Question 1106856
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The Factor Theorem (whose correct name is the "<U>Remainder theorem</U>") 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*2^2 - 3*2 + 22}}} = 4*4 - 6 + 22 = 16 - 6 + 22 = 32.



So, the value of 2  <U>IS NOT</U>  the root of the polynomial;  hence, the binomial (x-2)  <U>IS NOT</U>  the factor of  4x^2 - 3x + 22.
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On the "Remainder Theorem" see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Divisibility-of-polynomial-f%28x%29-by-binomial-x-a.lesson>Divisibility of polynomial f(x) by binomial (x-a) and the Remainder theorem</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Solved-problems-on-the-Remainder-theorem.lesson>Solved problems on the Remainder thoerem</A>

in this site.