What you’ll learn
Factor x² + bx + c.
Key idea
A monic binomial product has middle coefficient equal to its constants' sum and constant term equal to their product.
Both signed sum and product constraints must match; constant product alone is insufficient.
Worked example
Enter the exact value or ordered values in the format requested below.
Factor x²-12x+35 into two integer binomials. Enter their product rather than expanded polynomial.
- Signed constants must multiply to 35 and add to -12; -7×-5=35, -7+(-5)=-12.
- (x-7)(x-5) expands to x²-12x+35; pair 1,35 has the same constant product but middle coefficient 36, not -12.
Answer: (x-7)(x-5)
Quick Check
Evaluate a worked attempt at factor x² + bx + c, identify the first invalid step, and provide the correction.
Factor x²-3x-10: Step 1 seeks constants whose product is -10. Step 2 picks 1 and -10, writing (x+1)(x-10) without checking their sum. Locate the first invalid step and repair it.