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.