To find the remainder when the polynomial x3 + 6x2 + 42x + 79 is divided by x – 5, we can use the Remainder Theorem. This theorem states that the remainder of a polynomial f(x) when divided by x – c is equal to f(c).
In our case, we will substitute c = 5 into the polynomial:
Let f(x) = x3 + 6x2 + 42x + 79. We need to calculate f(5):
- f(5) = (5)3 + 6(5)2 + 42(5) + 79
- = 125 + 6(25) + 210 + 79
- = 125 + 150 + 210 + 79
- = 564
Thus, the remainder when x3 + 6x2 + 42x + 79 is divided by x – 5 is 564.