Welcome to the Math Salamanders' Factoring Quadratic Equations Worksheets.

Here you will find a range of worksheets to help you to learn to factorise a range of different quadratic equations of the form ax2 + bx + c = 0

All the quadratic equation worksheets in this section factorise with integer values inside each bracket.

### Definition of a Quadratic Equation

A quadratic equation is an equation involving the square of a number which is the highest power in the equation.

It is usually in the standard form:

ax2 + bx + c = 0

where a, b and c are numbers, and x is an unknown. The variable a cannot be 0 (but b and c can be 0)

Note that the operations can be '+' or '-'.

It is also sometimes called a second degree polynomial equation.

Examples

The following ARE quadratic equations in standard form:

• x2 + 7x + 4 = 0
• z2 - 25 = 0
• 2w2 + 7w = 0
• 2y2 - 28 = 0
• 4a 2 - ½ a + 15 = 0

The following ARE quadratic equations but not yet in standard form:

• x2 + 6x = 4
• can be rewritten as x2 + 6x - 4 = 0 (which is in standard form)
• 3n2 - 10 = 6n
• can be rewritten as 3n2 - 6n - 10 = 0 (which is in standard form)

The following are NOT quadratic equations:

• x3 + 7x + 4 = 0 (because of the x3)
• 2y - 28 = 0 (because there is no y2 term)
• 4a5 - ½ a + 15 = 0 (because a has been raised to the 5th power)

### How to solve a quadratic equation

Section 1: Beginning Section

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