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Chapter 7: Q11E (page 371)

Express the polynomial f(位)=位3-3位2+7位-5 as a product of linear factors over 鈩�.

Short Answer

Expert verified

A product of linear factors over C isf位=位-1位-1-2i位-1+2i

Step by step solution

01

Define the product of linear factors

To express this polynomial as a product of linear factors you have to find the zeros of the polynomial by the method of your choosing and then combine the linear expressions that yield those zeros.

02

A product of linear factors over C

It appliesf1=0, so位=1is a root of f. Therefore,

fx=位-1补位2+产位+c

Which we get is

a=1,b=-2,c=5

Now, we solve 位2-2位+5=0

位1,2=2卤4-202=1卤21

Therefore,f位=位-1位-1-2i位-1+2i

The solution is a product of linear factors over C is f位=位-1位-1-2i位-1+2i.

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