Using synthetic division, what is the quotient and the remainder for polynomial $P (x) = x^{3} - 2 x^{2} - 5 x + 6$ $P(x) = x^3 - 2x^2 - 5x +6$ divided by $(x - 1)$ $(x-1)$ ?

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Using synthetic division, what is the quotient and the remainder for polynomial $P (x) = x^{3} - 2 x^{2} - 5 x + 6$ $P(x) = x^3 - 2x^2 - 5x +6$ divided by $(x - 1)$ $(x-1)$ ?

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Answer 1 · 2017-11-20T11:09:34

$(x^{2} - x - 6)$ $(x^2-x-6)$

Explanation:

we need $x^{3}$ $x^3$ so we add $x^{2}$ $x^2$

$\Rightarrow$ $=>$
$(x - 1) (x^{2}$ $(x-1)(x^2$
$\Rightarrow x^{3} - x^{2}$ $=>x^3-x^2$
we need $- 2 x^{2}$ $-2x^2$ so we add $- x$ $-x$

$\Rightarrow$ $=>$
$(x - 1) (x^{2} - x$ $(x-1)(x^2-x$
$\Rightarrow x^{3} - x^{2} - x^{2} + x$ $=>x^3-x^2-x^2+x$
we need $- 5 x$ $-5x$ so we add $- 6$ $-6$

$\Rightarrow$ $=>$
$(x - 1) (x^{2} - x - 6$ $(x-1)(x^2-x-6$
$x^{3} - x^{2} - x^{2} + x - 6 x + 6$ $x^3-x^2-x^2+x-6x+6$

we have what we need so we can close it

$\Rightarrow$ $=>$
$(x - 1) (x^{2} - x - 6)$ $(x-1)(x^2-x-6)$
$x^{3} - 2 x^{2} + 5 x + 6$ $x^3-2x^2+5x+6$

$\Rightarrow$ $=>$
$\frac{x^{3} - 2 x^{2} + 5 x + 6}{x - 1} = (x^{2} - x - 6)$ $(x^3-2x^2+5x+6)/(x-1)=(x^2-x-6)$

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Using synthetic division, what is the quotient and the remainder for polynomial $P (x) = x^{3} - 2 x^{2} - 5 x + 6$ $P(x) = x^3 - 2x^2 - 5x +6$ divided by $(x - 1)$ $(x-1)$ ?

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Explanation:

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Science

Math

Humanities

... and beyond

Using synthetic division, what is the quotient and the remainder for polynomial P(x)=x3−2x2−5x+6P(x) = x^3 - 2x^2 - 5x +6 divided by (x−1)(x-1)?

1 Answer

Explanation:

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Impact of this question

Using synthetic division, what is the quotient and the remainder for polynomial $P (x) = x^{3} - 2 x^{2} - 5 x + 6$ $P(x) = x^3 - 2x^2 - 5x +6$ divided by $(x - 1)$ $(x-1)$ ?