Question

I need help long dividing this equation.

(x^2 - x +5) / (x + 1)

I already know the answer however I’m having a bit of trouble understanding how to get to it. At the second to last operation you come to,
- x^2 + 4x
- x^2 - x
= 5x

I’m having trouble understanding how you get 5x from that? Someone please help!

Answer 1

Explanation:

x - 2 <--- quotient

x + 1) x^2 - x + 5 First divide x^2 by x giving x then multiply x + 1 by x:

x^2 + x Now subtract x^2 + x from x^2 - x and bring down +5:

-2x + 5 Now divide -2x by x to get -2 and multiply X+1 by -2 -2x - 2 Subtract:

7

The result is x - 2 (see above) remainder 7

or you could write it as

x - 2 + 7/(x + 1)

Answer 2

First, we'll look at the first term of each expression.

---x times what is equal to x^3? = x times x^2 = x^3

So, we'll multiply everything in the divisor by x^2 and subtract that from the dividend.

x^2(x + 1) = x^3 + x^2

(x^3 + 4x + 5) - (x^3 + x^2)

x^3 - x^3 = 0

0 - x^2 = -x^2

4x - 0 = 4x

5 - 0 = 5

Our new expression is -x^2 + 4x + 5.

So we again ask ourselves, x times what is equal to -x^2? = -x

-x(x + 1) = -x^2 - x

And subtract!

(-x^2 + 4x + 5) - (-x^2 - x)

-x^2 - - x^2 = -x^2 + x^2 = 0

4x - - x = 4x + x = 5x

5 - 0 = 5

Our new expression is 5x + 5. Let's ask ourselves once again, x times what is equal to 5x? = 5.

Multiply, then subtract!

5(x + 1) = 5x + 1

(5x + 1) - (5x + 1) = 0

Now that we have nothing left to divide, let's go back and get our answer.

x^2 - x + 5

Notice that when I was dividing, I always looked at the first term of the dividend (as the expression changed) and divisor. Whatever comes after the first term doesn't matter at the time.

Hope this helps and if you have any further questions, please let me know! :)