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Based on the polynomial remainder theorem, what is the value of the function when x = 4? x^(4)+13x^(3)-12x^(2)-18x-51

User PhilTrep
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Answer: You're Welcome!

Explanation:

The Polynomial Remainder Theorem states that if you divide a polynomial P(x) by a linear divisor of the form x - a, the remainder is equal to P(a). In other words, if you substitute x = a into the polynomial, the result is the remainder.

In your case, you have the polynomial P(x) = x^4 + 13x^3 - 12x^2 - 18x - 51, and you want to find the value of P(x) when x = 4. According to the Polynomial Remainder Theorem, this is equivalent to finding the remainder when P(x) is divided by x - 4.

So, let's evaluate P(4):

P(4) = 4^4 + 13 * 4^3 - 12 * 4^2 - 18 * 4 - 51

Calculating this expression will give you the value of the polynomial when x = 4:

P(4) = 256 + 832 - 192 - 72 - 51

P(4) = 773

Therefore, the value of the polynomial P(x) when x = 4 is 773.

User Inemanja
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