High School

Based on the polynomial remainder theorem, what is the value of the function when [tex]x = -5[/tex]?

[tex]F(x) = x^4 + 12x^3 + 30x^2 - 12x + 70[/tex]

Answer :

Final answer:

The value of the function when x = -5 is 505.

Explanation:

The polynomial remainder theorem states that if we divide a polynomial f(x) by (x-r), the remainder is equal to f(r). In this case, the polynomial is f(x) = x⁴ + 12x³ + 30x² - 12x + 70 and we want to find the value when x = -5.

Substituting -5 into the polynomial, we get f(-5) = (-5)⁴ + 12(-5)³ + 30(-5)² - 12(-5) + 70 = 625 - 3000 + 750 + 60 + 70 = 505.

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