Question

How is the Remainder Theorem used to find the remainder of (4x^4-2x^3-52x^2-15x)/(x-4)? Find the remainder.

Answer 1

One way to do this would be to use synthetic division. Use 4 as the divisor and use the coefficients 4, -2, -52, -15, 0 (yes, the last coeff. is a zero):

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4 / 4 -2 -52 -15 0
16 56 16 4
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4 14 4 1 4 The remainder is 4. That means that if you divide the given 4th order polynomial by (x-4), the remainder is 4.

Note also, that the value of the polynomial, when x = 4, is 4.