Question 1041072
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{{{f(x)}}} = {{{3x^3-8x^2+5x-k}}}
In the polynomial function above, k is a constant. If (x-2) is a factor of f(x). What is the value of k.
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The fact that (x-2) divides f(x) means that x=2 is the root of the polynomial,
based on the Remainder theorem ( see the lesson <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</A> ).

In other words, {{{3*2^3 - 8*2^2 + 5*2 - k}}} = {{{0}}}.

From this equality, k = {{{3*2^3 - 8*2^2 + 5*2}}} = 3*8 - 8*4 + 10 = 2.
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