Factorise 2c2 + 8c + 8.
Use the following steps to factorise a quadratic:
-Take out a common factor
-Split into two brackets with the x term at the start of each bracket
-Write out the factor pairs of the last number
-Identify the pair that can be added or subtracted to give the middle number
-Add the pair of numbers to the brackets, being careful to use the right + or – sign
-Check if there’s time by multiplying out the brackets
Well we can recognise that this is a quadratic equation because of the c2, and so the factorised version will be in two brackets.
The first thing to do when factorising a quadratic is to see if there’s any common factor in all three terms: 2c2, 8c, and 8. First of all, look at the letter c. It isn’t in all three terms and so it is not a common factor. Now look at the numbers: 2, 8, and 8. The only numbers common factor of these is 2.
Therefore, we can “take a 2 out of each term” – divide each term by 2.
(2c2 + 8c + 8)/2 --> 2(c2 + 4c + 4)
Now, because the first term is c2, the start of each bracket must be c. So that the two “c” can multiply to give c2.
So we can write this as follows:
2(c + …)(c + …)
Now, we look at the last number of the previous step: 2(c2 + 4c + 4), which is the 4 on the end. We write out the factor pairs of 4, giving us 1 and 4, and 2 and 2.
The pair that can be added to give us the middle number 4 from the 4c is 2 and 2.
Therefore, it is 2 and 2 that will be added to the brackets to complete the factorisation:
2(c + 2)(c + 2)