**Video Transcript**

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Transcript
**Adding Polynomials**

To hear long forgotten, but still glorious rock bands, Jack Rock is planning a music festival to be held near his hometown of Roc-n-roll. Jack needs to figure out how much **space** he’ll need for the festival. Like most musicians, he's a brilliant **mathematician**!

### Polynomials and monomials

To calculate the amount of space he'll need, he **adds** polynomials. Polynomials are made up of **terms**. Terms can be variables with exponents, variables with coefficients, or **constants**. Polynomials with one term are called **monomials**. This polynomial, 2x² + 6x+ 5 , is made up of three monomials. We can also call this expression a trinomial because it has three monomials.

Polynomials are classified by **degree**, and the degree of a polynomial is determined by the highest **exponent** found in the polynomial. This visual aid will really help you understand, so take a look. For this term, 2x², the exponent is equal to 2 so the degree is 2. How do you count the degrees if there are two exponents in a term, you ask? Here we have the monomial 3x⁴y².

### The degree of a term

To find the degree of a term with more than one **variable**, just add the exponents of the variables **together**: 4 + 2 = 6, so it has a degree of 6. What if there’s no exponent? There’s always an exponent, but you may not see it. Take 5x for example. 5x is the same as 5x¹, so it's a first degree polynomial.

### Order the term in Standard Form

The **constant**, 3, has a hidden variable and a hidden exponent! ...it’s the same as 3x⁰, making it a **zero** degree mononomial. So what, you may be thinking. Who cares? Why do we need to know the degrees? Well, if you have several terms in a polynomial, it can get pretty hairy, so when we write polynomials, we use the Standard Form to order the terms from the highest degree to the lowest. It’s good to use the Standard Form to write polynomials because it makes the expression easier to read and **calculate**. Let's order these terms in Standard Form 3x⁴y² + 2x² + 5x + 3.

Back to Jack Rock. He's working very hard to figure out how much space he needs for the festival... So far, he's **determined** that every person attending the festival will need space for camping. He uses x to represent the unknown number of people and y₁ to **represent** the total amount of space needed for camping.

The expression is y₁ is equal to 5+3x+½ x². Plus, he knows it’s important to have enough space in front of the **stage** for people to see the show. .. So, using his mad math **skills**, he figures out the expression to calcualate this amount of space is y₂ is equal to 3x²+4-3x. Told you. He's a **genius**!

### Calculate the total area

To calculate the total area, Jack adds the two polynomials together, but first he must put them in Standard Form. To start, he determines the degree of each term. He knows that **'x'** without an exponent has a degree of 1, and constant terms have a degree of zero. Next he knows he should order the terms from the **highest** degree to the lowest. Notice how Jack has set up the two expressions **vertically**. Add the polynomials together by **combining** all like terms. What are like terms? Numbers with the same variable and the same degree. Let's see how he combines like terms...

A video image is worth a thousand words, how he combines the like terms. You can see how the 'X's cancel out..now add the last **constants**. There’s more than one way to go about combining these polynomials. The **expression** can also be set up horizontally. Use **parentheses** to help you stay organized.

### Unlike terms

Again, Jack will combine like terms. Watch how the 'x' terms cancel out. As you can see, it’s the same sum as before. When you add polynomials, use the method that’s easiest for you. But, be careful and only combine like terms! Variables and exponent powers must be equal. Sometimes terms look similar, but they may have slightly different **variables** and exponents and cannot be combined. These are called **unlike terms**.

Whoo Hoo! Now Jack Rock can calculate the **exact** amount of space he needs for 'x' number of people. Look at the turnout! The concert sold out! It's time to party to the MAX!

2 commentsMe too!

te amo!