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- Solving quadratics by factorising
Solving quadratics by factorising
A quadratic has an x2 term. Factorising turns it into two brackets, and then the solutions almost fall out.
Find the magic pair
To factorise x2 + bx + c, find two numbers that multiply to c and add to b.
x2 + 7x + 12: 3 × 4 = 12 and 3 + 4 = 7
So x2 + 7x + 12 = (x + 3)(x + 4)
x2 + 7x + 12: 3 × 4 = 12 and 3 + 4 = 7
So x2 + 7x + 12 = (x + 3)(x + 4)
Zero makes it easy
If two things multiply to make 0, one of them must be 0.
(x + 3)(x + 4) = 0 means x + 3 = 0 or x + 4 = 0
So x = −3 or x = −4
Always rearrange to = 0 before you factorise.
(x + 3)(x + 4) = 0 means x + 3 = 0 or x + 4 = 0
So x = −3 or x = −4
Always rearrange to = 0 before you factorise.
Difference of two squares
x2 − 9 = (x + 3)(x − 3)
The middle terms cancel: +3x − 3x = 0.
The middle terms cancel: +3x − 3x = 0.
Solve x2 − x − 20 = 0
- Two numbers that multiply to −20 and add to −1: −5 and +4
- (x − 5)(x + 4) = 0
- x − 5 = 0 or x + 4 = 0
- x = 5 or x = −4
Answer: x = 5 or x = −4
Rearrange to = 0. Find two numbers that multiply to c and add to b. Set each bracket equal to 0. The signs in the answers flip.
The interactive lesson includes the diagrams for this topic.
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