Unit 6 Review: Factoring Polynomial Expressions
Common factors, trinomials, difference of squares, factoring \(ax^2+bx+c\), and solving by factoring.
GCF
\((x+m)(x+n)=x^2+(m+n)x+mn\)
AC-method for \(ax^2+bx+c\)
Diff. of Squares \(a^2-b^2=(a-b)(a+b)\)
Zero-Product Property
What You Should Be Able To Do
- Factor out the greatest common factor (numeric and powers of \(x\)).
- Factor trinomials \(x^2+bx+c\) using integer factor pairs of \(c\) that sum to \(b\).
- Factor quadratics \(ax^2+bx+c\ (a\neq 0)\) using the AC-method or grouping.
- Recognize and factor differences of squares.
- Factor completely and verify by expansion.
- Solve quadratic equations by factoring and relate factors to x-intercepts.
Progress autosaves to this device.
Video Library
Greatest Common Factor (GCF)
Factor out numeric and variable common factors.
youtube.com – “factoring greatest common factor polynomials”Trinomials \(x^2+bx+c\)
Find factor pairs of \(c\) that sum to \(b\).
youtube.com – “factor x^2+bx+c trinomials”AC-Method for \(ax^2+bx+c\)
Split the middle term and factor by grouping.
youtube.com – “ac method factoring ax^2+bx+c”Difference of Squares
Recognize \(a^2-b^2\) and factor.
youtube.com – “difference of squares factoring”Interactive Tools
GCF Extractor
| Term | After GCF |
|---|
Trinomial Factorer: \(x^2 + bx + c\)
| Pair (m,n) | m+n | m·n |
|---|
Quadratic Factorer & Solver: \(ax^2 + bx + c\)
Difference of Squares Checker
Factor Fully – Practice
Enter your factorization with parentheses, e.g., 3x(x+4), (2x-3)(x+5).
Unit 6 Quizzes
Downloadable Review
Quick Practice Scratchpad
Try: \(12x^2-8x\), \(x^2+9x+14\), \(6x^2+11x-10\), \(49x^2-25\), solve \(2x^2-5x-12=0\).