Answer:
The remainder of the function is 17
Step-by-step explanation:
-›In algebra, the polynomial remainder theorem or little Bézout's theorem is an application of Euclidean division of polynomials. It states that the remainder of the division of a polynomial f(x) by a linear polynomial
therefore,
[tex]f(x) = x {}^{4} + 3x {}^{3} - 16x { }^{2} + 2x - 7 \\ f(3) = (3) {}^{4} + 3(3) {}^{3} - 16(3) {}^{2} + 2(3) - 7 \\ f(3) = 81 + 81 - 144 + 6 - 7 \\ f(3) = 17[/tex]
therefore,
the remainder of the given function at the given x value is 17
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