Polynomials Operations Quiz

Study Notes

Polynomials

Addition and Subtraction

To add or subtract polynomials, combine like terms:
- Combine terms with the same variable(s) and coefficient(s)
- Add or subtract coefficients of like terms
- Simplify the resulting polynomial

Factoring

Factoring is the process of expressing a polynomial as a product of simpler expressions
Types of factoring:
- Greatest Common Factor (GCF): factor out the largest common factor of all terms
- Difference of Squares: factor a² - b² as (a + b)(a - b)
- Sum and Difference: factor a² + 2ab + b² as (a + b)²
- Factoring by Grouping: factor a polynomial by grouping terms with common factors

Synthetic Division

Synthetic division is a method for dividing a polynomial by a linear factor (x - a)
Steps:
1. Write the dividend (the polynomial being divided) and the divisor (x - a)
2. Bring down the leading coefficient of the dividend
3. Multiply the divisor by the leading coefficient and subtract from the dividend
4. Repeat steps 2-3 until the remainder is 0 or the degree of the remainder is less than the degree of the divisor

Rational Expressions

A rational expression is a fraction of two polynomials
To simplify a rational expression:
- Factor the numerator and denominator
- Cancel out any common factors
- Simplify the resulting expression

Multiplication

To multiply two polynomials, multiply each term of one polynomial by each term of the other:
- Multiply the coefficients and add the exponents of like variables
- Simplify the resulting polynomial by combining like terms

Description

Test your knowledge of polynomial operations, including addition, subtraction, factoring, synthetic division, rational expressions, and multiplication. Practice combining like terms, simplifying expressions, and dividing polynomials by linear factors.