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The Factor Theorem (whose correct name is the "Remainder theorem") says that
the binomial (x-a) is the factor of the polynomial p(x) if and only if p(a) = 0.
In your case, check if the number "2" is the zero of the given polynomial:
= 4*4 - 6 + 22 = 16 - 6 + 22 = 32.
So, the value of 2 IS NOT the root of the polynomial; hence, the binomial (x-2) IS NOT the factor of 4x^2 - 3x + 22.
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On the "Remainder Theorem" see the lessons
- Divisibility of polynomial f(x) by binomial (x-a) and the Remainder theorem
- Solved problems on the Remainder thoerem
in this site.