EDEXCEL GCSE HIGHER MATHS - What is Solving Equations Using Factorising

Edexcel GCSE Higher Maths: Solving Equations Using Factorising

What is Factorising?

Factorising is the process of breaking down an expression into smaller parts (factors) that multiply together to give the original expression. It's like reversing the process of expanding brackets.

Why is factorising useful for solving equations?

When you have an equation in the form:

ax^2 + bx + c = 0

Where a, b, and c are constants, you can use factorising to find the values of x that make the equation true (the solutions or roots). This is because:

• If the product of two factors is zero, then at least one of the factors must be zero.

Steps for Solving Equations Using Factorising:

1. Rearrange the equation to make it equal to zero. For example: x^2 + 5x + 6 = 0

2. Factorise the quadratic expression on the left-hand side.

3. Find two numbers that multiply to give 'c' and add to give 'b'. In the example above, the numbers are 2 and 3, as 2 * 3 = 6 and 2 + 3 = 5.

4. Rewrite the expression in factored form: (x + 2)(x + 3) = 0

5. Set each factor equal to zero and solve for x. x + 2 = 0 or x + 3 = 0 x = -2 or x = -3

Therefore, the solutions to the equation x^2 + 5x + 6 = 0 are x = -2 and x = -3.

Example:

Solve the following equation by factorising:

2x^2 - 5x - 3 = 0

1. Rearrange: The equation is already in the correct form.

2. Factorise: Find two numbers that multiply to give (2 * -3) = -6 and add to give -5. These numbers are -6 and 1. Now rewrite the expression: 2x^2 - 6x + x - 3 = 0 2x(x - 3) + 1(x - 3) = 0 (2x + 1)(x - 3) = 0

3. Solve for x: 2x + 1 = 0 or x - 3 = 0 x = -1/2 or x = 3

Therefore, the solutions to the equation 2x^2 - 5x - 3 = 0 are x = -1/2 and x = 3.

Key Points:

• Not all quadratic equations can be solved by factorising. Sometimes you need to use the quadratic formula.
• Remember to check your solutions by substituting them back into the original equation.

Practice:

Try solving these equations by factorising:

1. x^2 - 7x + 12 = 0
2. 3x^2 + 10x - 8 = 0

Remember to check your answers!