What is the remainder when the polynomial x³ + 3x² + 13x + 78 is divided by x – 4?

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To find the remainder when the polynomial x³ + 3x² + 13x + 78 is divided by x – 4, we can use the Remainder Theorem. The Remainder Theorem states that the remainder of the division of a polynomial f(x) by x – c is simply f(c). In this case, we will evaluate the polynomial at x = 4.

Let’s denote the polynomial as:

f(x) = x³ + 3x² + 13x + 78

Now, we calculate f(4):

  • f(4) = (4)³ + 3(4)² + 13(4) + 78
  • = 64 + 3(16) + 52 + 78
  • = 64 + 48 + 52 + 78
  • = 242

Thus, the remainder when x³ + 3x² + 13x + 78 is divided by x – 4 is 242.

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