Description
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.
Explanation & Answer
Thank you for the opportunity to help you with your question!
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.