Mathematics — first biennium · Lesson
When dividing P(x) by x−a, the remainder is P(a). Synthetic division organizes coefficient operations compactly.
Prerequisites: Polynomial division and factorization
Goal: Connect P(a) with the remainder on division by x−a and use synthetic division.
In this lesson: Connect P(a) with the remainder on division by x−a and use synthetic division.
New concept: When P(x) is divided by x−a, the remainder theorem says the remainder is P(a). If P(a)=0, then x−a is a factor of P(x); synthetic division organizes the coefficients efficiently.
How to proceed: First compute P(a): that is already the remainder. In synthetic division bring down the leading coefficient, then alternate multiplication by a and addition.
You can already assume: Polynomial division and factorization.
Completed exercises: 0/5 · Correct on first attempt: 0
First compute P(a): that is already the remainder. In synthetic division bring down the leading coefficient, then alternate multiplication by a and addition.
Data / situation: P(x)=x²+(0)x+(-17); divide by x−(4).
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.