(x^3-5x^2-33x-35) Divided By (x+3)

3 min read Jun 17, 2024
(x^3-5x^2-33x-35) Divided By (x+3)

Dividing Polynomials: (x^3-5x^2-33x-35) ÷ (x+3)

This article will guide you through the process of dividing the polynomial (x^3-5x^2-33x-35) by (x+3) using polynomial long division.

Understanding Polynomial Long Division

Polynomial long division is similar to long division with numbers. We'll be using the following steps:

  1. Set up: Arrange the polynomials in descending order of their exponents.
  2. Divide: Divide the leading term of the dividend by the leading term of the divisor. Write the result above the dividend.
  3. Multiply: Multiply the result by the divisor and write the product below the dividend.
  4. Subtract: Subtract the product from the dividend.
  5. Bring down: Bring down the next term of the dividend.
  6. Repeat: Repeat steps 2-5 until you reach a remainder that is either zero or has a degree less than the divisor.

The Division Process

Let's perform the long division:

         x^2 - 8x - 9 
    x+3 | x^3 - 5x^2 - 33x - 35
         -(x^3 + 3x^2)
                 -8x^2 - 33x
                 -(-8x^2 - 24x)
                         -9x - 35
                         -(-9x - 27)

Result and Interpretation

From the division, we find that:

  • Quotient: x^2 - 8x - 9
  • Remainder: -8

Therefore, the division of (x^3-5x^2-33x-35) by (x+3) can be expressed as:

(x^3-5x^2-33x-35) ÷ (x+3) = x^2 - 8x - 9 - 8/(x+3)

This means that (x^3-5x^2-33x-35) is equal to (x+3) multiplied by (x^2 - 8x - 9) with a remainder of -8.

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