division problems $x^{5} + 2 x^{4} - 3 x + 3$ $x^5 + 2x^4 - 3x + 3$ divided by x - 1?