Home > Preview
The flashcards below were created by user
randycapped
on FreezingBlue Flashcards.

Dividing a polynomial by a monomial.
Step 1: Divide each term in the numerator (dividend) by the single term in the denominator (divisor).
Step 2: Simplify to get your quotient.

Dividing a polynomial by a monomial.
Step 1: Divide each term in the numerator (dividend) by the single term in the denominator (divisor).
Step 2: Simplify to get your quotient.
Step 3: Check.

Using Long Division.
Divide 2x^{3} – 9x^{2} + 15 by 2x – 5
 First off,note that there is a gap in the degrees of the terms of the dividend: the polynomial
 2x^{3} – 9x^{2} + 15 has no x term. , so it is important that I leave space for a xterm column, just in case. I can create this space by turning the dividend into 2x^{3} – 9x^{2} + 0x + 15. This is a legitimate mathematical step: since I've only added zero, I haven't actually changed the value of anything.
 1st: What do I need to multiply 2x by to get 2x^{3}? That would be x^{2}.
2nd: Multiply x^{2 }by the divisor, 2x  5.
 3rd: Now, you will "add the opposite". Which is the same as subtracting.
 4th: Bring down the next column and start the process again. Now, you will determine what you need to multiply 2x by to get 4x^{2}. Which gives you 2x to place into the quotient.
 5th: Continue the process until you end up with a remainder. This time, we have a remainder of 10.
Step 6: When you have a remainder, you need to remember to add the remainder to the polynomial part of the answer. Simply add the remainder as shown below.

What procedure would you use to divide this polynomial? And why?
You would use long division because divisor (x+2) has more than one divisor.


Long Division. Zero Remainder. Easy Mode.

Long Division.

Long Division.
Solution: The dividend is obviously missing a lot of variable x. That means I need to insert zero coefficients in every missing powers of the variable.
I need to rewrite the problem this way to include all exponents of x: .
 Remember the main steps in long division:
 1. When going up, we divide
 2. When going down, we distribute
 3. Subtract
 4. Carry down
 5. Repeat the process until done.
 Verify if the steps are being applied correctly in the example below.
So the final answer is: .

Long Division. Animated guide.
Solution: We have a polynomial with five terms being divided by a trinomial. Both the dividend and divisor are in standard form, and all powers of the variable x are present. This is wonderful because we can now start solving it.

Long division. Missing "y" term in divisor.
Simply change your divisor to:
to make up for the missing "y" term. Then, proceed as normal.

