Operations with polynomials

Teachers:Javier Garza

&Sebastian Bernal

Addition of polynomials

• For adding polynomials you need to follow the following steps:1. Collect Like terms at one place2. Add the numerical coefficients of like term3. Write the sum in both standard and simplest form

• For exmple:( 2a + 3b) + (-4b + 5a) = 7a - b

Subtraction of polynomials

• For subtracting polynomials you need to follow the following steps:1. Subtract similar terms. To do this, change the algebraic

sign of what is to be subtracted and add it to the other. 2. To subtract unlike terms, just write the operation sign –

before what is to be subtracted 

For example:( -yz) – (–4yz ) = 3yz

Multiplication of polynomials

• For multiplying polynomials you need to follow the following steps:1. First multiply numerical coefficients and literal

coefficients separately. Next, multiply these two products.2. To multiply two polynomials when each one has more than

one term: Multiply each term of one polynomial with each term of the other polynomial and write like terms together.

• For example:(4x3 + 2)(2x2 + 3x) = 8x5 + 12x4 + 4x2 + 6x 

Division of polynomials

• For dividing polynomials you need to follow the following steps:1. To divide a monomial by another monomial, divide the

numerical coefficients and the literal coefficients separately. 

2. To divide a polynomial by a monomial, divide each term in the polynomial by the monomial.

• For example:40a5b4 + 55a3b5 + 35a3b4 + 70ab ÷ a2b2 = 40a3b2 + 55ab3 + 35ab2+ 70a-1b-1