# How do you Factorise quadratic expressions?

## How do you Factorise quadratic expressions?

In order to factorise a quadratic algebraic expression in the form ax2 + bx + c into double brackets:

1. Multiply the end numbers together ( a and c ) then write out the factor pairs of this new number in order.
2. We need a pair of factors that + to give the middle number ( b ) and ✕ to give this new number.

What is an example of factoring an expression?

Generally, factoring is the inverse operation of expanding an expression. For example, 3(x − 2) is a factored form of 3x − 6, and (x − 1) (x + 6) is a factored form of x2 + 5x − 6.

What is an example of a quadratic expression?

A quadratic expression (Latin quadratus ≡ ”squared”) is an expression involving a squared term, e.g., x2 + 1, or a product term, e.g., 3xy − 2x + 1. (A linear expression such as x +1 is obviously non-quadratic.)

### What are the examples of quadratic equation by factoring?

Example 1. Solve: 2(x 2 + 1) = 5x. Solution.

• Example 3. Solve the following quadratic equation (2x – 3)2 = 25. Solution.
• Example 4. Solve the quadratic equation: x2 + 7x + 10 = 0.
• Example 6. Solve x2 + 4x – 5 = 0.
• Example 7. x2 – 5x – 6.
• Example 8. x2 – 6x + 8 = 0.
• Example 9. Factorize x2 +8x+12.
• Example 10. Solve 2×2 – 14x + 20 = 0.
• How to factorise 2 and 3 quadratic expressions?

So 2 and 3 are the numbers we put into double brackets. x 2 + 5 x + 6 = ( x + 2) ( x + 3) . You can always check your answer by expanding and simplifying the brackets to make sure you arrive at your original expression. b) Factorise x 2 + 3 x − 10 . This time we need to find two numbers with a product of − 10 and a sum of 3 .

Which is an example of factorising an equation?

Factorising Factorising is the reverse of expanding brackets, so it is, for example, putting 2x² + x – 3 into the form (2x + 3) (x – 1). This is an important way of solving quadratic equations. The first step of factorising an expression is to ‘take out’ any common factors which the terms have.

## How to check if a quadratic is factorable?

When it comes to checking whether a quadratic is factorable or not, we will go through a similar process. We will ask whether two numbers can be multiplied to get our last number and added to get our middle number. Our very first expression, x ^2, when given that check, passes. Written in its full form, the quadratic expression becomes x ^2+0 x +0.

How many brackets do you need to factor a quadratic expression?

When factorising quadratic expressions you will need two pairs of brackets. A quadratic expression always contains an x 2 term. Before trying to factorise quadratic expressions you should first make sure you can expand and simplify double brackets and factorise linear expressions .