SOLUTION: find all zeros of the polynomial function and write the polynomial as a product of its leading coefficient and its linear factors. p(x)= 3x^5+2x^4+10x^3+6x^2-25x-20

Algebra ->  Trigonometry-basics -> SOLUTION: find all zeros of the polynomial function and write the polynomial as a product of its leading coefficient and its linear factors. p(x)= 3x^5+2x^4+10x^3+6x^2-25x-20      Log On


   

Question 1055267: find all zeros of the polynomial function and write the polynomial as a product of its leading coefficient and its linear factors.
p(x)= 3x^5+2x^4+10x^3+6x^2-25x-20
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
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Looks like x=-1 and x=4%2F3 are roots so then
x%2B1 and 3x-4 are factors.
Use polynomial long division to get the remaining polynomial with the complex solution.
Q%28x%29=%283x%5E5%2B2x%5E4%2B10x%5E3%2B6x%5E2-25x-20%29%2F%28%28x%2B1%29%283x-4%29%29
Q%28x%29=x%5E2%2B5
So then,
p%28x%29=%28x%2B1%29%283x-4%29%28x%5E2%2B5%29