Using a given zero to write a polynomial as a product of linear factors

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For the polynomial below, -1 is a zero. 

h(x) = x^3 + 5x^2 + 5x + 1

Express h(x) as a product of linear factors.

Oct 16th, 2015

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h(x) = x^3 - 5x^2 + 5x -1 ; 1 is a zero 

express h(x) as a linear product of two factors?

You cannot express a cubic polynomial as a linear function and there is no such thing as a linear product of factors. 

However, 1 is indeed a zero of h(x) (I checked) and this means that (x-1) is a factor of h(x). 
So you can divide h(x) by (x-1) and get a polynomial with no remainder. 

Use synthetic (or long division) to get: 

1 | 1 -5 .5 -1 
........ 1 -4 1 
....1..-4..1 == 

so h(x)=(x-1)(x²-4x+1) 

Hopefully this is what you need. 

Please let me know if you need any clarification. I'm always happy to answer your questions.
Oct 16th, 2015

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