Precalc first lesson

Understanding Prime Polynomials

• There exists a common choice labeled as "this is prime" in multiple-choice questions.

  • Some students tend to select this option without consideration.

• Example Polynomials:

  • For x² + 64, students would usually choose the prime bubble.

  • For x² - 37, they would also select prime.

  • Important: A negative sign doesn't guarantee that the polynomial can be factored.

  • Tools like PhotoMath may factor these with square roots, but this is beyond the present scope.

Using Formulas

• For polynomials, recognize that once the formula is identified (specifically for quadratics), you only need to find values for a and b, plug them in, and the solution appears directly.

• Practice and familiarity with formulas streamline the process further.

Understanding Notation

• Brackets vs. Parentheses

  • Distinguish between brackets and parentheses as they convey different meanings in mathematical notation.

  • Brackets are not interchangeable with parentheses and should be used appropriately.

• Set Notation

  • Common confusion arises with squiggly brackets {} versus parentheses ().

  • Squiggly brackets indicate a set of answers and are not necessary in most cases.

  • Ensure clarity by differentiating these two symbols.

Interval Notation

• When working with intervals, always express them from low to high.

  • Example: From -2 to 5 should be denoted as (-2, 5).

  • Underlined values suggest a bracket, while non-underlined values should be denoted with parentheses.

• A mixture of brackets and parentheses is allowed:

  • Example: If an interval is from 1 to 4, including 1 but not 4, it would be noted as [1, 4).

Inequality Notation

• Inequality symbols should be clearly understood and remembered:

  • < (less than), > (greater than).

  • Notation such as x > 0 means find values greater than 0 without overthinking complex symbols.

• Set notation concerning inequalities can appear confusing.

  • Focus on the core question rather than the formal structure of the notation.

Important Equation Skills

• When asked for an equation, it's acceptable to use an equal sign in responses.

  • Example: Providing x = 2 as an equation is correct when asked.

• Avoid using equal signs for answers unless specifically prompted.