x2 t02 01 factorising complex expressions (2013)
TRANSCRIPT
Factorising Complex Expressions
Factorising Complex Expressions
If a polynomial’s coefficients are all real then the roots will appear in complex conjugate pairs.
Factorising Complex Expressions
If a polynomial’s coefficients are all real then the roots will appear in complex conjugate pairs.
Every polynomial of degree n can be;• factorised as a mixture of quadratic and linear factors over the
real field
Factorising Complex Expressions
If a polynomial’s coefficients are all real then the roots will appear in complex conjugate pairs.
Every polynomial of degree n can be;• factorised as a mixture of quadratic and linear factors over the
real field• factorised to n linear factors over the complex field
Factorising Complex Expressions
If a polynomial’s coefficients are all real then the roots will appear in complex conjugate pairs.
Every polynomial of degree n can be;• factorised as a mixture of quadratic and linear factors over the
real field• factorised to n linear factors over the complex fieldNOTE: odd ordered polynomials must have a real root
Factorising Complex Expressions
22 .. 2 xxige
If a polynomial’s coefficients are all real then the roots will appear in complex conjugate pairs.
Every polynomial of degree n can be;• factorised as a mixture of quadratic and linear factors over the
real field• factorised to n linear factors over the complex fieldNOTE: odd ordered polynomials must have a real root
Factorising Complex Expressions
22 .. 2 xxige 11 2 x
If a polynomial’s coefficients are all real then the roots will appear in complex conjugate pairs.
Every polynomial of degree n can be;• factorised as a mixture of quadratic and linear factors over the
real field• factorised to n linear factors over the complex fieldNOTE: odd ordered polynomials must have a real root
Factorising Complex Expressions
22 .. 2 xxige 11 2 x
If a polynomial’s coefficients are all real then the roots will appear in complex conjugate pairs.
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Every polynomial of degree n can be;• factorised as a mixture of quadratic and linear factors over the
real field• factorised to n linear factors over the complex fieldNOTE: odd ordered polynomials must have a real root
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012 24 zzii 043 22 zz
012 24 zzii 043 22 zz
numbersRealover factorised 0433 2 zzz
012 24 zzii 043 22 zz
numbersRealover factorised
numbersComplex over factorised
0433 2 zzz
02233 izizzz
012 24 zzii 043 22 zz
numbersRealover factorised
numbersComplex over factorisedizz 2or 3
0433 2 zzz
02233 izizzz
012 24 zzii 043 22 zz
numbersRealover factorised
numbersComplex over factorisedizz 2or 3
0433 2 zzz
02233 izizzz
If (x – a) is a factor of P(x), then P(a) = 0
abPIf (ax – b) is a factor of P(x), then = 0
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numbersRealover factorised
numbersComplex over factorisedizz 2or 3
0433 2 zzz
02233 izizzz
If (x – a) is a factor of P(x), then P(a) = 0
abPIf (ax – b) is a factor of P(x), then = 0
5832 Factorise 23 xxxiii
012 24 zzii 043 22 zz
numbersRealover factorised
numbersComplex over factorisedizz 2or 3
0433 2 zzz
02233 izizzz
If (x – a) is a factor of P(x), then P(a) = 0
abPIf (ax – b) is a factor of P(x), then = 0
5832 Factorise 23 xxxiiias it is a cubic it must have a real factor
012 24 zzii 043 22 zz
numbersRealover factorised
numbersComplex over factorisedizz 2or 3
0433 2 zzz
02233 izizzz
If (x – a) is a factor of P(x), then P(a) = 0
abPIf (ax – b) is a factor of P(x), then = 0
5832 Factorise 23 xxxiiias it is a cubic it must have a real factor
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numbersRealover factorised
numbersComplex over factorisedizz 2or 3
0433 2 zzz
02233 izizzz
If (x – a) is a factor of P(x), then P(a) = 0
abPIf (ax – b) is a factor of P(x), then = 0
5832 Factorise 23 xxxiiias it is a cubic it must have a real factor
0
5443
41
5218
213
212
21 23
P
3 2
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x x x
x x x
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numbersRealover factorised
numbersComplex over factorisedizz 2or 3
0433 2 zzz
02233 izizzz
If (x – a) is a factor of P(x), then P(a) = 0
abPIf (ax – b) is a factor of P(x), then = 0
5832 Factorise 23 xxxiiias it is a cubic it must have a real factor
0
5443
41
5218
213
212
21 23
P
3 2
2
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numbersRealover factorised
numbersComplex over factorisedizz 2or 3
0433 2 zzz
02233 izizzz
If (x – a) is a factor of P(x), then P(a) = 0
abPIf (ax – b) is a factor of P(x), then = 0
5832 Factorise 23 xxxiiias it is a cubic it must have a real factor
0
5443
41
5218
213
212
21 23
P
3 2
2
2 3 8 5
2 1 2 5
x x x
x x x
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321
415
818
1614
21
P
factorais12 x
Given that has two rational zeros, find these zeros and factorise P(x) over the complex field.
(iv) 3584 234 xxxxxP
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321
415
818
1614
21
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factorais12 x
3 212 3 xxxP
Given that has two rational zeros, find these zeros and factorise P(x) over the complex field.
(iv) 3584 234 xxxxxP
0
321
415
818
1614
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factorais12 x
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Given that has two rational zeros, find these zeros and factorise P(x) over the complex field.
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415
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factorais12 x
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Given that has two rational zeros, find these zeros and factorise P(x) over the complex field.
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415
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factorais12 x
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Given that has two rational zeros, find these zeros and factorise P(x) over the complex field.
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495
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321
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818
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factorais12 x
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Given that has two rational zeros, find these zeros and factorise P(x) over the complex field.
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0
3235
495
8272
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factor ais32 x
23- and
21 are zeros rational
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Cambridge: Exercise 5A; 1b, 2, 3, 5, 6, 7b, 8, 9, 10, 12 to 15
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