Polynomial Division
Polynomial division is the process of dividing one polynomial by another, analogous to long division of integers, and is foundational for factorising higher-degree expressions.
What You Need to Know
Key Concept Diagram
Long division of polynomials follows the same Divide–Multiply–Subtract–Bring-down cycle as integer long division
The Remainder Theorem states that when P(x) is divided by (x - a), the remainder equals P(a)
The Factor Theorem states that (x - a) is a factor of P(x) if and only if P(a) = 0
Synthetic division is a streamlined method for dividing polynomials by linear factors of the form (x - a)
Key Vocabulary
Dividend
The polynomial being divided (the one inside the division bracket)
Divisor
The polynomial you are dividing by
Quotient
The result of the division, not including any remainder
Remainder Theorem
If P(x) is divided by (x − a), the remainder is P(a)
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
When P(x) = x³ - 2x + 5 is divided by (x - 1), what is the remainder?
Question 2
If (x - 2) is a factor of P(x) = x³ - 3x² + kx - 2, find k.
Question 3
Which statement correctly describes the Factor Theorem?
Key Concepts Summary
- ●Long division of polynomials follows the same Divide–Multiply–Subtract–Bring-down cycle as integer long division
- ●The Remainder Theorem states that when P(x) is divided by (x - a), the remainder equals P(a)
- ●The Factor Theorem states that (x - a) is a factor of P(x) if and only if P(a) = 0
- ●Synthetic division is a streamlined method for dividing polynomials by linear factors of the form (x - a)