Investigate the concept of a polynomial and apply the factor and remainder theorems to solve problems(VCMNA357)
LO: To understand the factor and remainder theorems
Know:
- What is a factor
- How to factorise expressions
- Divide polynomials
Understand:
- that the factor and remainder theorems help us to determine the factors of a polynomial,
Do:
- I can use the factor theorem to find the factors of a polynomial.
- I can use the remainder theorem to find the remainder of a polynomial.
What is a Polynomial?
A polynomial is an expression that contains only one variable. Each term contains the variable raised to a non-negative integer value (the degree always has to be positive).
What is the Remainder Theorem?
If a polynomial, f(x) is divided by x – k, the remainder is equal to f(k).
For example, when f(x) is divided by (x – 2), the remainder is f(2).
when f(x) is divided by (x + 3), the remainder is f(-3).
What is the Factor Theorem?
The polynomial, x – k is a factor of the polynomial f(x) if and only if f(k) = 0.
For example, dividing f(x) = x^3 + x^2 – 10x + 8 by (x -1) gives a quotient of x^2 + 2x – 8.
Long Division with Polynomials Videos
Factor Theorem and Remainder Theorem Videos
Textbook Questions
My Maths 10Ex 6A pg. 271 Q. 1-5 |
