How do you divide $\frac{x^{4} + x^{3} + 1 x - 1}{x^{2} + 1}$ $(x^4 + x^3 +1x -1 )/ (x^2 + 1)$ ?

Question

How do you divide $\frac{x^{4} + x^{3} + 1 x - 1}{x^{2} + 1}$ $(x^4 + x^3 +1x -1 )/ (x^2 + 1)$ ?

1 Answer

Impact of this question

1598 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-08-29T12:28:09

$x^{2} + x - 1$ $x^2+x-1$

Explanation:

$one way is to use the divisor as a factor in the numerator$ $"one way is to use the divisor as a factor in the numerator"$

$consider the numerator$ $"consider the numerator"$

$x^{2} (x^{2} + 1) - x^{2} + x^{3} + x - 1$ $color(red)(x^2)(x^2+1)color(magenta)(-x^2)+x^3+x-1$

$=color(red)(x^2)(x^2+1)color(red)(+x)(x^2+1)cancel(color(magenta)(-x))-x^2cancel(+x)-1$

$=color(red)(x^2)(x^2+1)color(red)(+x)(x^2+1)color(red)(-1)(x^2+1)cancel(color(magenta)(+1))cancel(-1)$

$"quotient "=color(red)(x^2+x-1)," remainder "=0$

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

Science

Math

Humanities

... and beyond

How do you divide $\frac{x^{4} + x^{3} + 1 x - 1}{x^{2} + 1}$ $(x^4 + x^3 +1x -1 )/ (x^2 + 1)$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you divide (x^4 + x^3 +1x -1 )/ (x^2 + 1)x4+x3+1x−1x2+1(x^4 + x^3 +1x -1 )/ (x^2 + 1)?

1 Answer

Explanation:

Related questions

Impact of this question

How do you divide $\frac{x^{4} + x^{3} + 1 x - 1}{x^{2} + 1}$ $(x^4 + x^3 +1x -1 )/ (x^2 + 1)$ ?