How do you divide 5x3−7x2−4x+13x−1?
1 Answer
Use long division.
Explanation:
53x2(3x−1)=(5x3−53x2)
This will leave a remainder of:
53x2
----------------------------
3x−1 ∣5x3−7x2−4x+1
−(5x3−53x2)
--------------
−163x2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So now we're left with
−169x(3x−1)=(−163x2+169x)
This will leave a remainder of:
53x2−169x
----------------------------
3x−1 ∣5x3−7x2−4x+1
−(5x3−53x2)
-----------------
−163x2−4x+1
−(−163x2+169x)
-------------------------
−529x
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So now we're left with
−5227(3x−1)=(−529x+5227)
This will leave a remainder of:
53x2−169x−5227
----------------------------
3x−1 ∣5x3−7x2−4x+1
−(5x3−53x2)
-----------------
−163x2−4x+1
−(−163x2+169x)
-------------------------
−529x+1
−(−529x+5227)
-------------------------
MMMMMMMMMMMMMM-−2527
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Since the degree of this remainder is smaller than the degree of our divisor, we will just divide it by the divisor as the last term in our answer:
53x2−169x−5227−25273x−1
53x2−169x−5227−2527(3x−1)
Final Answer