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Year 8 Factorising

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. ?.

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Year 8 Factorising

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  1. 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: 18thFebruary 2014

  2. 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 2x: 1, 2, x, 2x 1, 2, x, 2x, x2, 2x2 Factors of 2x2: ?

  3. Factorising Factorising means : To turn an expression into a product of factors. ? So what factors can we see here? Year 8 Factorisation Factorise 2x2 + 4xz 2x(x+2z) Year 9 Factorisation Factorise x2 + 3x + 2 (x+1)(x+2) A Level Factorisation Factorise 2x3 + 3x2 – 11x – 6 (2x+1)(x-2)(x+3)

  4. Factorising 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 2x + 4 So 2x + 4 = 2(x + 2) ? (You could always check this by expanding out the brackets)

  5. Factorising 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 = 3x 3x2 + 9x We could have just ‘factored out’ the 3, but we wouldn’t have fully factorised because there’s also a factor of x. So 3x2 + 9x = 3x(x + 3) ?

  6. Factorising xy + x = x(y + 1) ? ? 2xy + 4x = 2x(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.

  7. Factor Challenge 5 + 10x x – 2xz x2y – xy2 10xyz – 15x2y xyz – 2x2yz2 + x2y2 5(1 + 2x) x(1 – 2z) xy(x – y) 5xy(2z – 3x) xy(z – 2xz2 + xy)

  8. Exercise 1 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) ? Extension Question: What integer (whole number) solutions are there to the equation Answer: . So the two expressions we’re multiplying can be This gives solutions of ? ? ? ? ? ? ? ? ? ? ? ?

  9. Exercise 2 ? ? ? ? ? ? ? ? 16 factors: 1, 2, x, y, z, 2x, 2y, 2z, xy, xz, yz, 2xy, 2xz, 2yz, xyz, 2xyz ? ? 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. ?

  10. 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.

  11. Test Your Understanding ? ? ?

  12. Exercise 3 ? ? ? ? ? ? ? ? ? ?

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