Use synthetic division to find the quotient and remainder when: x^4+x^2+2 is divided by x-2

Name: Problem 12, Chapter 0: Algebra and Trigonometry
Uploaded: 2020-07-17T21:40:41-08:00
Duration: 1 min 54 s
Channel: Tiffany Tran
Description: Use synthetic division to find the quotient and remainder when: x^4+x^2+2 is divided by x-2

step 1 To use synthetic division, you need to make sure you have the coefficients for all of the terms,

Use synthetic division to find the quotient and remainder...

Key Concepts

Synthetic Division

Synthetic division is a streamlined method for dividing a polynomial by a binomial of the form x - c. It simplifies the process by focusing solely on the coefficients and eliminates many of the variables and powers involved in long division, making it faster and more efficient, especially when the divisor is linear.

Polynomial Division

Polynomial division involves breaking a polynomial into parts to express it as the product of a divisor and a quotient plus a remainder. This division is guaranteed by the division algorithm for polynomials, which states that any polynomial can be written as the divisor multiplied by a quotient plus a remainder, where the remainder has a lower degree than the divisor.

Handling Missing Coefficient Terms

When using synthetic division, it is crucial to account for any missing degree terms in the polynomial by inserting a coefficient of zero for those terms. This ensures that the proper alignment of coefficients is maintained and that the synthetic division process correctly computes each term in the quotient and the final remainder.

Remainder Theorem

The Remainder Theorem states that when a polynomial is divided by x - c, the remainder of the division is equal to the value of the polynomial evaluated at x = c. This theorem provides a quick way to find the remainder without performing the full synthetic or long division process.

Transcript

Please give Ace some feedback