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I think it's 4x + 542x + 10/ x^2 - x -5
4x3 + x2 + 17x – 15 is the numerator and -x2 – x – 5 is the denominator
Write it like a long division problem.. The 4x^3 part on the inside.
You ask yourself -x^2 times what gives you 4x^3 that answer is -4X so that is what you put above the 4x^3 in the answer. This is step 1.
Once you put -4x up on top.. you multiply it by every term in (-x^2 - x - 5) so under the 4x^3 you write 4x^3 + 4x^2 + 20x
You get that by -4x(-x^2 - x - 5)
change all the signs on the bottom because you want to subtract so
on the bottom you get
-4x^3 - 4x^2 - 20x draw your line under this and add them up
the 4x^3 and the -4x^3 add to 0 so you don't write that down.
the x^2 - 4x^2 should give you -3x^2
the 17x - 20x should give you -3x
then bring down the next term (-15)
you should see -3x^2 - 3x - 15 on the bottom
Then you ask yourself -x^2 times what give you -3x^2 (just like the first step)
The answer is 3 so you write + 3 up in your answer next to your -4x
Once you write +3 then you "distribute" with the (-x^2 - x - 5)
and you write down "on the bottom"
-3x^2 - 3x - 15
because we are subtracting.. change all of the signs
3x^2 + 3x + 15 and draw a line
add them up.. you should get all zeros. So your answer is
-4x + 3 that means (-4x + 3) times (-x^2 - x - 5) = your original
4x^3 + x^2 + 17x + 15