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)

a) Solve 6x + 13 =2x +5 (2 marks) b) Expand and simplify (q + 7)(q - 3) (2 Marks)

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