OCR GCSE MATHS 7.2 FACTORISING QUADRATIC EXPRESSIONS(Further algebraic expressions)EXAM WITH CORRECT ANSWERS

7.2 Factorising quadratic expressions ©Cambridge University Press and OCR 2021 1 7 Further algebraic expressions 7.2 Factorising quadratic expressions • factorising quadratic expressions of the form Reminder Two examples of quadratic expressions in the form are and . The highest power of x in these expressions is . Factorising an expression involves writing it as a product of its factors. You will need to recall how to factorise an expression by taking out the HCF (highest common factor). This was studied in sheet 3.4. WORKED EXAMPLE Factorise . Solution Write (x )(x ). Find pairs of factors that multiply to give +12. Remember the factors could be negative. +1 × +12 or −1 × −12 +2 × +6 or −2 × −6 +3 × +4 or −3 × −4 Identify which pair of factors add together to give +8. In this case it’s +2 and +6, so write (x + 2)(x + 6). Exercise 1 1 Factorise these quadratic expressions. a b c d e f g h 7.2 Factorising quadratic expressions ©Cambridge University Press and OCR 2021 2 WORKED EXAMPLE Factorise . Solution Write (x )(x ). Find pairs of factors that multiply to give −10. +1 × −10 or −1 × +10 +2 × −5 or −2 × +5 Identify which pair of factors add together to give −3. In this case it’s +2 and −5, so write (x + 2)(x − 5). 2 Factorise these quadratic expressions. a b c d e f g h WORKED EXAMPLE Factorise . Solution Write the expression as . Write (x )(x ). Find pairs of factors that multiply to give −25. +1 × −25 or −1 × +25 +5 × −5 or −5 × +5 Identify which pair of factors add together to give 0. In this case it’s +5 and −5, so write (x + 5)(x − 5). 3 Factorise these quadratic expressions. a b c d TIP Notice that when is factorised the result is (x + 5)(x − 5). The square roots of 25 are +5 and −5. So, factorising = , since the square roots of 3 are and 4 Factorise these quadratic expressions. a b