1. Polynomials
Thursday, 31 October 2019

2. Long Division Example Work out each of the following
a)  b)  15

3. Example
Divide by

4. Example
Divide by

5. Factor theorem
Example
What is the remainder when is divided by

6. Example
What is the remainder when is divided by
Example
What is the remainder when is divided by

7. That is the remainder is P(a)
Let P(x) be a polynomial in x to be divided by the linear function x – a
Where Q(x) = Quotient
R = Remainder
Putting x = a
That is the remainder is P(a)
If R = 0 when P(x) is divided by (x – a)
i.e. If P(a) = 0 then (x – a) is a factor of P(x)

8. Example
Show that (x + 1) is a factor of the cubic
and hence factorise completely

9. Example
Show that (x – 2) is a factor of x3 – 4x2 + x + 6
Hence factorise completely x3 – 4x2 + x + 6
Solve the equation x3 – 4x2 + x + 6 = 0

10. Example
Solve the equation

11. Past A – Level paper question
a) When ax3 – 12x2 – 6x + 5 is divided by x + 1, the remainder is –3.
Find the value of the constant a.
b) Factorise 8x3 – 14x2 – 7x +6