Factorisation

Question 1

Remainder theorem

Answer 1

If a polynomial f(x) is divided by (x-a)
remainder = f(a)
= the value of the polynomial f(x) at x = a

Question 2

Give the two corollaries of remainder theorem

Answer 2

1. If a polynomial f(x) is divided by (x+a), rem = f(-a)

2. If f(x) is divided by (ax+b), rem = f(-b/a)

Question 3

Factor theorem

Answer 3

(x-a) is a factor of polynomial f(x) if f(a) [remainder] = 0

Question 4

Give the three corollaries of factor theorem

Answer 4

1. (x+a) is a factor of f(x) if f(-a) = 0
2. (ax+b) is a factor of f(x) if f(-b/a) = 0
3. (x-a) is factor of f(x) if a is a root of the equation f(x)=0

Question 5

What are trials?

Answer 5

A factor of f(x) is found by trials. Calculate f(1), f(-1), f(2), f(-2) and see which one is zero

Question 6

Form of a polynomial

Answer 6

f (x) = g (x) [divisor] . q(x) [quotient] + r(x)