Polynomials - [Pure 3].

Question 1

What is a Polynomial?

Answer 1

An expression involving different powers of x. A quadratic has a degree of 2 as the highest power is the x² term.A cubic has a degree of 3 as the highest power is the x³ term.

Question 2

What 2 methods can you use to solve Polynomials?

Answer 2

1. Long Divison.
2. Grid Method.

Question 3

What is the Factor Theorem?

Answer 3

The Factor Theorem is a case of the Remainder Theorem where if the remainder is 0, there is a factor.

Question 4

How do you show something is a factor using the Factor Theorem?

Answer 4

If (x-a) is a factor of the polynomial p(x), then p(a) = 0.
[e.g. if (x-2) is a factor, sub x=2 in the polynomial and it should equal zero].

If (bx-a) is a factor of the polynomial p(x), then p(a/b) = 0.

Question 5

What is the statment you must use in the exam?

Answer 5

Therefore, by the Factor Theorem, (x-a) is a factor.