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# Operations with polynomials — Basic example

Watch Sal work through a basic Operations with polynomials problem.

## Want to join the conversation?

• How is Sal so smart?! I literally don't understand a word he's saying, and I've watched like 50 videos!
• So just double checking, at , the -2 comes because the minus sign in front of the equation at the part before?
• Just wondering - How many colors does he have?
• why did he start subtracting?
• Because when he simplified the parenthesis(by multiplying everything inside) all the terms in the parenthesis became negative. That is why he is subtracting.
(1 vote)
• how does 1 + 1/2 =3/2
• You can think of this as adding two fractions with unlike denominators, 1/1 and 1/2. In order to do this, we have to change the denominator of one of the function to match the other, so that we can add the numerators to each other and keep the denominator the same. We can change the denominator of a fraction by multiplying the numerator and denominator by the same number, and then add across:
1 + 1/2
= 1/1 + 1/2
= (1*2)/(1*2) + 1/2
= 2/2 + 1/2
= (2+1)/2
= 3/2
(For a more detailed explanation of this, Khan has a nice video on this exact topic)
• Wait why isn't it -1/44 since 1/88y^100 and -1/44y^100 are common factors? Where did multiplying the 2 with 1/44 come into play?
• Yes, 1/88 y^100 and -1/44 y^100 are like terms. You multiply the numerator and denominator of -1/44 by 2 to be able to add it to the 1/88. 1/44 is twice 1/88, so when you subtract it from 1/88, you get the negative of 1/88. Does this make it more clear?
• so, considering the fact that someone I know has their psat coming up, can anyone explain to me the different ways of solving polynomials. (Addition, subtraction, etc)
• When you add polynomials, all you do is add the like terms. You can't add an x term with an x^3 term, for example.
Ex: (5k^3 + 3k^2) + (6k^3 + 5mk^2 + 12m)
The only like terms here are 5k^3 and 6k^3, so they are the only terms you'll combine:
= (6 + 5)k^3 + 3k^2 + 5mk^2 + 12m
= 11k^3 + 3k^2 + 5mk^2 + 12m
Subtracting polynomials is the same process as adding, but with one additional step. Since subtracting is the same as adding the negative, make every term in the polynomial you're subtracting the opposite. Then add as normal.

To multiply polynomials, you multiply every possible pair of polynomials, and add those products up. When you multiply, you multiply the coefficients and add exponents if they have the same base.
Ex: (k^2 + 5) * (5m^4 - k^2 + 9)
= (k^2 * 5m^4) + (k^2 * -k^2) + (k^2 * 9) + (5 * 5m^4) +(5*-k^2)+(5*9)
= 5m^4k^2 - k^4 + 9k^2 + 25m^4 - 5k^2 + 45
= 25m^4 + 5m^4k^2 - k^4 +4k^2 + 45

Polynomial division won't be directly tested on the SAT. If you're curious, you can check out this Khan Academy playlist: https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-div
• How did you get 1 + 1/2 to equal 3/2. I thought it equal 2/2.
(1 vote)
• You can't add the numerators of fractions unless their denominators are the same. Then, to add fractions, the numerator of the sum is the sum of the 2 numerators and the denominator of the sum is the same.
Here, we can think of whole numbers as having a denominator of 1. So 1 would be 1/1. Because of this, you cannot add it to a fraction with denominator 2. Instead, we have to convert it by multiplying both the numerator and denominator by the same constant (in this case 2).
1 + 1/2 = 1/1 + 1/2
= ((1 * 2) / (1 * 2)) + 1/2
= 2/2 + 1/2
= 3/2
Does this clear it up for you?