Multiplying Polynomials

Today in class we went over our homework then we went on to 11-2. We were all curious on how to multiply polynomials so we got our 11-2 note sheets and began the new unit.

First we need to learn how to classify polynomials by the number of terms. Here are some examples on how you would classify them.

Monomial: polynomial with one term. Ex: 2, 3x^5

Binomial: Polynomial with two terms. Ex: x+2, X^2-7x

Trinomial: polynomial with three terms. Ex: 2x^4-3x^2+7

Example 1: expand and write in standard form...(5x^2-4x+3)(x-7) so you would multiply the first term in the first parenthesis by the first term in the second parenthesis and then multiply it by the second term in the second parenthesis. Then you would go on to do the same thing again except you would multiply the second term in the first parenthesis by the first and second terms in the second parenthesis. And lastly you would do the same thing again except you would multiply the third term in the first parenthesis by the first and second terms in the second parenthesis, so the answer would come out to 5x^3-35x^2-4x^2+28x+3x-21. But don't forget to combine like terms! After the terms are combined the final answer comes out to, 5x^3-39x^2+31x-21.

Activity: We had to take an 8.5 inch by 11 inch piece of paper and cut out squares of various side lengths from the corners. We had four cut out lengths and we had to find the volume of the resulting box.
For the first box we did 1*9*6.5 which equaled, 58.5in^3.
For the second box we did 2*7*4.5 which equaled, 63in^3.
For the third box we did 3*5*2.5 which equaled, 32.5in^3.
And for the last one we did 4*3*.5 which equaled, 6in^3.
We concluded that box 2 had the largest volume.

Then we made a volume function with the equation, V(x)=x(11-2x)(8.5-2x) and graphed it on our calculator. And that was the end of our activity.

Since we spent lots of the class period doing the activity we did not have time to get to the back side of the note sheet. But we did have enough time for one more example.

Example: Without expanding, we had to find the leading term of the product (5x^2+2)(4x^2+8)(11x-3). It was much easier than I thought. All we had to do was multiply the first term in each set of parenthesis by each other to find the leading coefficient. Then we had to add the exponents of the first terms in each set of the parenthesis. The leading term came out to be 220x^5.

That is all we had time for. Mr. Cope assigned us our homework and before we knew it class was over.

I hope this helped and if it didn't you can always go see Mr. Cope for some more help!