Quadratics and Cubics (C2)

Question 1

How do you factorise a quadratic with a > 1 ?

Answer 1

1) Multiply a by c from ax + bx + c
2) Ask yourself what two numbers multiply to make the result of this and also add to make b.
3) Put (ax )(ax )
4) Put the results of 2) in the brackets: (ax + ?)(ax + ?)
5) Ask yourself if you can simplify either side.
6) Write the final answer in factorised form.

Question 2

How do you complete the square of ax + bx + c = 0 ?

Answer 2

1) Put (x+b/2)^2 - (b/2)^2 + c

Example:
y = x^2 - 5x + a
(x - 5/2)^2 + a - 25/4

Question 3

What is the remainder theorem?

Answer 3

1) When you divide f(x) by (x-a) the remainder is f(a)

2) When you divide f(x) by (ax-b) the remainder is f(b/a)

Question 4

What does the completed square format tell you ?

Answer 4

1) p(x + q)^2 + r
2) If p is positive the graph will be u shaped.
3) If p if negative the graph will be n shaped.
4) The min/ max point is (-q, r).
5) If p and r have different signs, the are 2 real roots.
6) If p and r have the same sign there are no real roots.
7) If r = 0 then the function has 1 root.