Polynomial Arithmetic

Polynomial Arithmetic

Adding Polynomials

• Group Like Terms Together

• Add coefficients, do not change variables/exponents

Adding Polynomials

• You can also stack like terms together in columns

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Multiple Choice

What are the like terms in the following expression:

 $Add:\ \ \left(2x\ +\ 9\right)\ +\ \left(8x^2+x+1\right)$  

•  $10x^2+x+10$  

•  $8x^2+2x+10$  

•  $11x^{4\ }+\ 10$  

•  $8x^2+3x+10$  

Subtract Like Terms

• Subtract EVERY term in the parenthesis following the minus sign

• Group Like Terms together

• Combine the like terms by adding/subtracting the coefficients and keeping the variables/exponents the same

Multiple Choice

Subtract:

 $\left(10a+6\right)-\left(4a+2\right)$  

•  $40a-12$  

•  $6a+8$  

•  $6a+4$  

•  $14a+8$  

Multiple Choice

Subtract:

 $\left(5y^2+2y-5\right)-\left(3y^2-2\right)$  

•  $\left(2y^2+2y-3\right)$  

•  $\left(2y^2+2y-7\right)$  

•  $\left(8y^2+2y-7\right)$  

•  $\left(5y^2-y-3\right)$  

Multiply Monomial x Monomial

• Group the numbers together and group like variables together

• Multiply numbers together

• To multiply like variables, you add the exponents

Multiple Choice

Multiply:

 $\left(-2a^2b\right)\left(5a^4\right)$  

•  $-10a^6$  

•  $10a^8b$  

•  $10a^6b$  

•  $-10a^6b$  

Multiply Monomial x Binomial

Distributive Property

• Multiply the term in front of the parenthesis by every term inside the parenthesis

Multiple Choice

Multiply:

 $3xy\left(2x^2-3\right)$  

•  $6x^2y-9xy$  

•  $6x^3-3xy$  

•  $3x^3-9$  

•  $6x^3y-9xy$  

Multiply Binomial by Binomial

• Distribute each term in the first set of parenthesis to each term in the second set of parenthesis.

Multiply Binomial by Binomial

• You can also use the box method.

• The is great to use when multiplying a binomial x trinomial or something even larger.

Multiple Choice

Multiply:

 $\left(4x\ -\ 10\right)\left(2x+4\right)$  

•  $8x^2+4x-40$  

•  $8x^2-4x-40$  

•  $6x^2-4x-6$  

•  $8x^2-40$