SOLUTION: Use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial. x - 2; 4x^2 - 3x + 22

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial. x - 2; 4x^2 - 3x + 22      Log On


   

Question 1106856: Use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial.
x - 2; 4x^2 - 3x + 22
Answer by ikleyn(52890) About Me  (Show Source):
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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%2A2%5E2+-+3%2A2+%2B+22 = 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.