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Factorising Quadratic Expressions (IGCSE)
Factorising expressions in GCSE mathematics is essential. The use of algebraic expressions are extremely useful in these courses, and this includes the basics of Factorisation.
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1Factorising Harder Quadratic Expressions ( + and - )
‣ Example:
2x² + 7x + 5
Find 2 numbers that multiply to make 5, and later on add up to 7. = 1,,1
= (2x + 5 ) (x + 1) FINAL ANSWER
(2x + 5) (x + 1) CHECKED ANSWER = 2x + 5x = 7x
AS YOU CAN SEE, THESE NUMBERS MAKE 7.
‣ IF YOU DO DIFFERENT NUMBERS, OR IN A DIFFERENT ORDER, THE ANSWER
WILL BE WRONG. YOU MIGHT HAVE TO REDO THE EQUATION IN A DIFFERENT
ORDER, SIGNS (SUCH AS ADDITION AND SUBTRACTION), AND NUMBERS.
In this equation, all numbers are positive (we can see this by the addition signs),
so the final answer should only be addition signs.
However, if they share addition and subtraction, (positive and negative numbers),
there are different orders. That is why checking your answer is vital in these types
of questions.
________________________________________________
‣ We need 2 brackets, especially in a situation when x².
(x) x (x) = x² | (4x) x (x) = 4x² |
(5x² + 23x + 12) FACTORS OF 12 THAT LATER ON ADD UP TO 23:
12,1 | 1,12 | 6,2 | 2,6 | 4,3 | 3,4 |
= (5x + 3) (x + 4) = FINAL ANSWER
(5x + 3) (x + 4) = | 20x + 3x = 23x | CHECKED ANSWER |
_________________________________________________
‣ Different Signs:
4x² - 8x - 5 = 1,5 | 5,1
THIS TIME, THE NUMBERS ARE NEGATIVE. 4x² this time, instead of being (4x) x (x),
it will be split into (2x) x (2x).
= (2x + 1) (2x – 5) = FINAL ANSWER
(2x + 1) (2x – 5) = | -10x + 2x = -8x | CHECKED ANSWER |
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