(x^3-2 x^2-9) ÷(x-3)

Name: Problem 60, Chapter 4: Beginning and Intermediate Algebra
Uploaded: 2022-02-07T22:07:15-08:00
Duration: 2 min 13 s
Channel: Nick Johnson
Description: (x^3-2 x^2-9) ÷(x-3)

step 1 Hello. So here we have the polymer division problem of x cubed minus 2x squared minus 9 dividing

Question

$\left(x^{3}-2 x^{2}-9\right) \div(x-3)$

   $\left(x^{3}-2 x^{2}-9\right) \div(x-3)$

Beginning and Intermediate Algebra

Margaret L. Lial,… 7th Edition

Chapter 4, Problem 60

Instant Answer

Solved by Expert Nick Johnson

02/07/2022

Step 1

We have one $x^{3}$, negative two $x^{2}$, and negative nine. Show more…

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$\left(x^{3}-2 x^{2}-9\right) \div(x-3)$

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Key Concepts

Synthetic Division

A shortcut method for dividing a polynomial by a binomial of the form (x - c) that simplifies the division process. It streamlines the calculation by handling the coefficients directly and is especially efficient when testing potential roots or applying the factor theorem.

Factor Theorem

A principle that states if a polynomial f(x) has a factor (x - c), then f(c) = 0, and conversely if f(c) = 0, then (x - c) is a factor of f(x). This theorem is useful for determining factors of polynomials and for verifying if a given value is a root.

Polynomial Division

This is a method used to divide one polynomial by another, finding a quotient and a remainder such that the original polynomial equals the divisor multiplied by the quotient plus the remainder. It is analogous to long division with numbers and is particularly useful when simplifying rational expressions or solving polynomial equations.

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