SAT Math: Advanced Polynomial Factoring Techniques
30+ practice questions in Praczo
The concept, explained
- 1
Difference of Squares: a² - b² = (a - b)(a + b). This is commonly tested and sometimes hidden (e.g., x⁴ - 16).
- 2
Perfect Square Trinomial: a² + 2ab + b² = (a + b)² and a² - 2ab + b² = (a - b)². Recognizing these saves time.
- 3
Factoring by Grouping: Used for 4-term polynomials. Group the first two and last two terms, factor out the GCF from each, then factor out the common binomial.
- 4
Sum and Difference of Cubes (rare but useful): a³ + b³ = (a + b)(a² - ab + b²).
- 5
Always start by factoring out the greatest common factor (GCF) if there is one.
- ✗ Trying to apply difference of squares to a sum of squares (a² + b²) — it doesn't factor over the real numbers.
- ✗ Overcomplicating perfect square trinomials instead of recognizing the pattern directly.
SAT-style practice
Which of the following is equivalent to 9x² - 24x + 16?
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