factorise: x^4-5x^2-6

Question

x to the power 4, minus five x to the power 2 minus six 

Answer 1

 x^4-5x^2-6

 

When you factor this the first element in each parenthesis

will be x² because the product is x⁴

(x² + a)(x²+b)

 

To find the value of a and b look at the constant, -6.

You need factors of -6 that add to the coefficient of

the x² term, -5.   That will be (-6)(1)

 

x⁴-5x²-6 = (x²+1)(x²-6)

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If you need to factor farther, which I don't believe you do,

you could take (x²-6) as the difference of two squares and

break this down to: (x²+1)(x+√6)(x-√6)

 

Answer 2

You are going to factor using FOIL.  Each factor will have a degree of 2.  So we have

 

(x² + 2)(x² - 3)

 

 

To factor completely (since  x²-3   is a difference in perfect square), we can obtain

 

(x² + 2)(x - √3)(x + √3)