Mathematics — first biennium · Lesson
For a monic trinomial x²+sx+p, find two numbers whose sum is s and whose product is p. Always verify by expanding the two binomials again.
Prerequisites: Notable products and factoring by grouping
Goal: Factor simple monic trinomials by finding two numbers with the required sum and product.
In this lesson: Factor simple monic trinomials by finding two numbers with the required sum and product.
New concept: For x²+sx+p, find two numbers r and t such that r+t=s and r·t=p. Only when both conditions hold can we write (x+r)(x+t).
How to proceed: Do not choose the two numbers from the product alone: they must satisfy both the product and the sum.
You can already assume: Notable products and factoring by grouping.
Completed exercises: 0/5 · Correct on first attempt: 0
Do not choose the two numbers from the product alone: they must satisfy both the product and the sum.
Data / situation: Factor x^2+1x-12.
ConceptStep separates what is required from what is recommended or useful as reinforcement. Only required prerequisites block your progress.
Relationships: solid line = required · dashed line = recommended · dotted line = reinforcement.