1.4 Quadratic Equations

Question 1

Quadratic Factorisation.

Factor xa + xb + ya + yb

Answer 1

= xa + xb +ya + yb
= x(a + b) + y(a + b)
=(x + y)(a + b)

Question 2

Split the Middle Term.

x^2 + 7x + 12

Answer 2

= x^2 + 4x + 3x + 12
= x(x + 4) + 3(x + 4)
= (x + 3)(x + 4)

(4 and 3 are factors of the constant 12 and can be added to equal 7)

Question 3

How do we know when to split the middle term?

Answer 3

Look for two numbers that when ADDED equal the middle coefficient term and when MULTIPLIED equal the constant term.

Question 4

How do you split the middle term when the first term has a coefficient?

For Example: 6x^2 + x - 12

Answer 4

M.A.M.S.

1. Multiply the two outside terms together.
6 x (-12) = -72

2. Look for two numbers that ADD to give the coefficient of the MIDDLE term and MULTIPLY to give -72.
   (+9) + (-8) = +1 (the coefficient of x is +1)
   (+9) x (-8) = -72
3. Split the middle term.
   = 6x^2 + 9x - 8x - 12
   = 3x(2x + 3) - 4(2x + 3)
   = (3x - 4)(2x + 3)