Lecture Notes on Polynomials and Multiplication

Assignment Reminder

• Late assignment from last Friday due Sunday at 11:00 results in a grade of zero.
• Opportunity exists on Thursday to raise grades, especially if currently a C or higher before an upcoming quiz.

Quiz Details

• Quiz will cover material discussed last Thursday and the current lesson. Important to take thorough notes.
• This quiz counts significantly towards the overall grade.

Multiplication of Polynomials

• Focus on multiplying a monomial by a polynomial.
• Example: Multiplication of a monomial (3x) by a trinomial (x² + 2x + 8).
• Use the Distributive Property:
  • 3x * x² = 3x³ (since 3 * 1 = 3 and x * x² = x³)
  • 3x * 2x = 6x²
  • 3x * 8 = 24x
• Final expression in standard form: 3x³ + 6x² + 24x.
• Leading Coefficient is 3.

Multiplication of Binomials

• When multiplying two binomials, use the FOIL Method:
• First: Multiply the first terms of each binomial.
• Outside: Multiply the outside terms.
• Inside: Multiply the inside terms.
• Last: Multiply the last terms of each binomial.
• Specific Example:
• (x - 4)(x + 9)
• First: x * x = x²
• Outside: x * 9 = 9x
• Inside: (-4) * x = -4x
• Last: (-4) * 9 = -36
• Combine like terms: 9x - 4x = 5x
• Result: x² + 5x - 36.

Handling Different Terms

• Attention to the order when multiplying terms that include coefficients and the variables may be switched around.
• Another Example with different coefficients:
• (5y + 8)(-9 + 2y)
• F: 5y * -9 = -45y
• O: 5y * 2y = 10y²
• I: 8 * -9 = -72
• L: 8 * 2y = 16y
• Combine: -45y + 16y = -29y
• Standard form: 10y² - 29y - 72.

Standard Form and Importance

• Always express final answers in standard form, ordered by the descending powers of the variables.
• Lack of standard form can result in loss of credit on assignments.

Distribution Principle

• FOIL essentially distributes each term in the first set of parentheses to each term in the second set.
• Not applicable for adding binomials; combining like terms is used instead.

Practice Assignment

• Complete problems 3 through 18 on page 349 using the FOIL method, focusing primarily on multiplication topics mentioned.
• Review will occur at the beginning of the next class (at 10:08 AM).