year 8 factorising
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Year 8 Factorising. Dr J Frost ([email protected]). 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. ?. - PowerPoint PPT PresentationTRANSCRIPT
Year 8 FactorisingDr J Frost ([email protected])
Last modified: 18th February 2014
Objectives: Be able to factorise a single term out of a bracket.
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 2x2: 1, 2, x, 2x, x2, 2x2
Factors of 2x: 1, 2, x, 2x
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Factors
Factorising means : To turn an expression into a product of factors.?
2x2 + 4xz 2x(x+2z)
x2 + 3x + 2 (x+1)(x+2)
2x3 + 3x2 – 11x – 6 (2x+1)(x-2)(x+3)
Year 8 Factorisation
Year 9 Factorisation
A Level Factorisation
Factorise
Factorise
Factorise
So what factors can we see here?
Factorising
2x + 4
Common factor = 2 ?
So 2x + 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.
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.
3x2 + 9x
Common factor = 3x?
So 3x2 + 9x = 3x(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
2xy + 4x = 2x(y + 2)
xy + x = x(y + 1)?
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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.
Factorising
5 + 10x x – 2xz x2y – xy2 10xyz – 15x2y xyz – 2x2yz2 + x2y2
Factor Challenge
5(1 + 2x) x(1 – 2z) xy(x – y) 5xy(2z – 3x) xy(z – 2xz2 + xy)
1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12)
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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 ?
Exercise 1
Exercise 2
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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.
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Dealing with fractionsWhen factorising, it’s convention to have any fractions outside the bracket.
Bro Tip: Make sure the fractions have a common denominator.
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Test Your Understanding
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Exercise 3
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