How do you use synthetic division to divide $x^4+4x^3+6x^2+4x+1$ by $x+1$ ?

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How do you use synthetic division to divide $x^4+4x^3+6x^2+4x+1$ by $x+1$ ?

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Answer 1 · 2018-07-21T12:09:52

The remainder is $0$ and the quotient is $=x^3+3x^2+3x+1$

Explanation:

Let's perform the synthetic division

$color(white)(aaaa)$ $-1$ $|$ $color(white)(aaaa)$ $1$ $color(white)(aaaa)$ $4$ $color(white)(aaaaaa)$ $6$ $color(white)(aaaa)$ $4$ $color(white)(aaaaa)$ $1$

$color(white)(aaaaaaa)$ $|$ $color(white)(aaaa)$ $color(white)(aaa)$ $-1$ $color(white)(aaaa)$ $-3$ $color(white)(aaa)$ $-3$ $color(white)(aaa)$ $-1$

$color(white)(aaaaaaaaa)$ _________

$color(white)(aaaaaaa)$ $|$ $color(white)(aaaa)$ $1$ $color(white)(aaaa)$ $3$ $color(white)(aaaaaa)$ $3$ $color(white)(aaaa)$ $1$ $color(white)(aaaaa)$ $color(red)(0)$

The remainder is $0$ and the quotient is $=x^3+3x^2+3x+1$

$(x^4+4x^3+6x^2+4x+1)/(x+1)=x^3+3x^2+3x+1$

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How do you use synthetic division to divide $x^4+4x^3+6x^2+4x+1$ by $x+1$ ?

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Explanation:

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How do you use synthetic division to divide x^4+4x^3+6x^2+4x+1x^4+4x^3+6x^2+4x+1 by x+1x+1?

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How do you use synthetic division to divide $x^4+4x^3+6x^2+4x+1$ by $x+1$ ?