What is the remainder x2+8x+12 when divided by x-2

Mathematics
1

what is the remainder x2+8x+12 when divided by x-2

2

What is the remainder x^2 + 8x + 12 when divided by x - 2?

Answer:

To find the remainder of the polynomial x^2 + 8x + 12 when divided by x - 2, we can use the Remainder Theorem. This theorem states that the remainder of the division of a polynomial f(x) by a linear divisor (x - a) is simply f(a).

  1. Identify the polynomial and the divisor:

    • Polynomial: f(x) = x^2 + 8x + 12
    • Divisor: x - 2

  2. Find the value of a in the divisor x - a:

    • Here, a = 2.

  3. Apply the Remainder Theorem:

    • According to the Remainder Theorem, the remainder is f(a), where a = 2.

    • Therefore, calculate f(2):

      f(2) = (2)^2 + 8(2) + 12

  4. Perform the calculations:

    • Calculate each term:

      (2)^2 = 4
      8 \cdot 2 = 16
      4 + 16 + 12 = 32

Therefore, the remainder when x^2 + 8x + 12 is divided by x - 2 is \boxed{32}.