**Polynomial long division**

**What is a Polynomial?**

Polynomials are algebraic expressions that add constants and variables. Coefficients multiply the variables, which are raised to various powers by non-negative integer exponents.

the steps of Polynomial Long Division

Example: • Divide x2 – 9x – 10 by x + 1

How do we use polynomials in real life?

Since polynomials are used to describe curves of various types, people use them in the real world to graph curves. For example, roller coaster designers may use polynomials to describe the curves in their rides. Combinations of polynomial functions are sometimes used in economics to do cost analyses, for example.

Examples of using polynomial division in real life

Polynomial division is widely used by pharmacists in field of pharmacy and drug manufacturers in order to determine whether proper amount of drug is being given to patients and proper amount of elements is added into medicine during its composition. A chemist may use a polynomial division to derive a chemical formula for a chemical compound.

What is Polynomial Long Division?

• Polynomial Long Division is the same as long division for numbers, but it can be used to an improper and proper rational expression as the sum of a polynomial.

Step 1: I set up the division:

For the moment, I'll ignore the other terms and look just at the leading x of the divisor and the leading x2 of the dividend.

Step 2: If I divide the leading x2 inside by the leading x in front, what would I get? I'd get an x. So I'll put an x on top.

Step 3: Now I'll take that x, and multiply it through the divisor, x + 1. First, I multiply the x (on top) by the x (on the "side"), and carry the x2 underneath.

Step 4: Then I'll multiply the x (on top) by the 1 (on the "side"), and carry the 1x underneath

Step 5: Then I'll draw the "equals" bar, so I can do the subtraction.

To subtract the polynomials, I change all the signs in the second line...

Step 6: Then I add down. The first term (the x2) will cancel out:

Step 7: Now I look at the x from the divisor and the new leading term, the –10x, in the bottom line of the division. If I divide the –10x by the x, I would end up with a –10, so I'll put that on top.

Step 8: Now I'll multiply the –10 (on top) by the leading x (on the "side"), and carry the –10x to the bottom.

Step 9: ...and I'll multiply the –10 (on top) by the 1 (on the "side"), and carry the –10 to the bottom.

So the solution to the problem is x - 10

Polynomials can also be used to model different situations, like in the stock market to see how prices will vary over time. Business people also use polynomials to model markets, as in to see how raising the price of a good will affect its sales. Additionally, polynomials are used in physics to describe the trajectory of projectiles. Polynomial integrals (the sums of many polynomials) can be used to express energy, inertia and voltage difference, to name a few applications.

Polynomial division can also be used in mathematics and engineering or any scientific work. Let’s take an example in which area of Rectangle is given as p2 + 4a + 4 (inch) 2 and width of rectangle is (p + 2) then to calculate length of rectangle.

**Omar Lamie**

Ali Maged

Nour eldin Adel

Youssef Labib

Ali Maged

Nour eldin Adel

Youssef Labib