Polynomials Operations Quiz

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