Factoring quadraticsBoth numbers negative
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Factor each one. Both numbers are negative.
1x² − 32x + 231
2x² − 46x + 529
3x² − 29x + 210
4x² − 20x + 64
5x² − 9x + 14
6x² − 4x + 4
7x² − 27x + 50
8x² − 30x + 176
Factoring x² − bx + c worksheets
x² − 9x + 20 factors into (x − 4)(x − 5) — two negative numbers that multiply to 20 and add to −9. These free printable worksheets drill the both-negative case on its own.
If they get stuck
Factoring x² − bx + c
The answer key prints on a separate page.
What's on this sheet
Factoring x² + bx + c is a search for two numbers that multiply to c and add to b, and this sheet fixes both signs so the search has a shape. When c is positive and b is negative, the two numbers are both negative: they multiply to a positive and add to a negative. Knowing that before you start turns a hunt into a short check of a few pairs.
Why this sheet works
The middle term is where the sign lands. Both numbers of the pair are negative, so (x − 4)(x − 5) gives −4x and −5x, which add to the −9x in the middle, and the +20 is negative times negative. A child who writes (x + 4)(x + 5) has the product right and the sum wrong, which is exactly the mistake this narrow sheet is built to surface.
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