Factoring Polynomials and Exam Prep (Lecture Notes Review)

Flashcards cover core concepts from the lecture: factoring techniques (GCF, grouping, quadratic factoring, binomial factoring), FOIL, rational exponents, zeros, and exam prep policies, plus practical verification steps.

What is factoring polynomials?

Expressing a polynomial as a product of two or more polynomials.

What is the Greatest Common Factor (GCF)?

The highest-degree factor that divides evenly into every term of a polynomial.

How do you factor out the GCF from an expression?

Factor out the GCF from all terms, leaving the remaining polynomial inside parentheses.

What is factoring by grouping?

Group terms into two pairs, factor out the common factor from each pair, and factor the resulting common binomial.

What indicates success in factoring by grouping?

Both grouped expressions share a common binomial factor.

What does FOIL stand for?

First, Outer, Inner, Last — the steps used to multiply two binomials.

Why is factoring important in real life?

Used in nursing/health for medication concentration models; in business for profit vs. cost; in social sciences for trends; zeros define start/end points in models.

What are zeros (roots) of a polynomial?

Solutions to P(x) = 0; the x-intercepts of the graph; points where the graph crosses the x-axis.

What is a rational exponent?

An exponent that is a fraction, representing roots and powers (e.g., x^(m/n) = (x^m)^(1/n)).

What is the slope formula in calculus?

m = (y2 − y1) / (x2 − x1).

What is the exam practice platform Alex?

An online practice test system that you can repeat until you master the material.

What is LockDown Browser used for?

A secure browser used to take tests in class.

What is the policy on retakes described in the lecture?

There is no retake policy stated in the syllabus; attendance and consistent effort are encouraged; no retakes guaranteed.

How do you factor a quadratic by splitting the middle term?

Find two numbers that multiply to ac and sum to b; rewrite the middle term using those numbers; then factor by grouping. Example: x^2 − x − 12 = (x − 4)(x + 3).

What is the general strategy when factoring by grouping four-term polynomials?

Group into two pairs, factor out a common factor from each pair, then factor the remaining common binomial.

What is a quick check after factoring to confirm your result?

Distribute the factors to ensure you recover the original polynomial (verify with the distributive property).