Factorise each of the following 1) 3x + xy 2) 4x2 2xy – 3) pq2 p2q – 4) 3pq - 9q2 5) 2x3 6x2 – 6) 8a5b2 12a3b4 – 7) 5y(y 1) + 3(y 1) – – Factorising quadratics Simple quadratics: Factorising quadratics of the form The method is: Step 1: Form two brackets (x ) … )(x … Step 2: Find two numbers that multiply to give and add to make These two numbers get c b. written at the other end of the brackets. Example 1: Factorise 9x 10. x2 – – We need to find two numbers that multiply to make -10 and add to make -9. These Solution: numbers are -10 and 1. Therefore 9x 10 = (x 10)(x + 1). x2 – – – General quadratics: Factorising quadratics of the form The method is: Step 1: Find two numbers that multiply together to make and add to make ac b. Step 2: up the term using the numbers found in step 1. bx Step 3: Factorise the front and back pair of expressions as fully as possible. Step 4: There should be a common bracket. Take this out as a common factor. Example 2: Factorise 6x2 + 12. x – Solution: We need to find two numbers that multiply to make 6 × -12 = -72 and add to make 1. These two numbers are -8 and 9. Therefore, 6x2 + 12 = 6x2 - 8x + 9x 12 x – – = 2x(3x 4) + 3(3x 4) (the two brackets must be identical) – – = (3x 4)(2x + 3) – Difference of two squares: Factorising quadratics of the form Remember that = (x + a)(x a). – Therefore:
Factorise each of the following 1) 3x + xy 2) 4x2 – 2xy 3) pq2 – p2q 4) 3pq - 9q2 5) 2x3 – 6x2 6) 8a5b2 – 12a3b4 7) 5y(y – 1) + 3(y – 1) Factorising quadratics Simple quadratics: Factorising quadratics of the form The method is: Step 1: Form two brackets (x … )(x … ) Step 2: Find two numbers that multiply to give c and add to make b. These two numbers get written at the other end of the brackets. Example 1: Factorise x2 – 9x – 10. Solution: We need to find two numbers that multiply to make -10 and add to make -9. These numbers are -10 and 1. Therefore x2 – 9x – 10 = (x – 10)(x + 1). General quadratics: Factorising quadratics of the form The method is: Step 1: Find two numbers that multiply together to make ac and add to make b. Step 2: up the bx term using the numbers found in step 1. Step 3: Factorise the front and back pair of expressions as fully as possible. Step 4: There should be a common bracket. Take this out as a common factor. Example 2: Factorise 6x2 + x – 12. Solution: We need to find two numbers that multiply to make 6 × -12 = -72 and add to make 1. These two numbers are -8 and 9. Therefore, 6x2 + x – 12 = 6x2 - 8x + 9x – 12 = 2x(3x – 4) + 3(3x – 4) (the two brackets must be identical) = (3x – 4)(2x + 3) Difference of two squares: Factorising quadratics of the form Remember that = (x + a)(x – a). Therefore: