When x^8 - 16 is factored completely, the result is the product of three binomials. Find them.
Thanks! xoxo
Thanks! xoxo
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x^8-16 = difference of two squares = (x^4)² - 4² = (x^4-4)(x^4+4)
x^4-4 = difference of two squares (x²)² - 2² = (x²-2)(x²+2)
Putting the two together:
x^8-16 = (x²-2)(x²+2)(x^4+4)
x^4-4 = difference of two squares (x²)² - 2² = (x²-2)(x²+2)
Putting the two together:
x^8-16 = (x²-2)(x²+2)(x^4+4)
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X^8-16 =(x^4-4)(x^4+4)
also x^4-4=(x^2-2)(x^2+2)
therefore x^8-16=(x^2-2)(x^2+2)(x^4+4) ans
since a^2-b^2=(a-b)(a+b)
also x^4-4=(x^2-2)(x^2+2)
therefore x^8-16=(x^2-2)(x^2+2)(x^4+4) ans
since a^2-b^2=(a-b)(a+b)
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(-2 + x^2) (2 + x^2) (2 - 2 x + x^2) (2 + 2 x + x^2)