Question

Consider the function f(x) = x³ - 6x² - 49x + 294. When f(x) is divided by x - 7, the remainder is:

a) x + 7
b) -x + 7
c) x - 7
d) -x - 7

Answer 1

The remainder of the function f(x) = x³ - 6x² - 49x + 294 divided by x - 7 is found to be 0 using the Remainder Theorem. Therefore, the remainder is 0, which is not among the options provided in the question. There may have been a mistake in the options given.

Step-by-step explanation:

To find the remainder when f(x) = x³ - 6x² - 49x + 294 is divided by x - 7, we can use the remainder theorem. The remainder theorem states that if a polynomial f(x) is divided by x - a, then the remainder is equal to f(a). So, substituting x = 7 into f(x), we get f(7) = 7³ - 6(7)² - 49(7) + 294 = -7.

The remainder when the function f(x) = x³ - 6x² - 49x + 294 is divided by x - 7 can be found by using either long division of polynomials or by applying the Remainder Theorem. The Remainder Theorem states that for a polynomial f(x), the remainder of dividing f(x) by (x - a) is f(a). Hence, to find the remainder when f(x) is divided by (x - 7), we simply evaluate f(7

Substituting 7 into the function, we get:
f(7) = 7³ - 6(7)² - 49(7) + 294
= 343 - 294 - 343 + 294
= 0.

Therefore, the remainder is 0, which is not among the options provided in the question. There may have been a mistake in the options given.