Question

Explain why f () cannot be written as the product of 3 linear factors.

Answer 1

Answer:

Step-by-step explanation:

Yes, because if zz is a complex root of P(x)P(x) with real coefficients, you can readily show that z¯z¯ is also a root since P(z¯)=P(z)¯¯¯¯¯¯¯¯¯¯P(z¯)=P(z)¯. Therefore u(x)=(x−z)(x−z¯)u(x)=(x−z)(x−z¯) divides P(x)P(x).

But u(x)u(x) is a quadratic polynomial with real coefficients.

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Answer 2

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. ... We can quickly synthetically divide the polynomial by its potential roots factors of .