Question

(20x^4+10x^3-49x^2+11) divided by (5x^2-1)

Answer 1

The first term in the result is 4x^2. What's next?

Answer 2

is it supposed to be 5x^2

Answer 3

I don't get it. ._.

Answer 4

oh well what im talking about is if its supposed to be divided by (5x^2 -1)

Answer 5

\(\dfrac{20x^{4}}{5x^{2}} = 4x^{2}\)

The first term in the result is \(4x^2\).

\(\dfrac{10x^{3}}{5x^{2}} = 2x\)

The second term in the result is \(2x\).

The third term is a little trickier.

Answer 6

You have to do a long division:

First write it like this: (on the dots the answer will gradually appear)

5x²-1 / 20x^4 +10x³ - 49x² + 11 \ ...

Then ask yourself what number times 5x² will be 20x^4. (we ignore the "-1" part of 5x²-1. It will be allright)

That number is 4x², because 5x² times 4x² = 20x^4. So write 4x² on the dots and multiply, including the "-1". Put the result below 20x^4+10x^3 and subtract:

5x²-1 / 20x^4 +10x³ - 49x² + 11 \ 4x²
20x^4 - 4x²
- ----------------------
10x³ - 45x² + 11

Now do the same trick again: 5x² times 2x is 10x³:

5x²-1 / 20x^4 +10x³ - 49x² + 11 \ 4x² + 2x
20x^4 - 4x²
- ----------------------
10x³ - 45x² + 11
10x² -2x
- ----------------
-45x² +2x +11

And again: 5x² times -9 is -45x²:

5x²-1 / 20x^4 +10x³ - 49x² + 11 \ 4x² + 2x - 9
20x^4 - 4x²
- ----------------------
10x³ - 45x² + 11
10x² -2x
- ----------------
-45x² +2x +11
-45x² +9
- --------------
2x +2

We're done!

The remainder is 2x+2, the quotient is 4x²+2x+9.