How to answer it
- Set the equation equal to zero.
- Factor if two numbers multiply to the constant and add to the middle coefficient.
- Set each factor to zero and check both answers.
Worked example
An original question in the SAT format, already answered.
SAT MathWorked example
x² − 5x + 6 = 0
What are the solutions of the equation?
- A−2 and −3
- B2 and 3
- C1 and 6
- D−1 and 6
Answer: B. −2 and −3 multiply to 6 and add to −5, so the equation factors as (x − 2)(x − 3) = 0. That gives x = 2 or x = 3.
The most common trap
Taking the signs from the factors. (x − 2) = 0 means x = 2, not −2.
Practice it
Hourly Prep’s daily sets mix nonlinear equations and systems with the rest of SAT Math, and send more of it your way when it’s a weak spot. See how the SAT prep plan works, or browse the other SAT skill guides.
For pacing and strategy across the whole section, read our guide to Desmos on the SAT. To fit this skill into a schedule, see the SAT study plan guide.