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The HCF of the polynomials $x^{4} - 16$ and $x^{2} - 5 x + 6$ is:

Competition practiceAlgebra

A $x + 2$
B $x - 3$
C $x - 2$
D $x^{2} - 4$

Step-by-Step Solution

x^{4} - 16 = (x^{2} - 4) (x^{2} + 4) = (x - 2) (x + 2) (x^{2} + 4)

, while

x^{2} - 5 x + 6 = (x - 2) (x - 3)

. The only factor common to both is

(x - 2)

.

Answer: C)

x - 2

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