Factoring quadraticsBoth numbers positive
Name: Date:
Factor each one.
1x² + 16x + 28
2x² + 27x + 140
3x² + 44x + 484
4x² + 13x + 36
5x² + 20x + 96
6x² + 41x + 408
7x² + 32x + 256
8x² + 37x + 330
Factoring x² + bx + c worksheets
Find two numbers that multiply to the last term and add to the middle one. These free printable worksheets drill that one search until it is automatic.
If they get stuck
Factoring x² + bx + c
The answer key prints on a separate page.
What's on this sheet
The method is a search, and a search is only teachable once you know what you are searching for. Two conditions decide the pair and both have to hold: they multiply to c and they add to b. A student who checks only the product finds 1 and 12 for x² + 7x + 12 and stops; one who checks only the sum never gets started. Every walk here states both before trying a single number.
Why this sheet works
The signs are three separate lessons, so they are three settings rather than one slider. With c positive the two numbers share a sign and b says which; with c negative they have opposite signs and b says which one is bigger. That is different reasoning, taught a week apart, and mixing it in from the first sheet is what makes factoring feel like guessing.
How this one works
One question from a sheet like this one, worked a step at a time — with a sentence saying what just happened and why.
Factoring x² + bx + c, step by step