What is (x^4-16)/(x-2) ?

The solution to (x^4-16)/(x-2) is (x^2+4)(x+2)

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simplify (x^4-16)/(x-2)

simplify

\frac{x ^{4} - 16}{x - 2}

(x^{2} + 4) (x + 2)

Solution steps

\frac{x ^{4} - 16}{x - 2}

Apply exponent rules

= \frac{( x ^{2} ) ^{2} - 4 ^{2}}{x - 2}

Apply Difference of Two Squares Formula:

x^{2} - y^{2} = (x + y) (x - y)

(x^{2})^{2} - 4^{2} = (x^{2} + 4) (x^{2} - 4)

= \frac{( x ^{2} + 4 ) ( x ^{2} - 4 )}{x - 2}

Factor

x^{2} - 4 : (x + 2) (x - 2)

= \frac{( x ^{2} + 4 ) ( x + 2 ) ( x - 2 )}{x - 2}

Cancel the common factor:

x - 2

= (x^{2} + 4) (x + 2)

(3 t^{2} - 5 t + 6) + (- 8 t^{2} + 7 t - 9)

(x - 1) 2

\frac{8}{14}

2 x + 4 x

(x - 7) (x + 5)