What is a quadratic?
The general quadratic looks like:
ax2 + bx + c
“Quad” means “square”, which in math means to the power of 2. So a quadratic is an equation that contains an x2, and this is the highest power. There can’t be, for example x3, nor x4, and so on. Only the square is the highest power. Quadratic expression contains three terms, which makes it a trinomial.
What is a coefficient?
A coefficient is a number that is multiplying (it is attached to) a variable, like an x or any other letter.
e.g.
3x2 + 2x - 4
3 is the coefficient of x2,
and 2 is the coefficient of x.
What is the leading coefficient?
The leading coefficient, is the number that is attached to the x with the highest power.
e.g. in the trinomial
4x2 + 3x + 9
the leading coefficinent is 4
What is a constant?
A constant is a number that is not attached to a variable (like an x, or any other number).
e.g. 3x2 + 4x + 7
7 is the constant.
3 and 4 are coefficients.
3 is the leading coefficient.
What is the standard recipe for factorising a simple quadratic?
- Factor out any common factors. (So anything that goes into all of the terms. i.e. 6x2-2x-8 = 2 (3x2-x-4))
- Make a list of all the factors that multiply to make axc.
- Check to see which two factors from step two add to the b term.
- Rewrite the equation, separating the middle term into the two factors you found.
- Take the common factors out of the first two terms and the last two, and regroup.
For example, 6x2-2x-8:
- 6x2-2x+8=2(3x2-x-4). Now I need to factorise 3x2-x-4
- 3• -4= -12, so the factors are 1• -12, -1•12, 2• -6, -2•6, 3• -4, -3•4
- Do any of the pairs add to -1? Yep, 3+ -4= -1.
- 3x2+3x-4x-4
- 3x(x+1) - 4(x+1) = (3x-4)(x+1). So the answer is 6x2-2x+8=2(3x-4)(x+1).
Factorise
x2 + 8x + 16
Factorise
x2 + 6x + 8
Factorise
x2 - 2x - 3
(Careful! The negative signs matter!)
Factorise
6x2 +17x + 12
