Factorise 3x^2 + 14x + 8
To factorise polynomials of the form ax^2 + bx + c, we want to rewrite the middle coefficient as the sum of two smaller numbers. The product of these two numbers should be equal to a * c (in this case, 3 * 8 = 24), and the sum of the two numbers should equal b (in this case, 14). Here, we can see that the values 2 and 12 fit this criteria. Rewriting the original expression would then look like this: 3x^2 + 2x + 12x + 8
From here we can factorise by grouping together the first two terms and the last two terms. By taking the greatest common factor of each group, we get x(3x+2) + 4(3x+2). As (3x+2) appears in both terms here, we can further simplify to (x+4)(3x+2).
AM
Related Maths GCSE answers
All answers ▸Why do square roots have more than 1 solution?
Jamil has 5 litres of water in a container. He pours 750 millilitres of water into each of 6 bottles. (c) How much water is left in the container? Give your answer in millilitres.
Yesterday it took 5 cleaners 4 and ½ hours to clean all the rooms in a hotel. There are only 3 cleaners to clean all the rooms in the hotel today. How much time will it take them?
What is the solution to the system of equations defined by (1) x+2y = 4 and (2) y+2x = 6?