How do you use the factor theorem to determine whether x-2 is a factor of #4x^4 – 15x^2 – 4#?

1 Answer
Daniel L.
Dec 1, 2015

The expression #x-2# is a factor of #4x^4-15x^2-4#

Explanation:

The factor theorem states that #(x-a)# is a factor of a polynomial #P(x)# if and only if #P(a)=0#

So to check if #(x-2)# is a factor of #4x^4-15x^2-4# we have to find the value of the polynomial for #x=2#

So we have to calculate:

#4*2^4-15*2^2-4=4*16-15*4-4=64-60-4=0#

The value is zero so according to the factor Theorem #x-2# is a factor of #4x^4-15x^2-4#

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