Year 8 Factorising Dr J Frost jfrosttiffin kingston

Year 8 Factorising Dr J Frost (jfrost@tiffin. kingston. sch. uk) Objectives: Be able to factorise a single term out of a bracket. Last modified: 18 th February 2014

Factors What does the factor of a number mean? ? Numbers which divide the original number without a remainder. Factors of 8: 1, 2, 4, 8 ? Factors of 2 x: 1, 2, x, 2 x? Factors of 2 x 2: ? 2, 2 x 2 1, 2, x, 2 x, x

Factorising means : To turn an expression into a product of factors. ? Year 8 Factorisation 2 x 2 + 4 xz Factorise So what factors can we see here? 2 x(x+2 z) Year 9 Factorisation x 2 + 3 x + 2 A Level Factorisation 2 x 3 + 3 x 2 – 11 x – 6 Factorise (x+1)(x+2) (2 x+1)(x-2)(x+3)

Factorising is the reverse of expanding. When you have a sum of terms, just identify the common factor. i. e. Find the largest expression each of your terms is divisible by. Common factor = 2 ? 2 x + 4 ? So 2 x + 4 = 2(x + 2) (You could always check this by expanding out the brackets)

Factorising is the reverse of expanding. When you have a sum of terms, just identify the common factor. i. e. Find the largest expression each of your terms is divisible by. Common factor = 3 x? 3 x 2 + 9 x ? So 3 x 2 + 9 x = 3 x(x + 3) We could have just ‘factored out’ the 3, but we wouldn’t have fully factorised because there’s also a factor of x.

Factorising xy + x ? = x(y + 1) ? 2 xy + 4 x = 2 x(y + 2) Now challenge your neighbour! Write out an expression in your book which can be factorised. Then swap books with your neighbour and get them to factorise it.

Factor Challenge 5 + 10 x 5(1 + 2 x) x – 2 xz x(1 – 2 z) x 2 y – xy 2 xy(x – y) 10 xyz – 15 x 2 y 5 xy(2 z – 3 x) xyz – 2 x 2 yz 2 + x 2 y 2 xy(z – 2 xz 2 + xy)

Exercise 1 ? ? ? ?

Exercise 2 ? ? ? 16 factors: 1, 2, x, y, z, 2 x, 2 y, 2 z, xy, xz, yz, 2 xy, 2 xz, 2 yz, xyz, 2 xyz 36 factors ? ? 2 can either appear in the factor or not (2 possibilities) x can either appear 0 times, 1 time, up to a times (a + 1 possibilities) y similarly has b + 1 possibilities and z has c +1 possibilities. So 2(a + 1)(b + 1)(c + 1) possible factors. ?

Dealing with fractions When factorising, it’s convention to have any fractions outside the bracket. ? ? Bro Tip: Make sure the fractions have a common denominator.

Test Your Understanding ? ? ?

Exercise 3 ? ? ? ? ?