SOLUTION: How do you solve polynomial equations such as: (x-3)(x-squaured+3x-4)=0 (x+2)(x-squared+5x+1)=0

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: How do you solve polynomial equations such as: (x-3)(x-squaured+3x-4)=0 (x+2)(x-squared+5x+1)=0      Log On


   

Question 2239: How do you solve polynomial equations such as:
(x-3)(x-squaured+3x-4)=0
(x+2)(x-squared+5x+1)=0
Answer by matthew_sessoms(39) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-3%29%28x%5E2%2B3x-4%29=0


Factor out the second equation that's in parentheses...
(x+4)(x-1)


Now we get the 3 factors...
(x-3)(x+4)(x-1)=0
Now solve for x in each parentheses, and we get..
x=3, x=-4, x=1
{3, -4, 1)


%28x%2B2%29%28x%5E2%2B5x%2B1%29=0


The second equation cannot be factored and therefore, must be solved using the quadratic formula, which is x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+


Plug the values in, like this
x+=+%28-5+%2B-+sqrt%28+5%5E2-4%2A1%2A1%29%29%2F%282%2A1%29
Which simplifies to...
x=%28-5%2B-sqrt%2821%29%29%2F2


So the answer to the second problem you gave is...
{-2,%28-5-sqrt%2821%29%29%2F2,%28-5-sqrt%2821%29%29%2F2}
Hope this helps!
MS