Factorising quadratic expressions 2
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This document provides instructions on how to factorize quadratic expressions into their prime factors. It includes the following steps: - Factorize expressions of the form ax^2 + bx + c by finding two terms whose product is a and sum is b. - Always expand the factors to check the factorization is correct. - To factorize expressions with negative constants, list the factors of the constant term and try different pairings with the variables until expanding checks. - More complex expressions may require trial and improvement to find the correct factors.
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Factorising quadratic expressions 2
- 4. Let's try to factorise Which two terms multiply to make ? 2x2 +7x+5 ( ) ( ) 2x2 ( ) ( ) Now, to make the :5 ( ) ( ) 2x x 2x x +1 +5 Let's expand: 2x2 +10x+x+5 2x2 +11x+5
- 5. ( ) ( )2x x +1 +5 We have to swap around the 1 and the 5 Now, expand again: Always expand to check !!!!!!
- 6. Factorise: 3x2 +16x+21 ( ) ( ) List the factors of 21: so it could be: (3x +7) ( x + 3)or(3x +3) ( x + 7) Expand to see which is the correct one. So 3x2 +16x+21 = (3x +7) ( x + 3)
- 7. Let's try to factorise 3x2 +13x10 ( ) ( ) List the factors of -10: The best way to find the correct pair is trial and improvement
- 8. Now even worse! 4x2 4x3 Which two terms multiply to make ?4x2 It could be: or(4x ) ( x ) (2x ) ( 2x ) List the factors of -3: Now try the different possibilities until you find the correct one