Factoring trinomials when a = 1
Use this page when the trinomial starts with x^2 and you want the fastest bracket-building pattern.
Start here if you want the short version before reading the full method.
- When a = 1, look for two numbers that multiply to c and add to b.
- Put those numbers directly into the brackets once the sign pattern works.
What this topic means and what to look for first.
This is the friendliest factoring pattern because the first term in each bracket is just x.
That means the real decision is the number pair, not a more complicated bracket structure.
One reliable route through the topic.
- 1Write the trinomial as x^2 + bx + c.
- 2List the factor pairs of c.
- 3Choose the pair that adds to b once the signs are included.
- 4Write the bracket form and expand it to check.
See the method in action.
x^2 + 6x + 8
- The factor pairs of 8 are 1 and 8, and 2 and 4.
- Only 2 and 4 add to 6, so the factorisation is (x + 2)(x + 4).
- Expanding confirms the middle term is 6x.
x^2 - 2x - 15
- Look for numbers that multiply to -15 and add to -2.
- The pair is -5 and 3, so the factorisation is (x - 5)(x + 3).
- One negative and one positive sign are needed because the constant term is negative.
Things that commonly send the method off track.
- Using a pair that multiplies correctly but adds to the wrong number.
- Missing the sign clue from the constant term.
- Forgetting that the bracket signs control the middle term too.
Use a short verification pass before moving on.
- Expand the brackets and confirm the x term matches b exactly.
- If the constant term is correct but the middle term is wrong, the number pair or sign pattern needs changing.
Try a few variations before switching to a calculator or solver tool.
- x^2 + 10x + 21
- x^2 - 9x + 20
- x^2 + x - 12
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Extra algebra revision resources
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Short answers worth checking.
Because each bracket starts with x, so you only need to find the correct number pair and sign pattern.
If the constant term is negative, one bracket sign must be positive and the other negative.
Continue with the next closely related topic.
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