Question

According to the rational root theorem, which is a factor of the polynomial

f(x) = 6x^4 - 21x^3 - 4x^2 + 24x - 35

A) 2x - 7

B) 2x + 7

C) 3x - 7

D) 3x + 7

Answer 1

Supposing 2x-7 were a factor, then 7/2 would be a root. Use synth. div. to determine whether 7/2 actually is a root:

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7/2 / 6 -21 -4 24 -35
21 0 -14 35
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6 0 -4 10 0

Since the remainder is zero, 7/2 is a root and 2x - 7 is a factor.

You could check out the other possible factors in the same manner.