Question

Divide. $$ \left(2 x^{3}-11 x^{2}+25\right) \div(x-5) $$

   Divide.
$$
\left(2 x^{3}-11 x^{2}+25\right) \div(x-5)
$$

Algebra for College Students

Algebra for College Students

Margaret L. Lial,… 9th Edition

Chapter 4, Problem 35

Instant Answer

Solved by Expert Hira Saeed

03/03/2022

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This gives us $2x^3 - 11x^2 + 0x + 25$. Show more…

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Divide. $$ \left(2 x^{3}-11 x^{2}+25\right) \div(x-5) $$

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Key Concepts

Polynomial Division

Polynomial Division is the process of dividing one polynomial by another, similar to how numerical long division works with numbers. This method helps to simplify complex expressions into a quotient and a remainder, allowing for further analysis or factoring of the polynomial expressions.

Division Algorithm for Polynomials

The Division Algorithm for Polynomials guarantees that for any two polynomials, where one is nonzero, there exist unique quotient and remainder polynomials such that the dividend equals the product of the divisor and the quotient, plus the remainder. Importantly, the degree of the remainder is always less than the degree of the divisor.

Synthetic Division

Synthetic Division is a simplified form of polynomial division that is used when dividing by a linear factor of the form x - c. It is an efficient shortcut that reduces the amount of writing and arithmetic needed, especially when determining both the quotient and the remainder quickly.

Remainder Theorem

The Remainder Theorem states that when a polynomial is divided by a linear divisor of the form x - c, the remainder of the division is equal to the value of the polynomial evaluated at x = c. This theorem provides a practical method for finding the remainder without carrying out the complete division process.

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