SOLUTION: how do you do the problem x^4-12x^2+11=0 when trying to factor the expression on the left side of each equation

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Question 855313: how do you do the problem x^4-12x^2+11=0 when trying to factor the expression on the left side of each equation
Found 2 solutions by ewatrrr, josgarithmetic:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

x^4-12x^2+11=0   factor  (Note: x%5E2+%2A+x%5E2+=+x%5E4)

(x^2 - 11)(x^2-1) = 0

Check factoring with FOIL

F	First terms

O	Outside terms

I	Inside terms

L	Last terms

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
The polynomial is in quadratic form. You can replace like, u=x%5E2. The constant terms in each binomial factor will need to give product of 11 and sum of -12. The obvious and correct choice will be -1 and -11.

%28x%5E2-1%29%28x%5E2-11%29=0
-
The solutions will be Real Numbers:
EITHER x%5E2-1=0
x%5E2=1
x=1 or x=-1
OR
x%5E2-11=0
x%5E2=11
x=sqrt%2811%29 or x=-sqrt%2811%29

SUMMARY: possible solutions for x are -1, 1, -sqrt(11), sqrt(11)