How do you use polynomial long division to divide $(- x^{5} + 7 x^{3} - x) \div (x^{3} - x^{2} + 1)$ $(-x^5+7x^3-x)div(x^3-x^2+1)$ and write the polynomial in the form $p (x) = d (x) q (x) + r (x)$ $p(x)=d(x)q(x)+r(x)$ ?

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How do you use polynomial long division to divide $(- x^{5} + 7 x^{3} - x) \div (x^{3} - x^{2} + 1)$ $(-x^5+7x^3-x)div(x^3-x^2+1)$ and write the polynomial in the form $p (x) = d (x) q (x) + r (x)$ $p(x)=d(x)q(x)+r(x)$ ?

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Answer 1 · 2018-07-09T16:25:50

Please see the explanation below

Explanation:

Perform the long division

$a a a a$ $color(white)(aaaa)$ $- x^{5} + 0 x^{4} + 7 x^{3} + 0 x^{2} - x$ $-x^5+0x^4+7x^3+0x^2-x$ $a a a a$ $color(white)(aaaa)$ $∣$ $|$ $x^{3} - x^{2} + 1$ $x^3-x^2+1$

$a a a a$ $color(white)(aaaa)$ $- x^{5} + x^{4} + 0 x^{3} - x^{2}$ $-x^5+x^4+0x^3-x^2$ $a a a a a a a a a$ $color(white)(aaaaaaaaa)$ $∣$ $|$ $- x^{2} - x$ $-x^2-x$

$a a a a a a$ $color(white)(aaaaaa)$ $0 - x^{4} + 7 x^{3} + x^{2} - x$ $0-x^4+7x^3+x^2-x$

$a a a a a a a a$ $color(white)(aaaaaaaa)$ $- x^{4} + x^{3} + 0 x^{2} - x$ $-x^4+x^3+0x^2-x$

$a a a a a a a a a$ $color(white)(aaaaaaaaa)$ $- 0 + 6 x^{3} + x^{2} + 0 x$ $-0+6x^3+x^2+0x$

Therefore,

$- x^{5} + 0 x^{4} + 7 x^{3} + 0 x^{2} - x = (x^{3} - x^{2} + 1) (- x^{2} - x) + 6 x^{3} + x^{2}$ $-x^5+0x^4+7x^3+0x^2-x=(x^3-x^2+1)(-x^2-x)+6x^3+x^2$

The remainder is $r (x) = + 6 x^{3} + x^{2}$ $r(x)=+6x^3+x^2$ and the quotient is $q (x) = - x^{2} - x$ $q(x)=-x^2-x$

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How do you use polynomial long division to divide $(- x^{5} + 7 x^{3} - x) \div (x^{3} - x^{2} + 1)$ $(-x^5+7x^3-x)div(x^3-x^2+1)$ and write the polynomial in the form $p (x) = d (x) q (x) + r (x)$ $p(x)=d(x)q(x)+r(x)$ ?

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Explanation:

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How do you use polynomial long division to divide (-x^5+7x^3-x)div(x^3-x^2+1)(−x5+7x3−x)÷(x3−x2+1)(-x^5+7x^3-x)div(x^3-x^2+1) and write the polynomial in the form p(x)=d(x)q(x)+r(x)p(x)=d(x)q(x)+r(x)p(x)=d(x)q(x)+r(x)?

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Explanation:

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How do you use polynomial long division to divide $(- x^{5} + 7 x^{3} - x) \div (x^{3} - x^{2} + 1)$ $(-x^5+7x^3-x)div(x^3-x^2+1)$ and write the polynomial in the form $p (x) = d (x) q (x) + r (x)$ $p(x)=d(x)q(x)+r(x)$ ?