Charles evaluates f(-2) and determines its value to be 30 Charles concludes that is not factor of f(x).
What is Factor theorem?
The factor theorem in algebra establishes a connection between a polynomial's factors and zeros. The polynomial remainder theorem has this particular special instance. A polynomial f(x) has a factor if and only if f=0, according to the factor theorem.
Given : f(x)=2x^4 -3x^3 +5x -16
By Factor theorem, If x+2 is a factor of f(x), then f(-2) should be equal to 0.
So, Charles can use factor theorem to determine whether x + 2 is a factor of f(x) by putting x=-2 in f(x),
f(x) = 2x^4 -3x^3 +5x -16
= 2×(-2)^4 - 3×(-2)^3 + 5(-2) - 16
= 2×16 + 3×8 - 10 - 16
= 32 + 24 -10 -16
= 56 -26
= 30.
Since, f(-2) ≠ 0, (x +2) is not a factor of f(x).
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