Part 02 · Algebra basics · Card 6 of 8
Factorising quadratics
Writing an expression like x^2 + 7x + 12 as two brackets multiplied together.
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Analogy
Like finding two numbers that fit a lock: they must multiply to one number and add to another.
Example
x^2 + 7x + 12
Need two numbers: multiply to 12, add to 73 and 4 work= (x + 3)(x + 4)
In practice
Engineers factorise quadratics to find where a thrown ball lands.
Practice
Flashcards
- Factorise x^2 + 7x + 12.(x + 3)(x + 4). 3 x 4 = 12 and 3 + 4 = 7.
Interview questions
- Factorise x^2 + 5x + 6 and explain how you know your answer is right.
- Find two numbers that multiply to 6 and add to 5
- They are 2 and 3
- Write (x + 2)(x + 3)
- Expand to check: x^2 + 3x + 2x + 6
Questions people ask
What do the two numbers need to do?
They must multiply to give the last number and add to give the middle number. For x^2 + 7x + 12, 3 x 4 = 12 and 3 + 4 = 7. So the brackets are (x + 3)(x + 4). Try factor pairs of the last number until the sum fits.
What if the last number is negative?
Then the two numbers have opposite signs, one positive and one negative. For x^2 + x - 12, you need numbers that multiply to -12 and add to 1. These are 4 and -3, so the answer is (x + 4)(x - 3).