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 Rocnroll. 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+43x. 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!

Introduction to Polynomials – Naming Polynomials by Number of Terms

Adding Polynomials

Multiplying Polynomials

Multiplying Special Case Polynomials

Factoring out the GCF

Factoring Trinomials with a = 1

Factoring Trinomials with a ≠ 1

Factoring Special Case Polynomials

Factoring by Grouping

Subtracting Polynomials
Me too!
te amo!