How To Factorise Quadratic Expressions: An Easy Guide With Examples

x²+3x-40

(x+8)(x-5)

To factorise the quadratic expression x² + 3x – 40, you need to find two numbers that multiply to give -40 and add up to 3.

Here’s one way to approach the problem:

1. Make a list of all the factor pairs of -40:
-1 and 40
-2 and 20
-4 and 10
-5 and 8

2. Find which pair of factors adds up to 3.
The pair -5 and 8 adds up to 3.

3. Rewrite the quadratic expression using the pair of factors that add up to 3.
x² – 5x + 8x – 40

4. Factorise by grouping.
(x² – 5x) + (8x – 40)
x(x – 5) + 8(x – 5)
(x – 5)(x + 8)

Therefore, the factorised form of the quadratic expression x² + 3x – 40 is (x – 5)(x + 8).

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