Question

F(x) = 3x³ + 5x² + 2, then what is the remainder when f(x) is divided by x - 2?

Answer 1

46

==============

The Remainder Theorem states that the remainder of the division of a polynomial by a linear divisor of the form (x - c) is equal to f(c).

Applying this, we substitute x = 2 into the polynomial, which gives us:

• f(2) =
• 3(2)³ + 5(2)² + 2 =
• 3(8) + 5(4) + 2 =
• 24 + 20 + 2 =
• 46

Therefore, the remainder is 46.

Answer 2

The remainder when f(x) = 3x³ + 5x² + 2 is divided by x - 2 is evaluated by substituting 2 into the function, yielding a remainder of 46.

Step-by-step explanation:

To find the remainder when the function f(x) = 3x³ + 5x² + 2 is divided by x - 2, we can use the Remainder Theorem. The Remainder Theorem states that if a polynomial f(x) is divided by x - k, then the remainder is f(k). Therefore, to find the remainder of f(x) when divided by x - 2, we simply need to evaluate f(2).

Let's substitute 2 into the function:

• f(2) = 3(2)³ + 5(2)² + 2
• = 3(8) + 5(4) + 2
• = 24 + 20 + 2
• = 46

Therefore, the remainder when f(x) is divided by x - 2 is 46.