Factor and Remainder Theorems (10A)

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 10

Ex 6A pg. 271 Q. 1-5