Divide. (2 x^3+9 x^2+14 x+5) ÷(2 x+1)

Name: Problem 37, Chapter 6: Algebra 2
Uploaded: 2019-11-29T17:42:02-08:00
Duration: 1 min 43 s
Channel: Aditya Sood
Description: Divide. (2 x^3+9 x^2+14 x+5) ÷(2 x+1)

Key Concepts

Polynomial Division

Polynomial division is a process similar to numerical division, where one polynomial (the dividend) is divided by another polynomial (the divisor) to yield a quotient and a remainder. This method relies on the division algorithm, which guarantees that for any two polynomials, with the divisor nonzero, there exist unique quotient and remainder polynomials such that the dividend equals the divisor multiplied by the quotient plus the remainder.

Long Division of Polynomials

Long division of polynomials is a systematic technique used to divide polynomials, analogous to the long division algorithm for numbers. It involves dividing the leading term of the dividend by the leading term of the divisor to obtain a term of the quotient, multiplying back, and subtracting from the dividend repeatedly until the degree of the remaining polynomial (the remainder) is less than that of the divisor.

Synthetic Division

Synthetic division is a simplified method for dividing a polynomial by a linear factor, typically of the form x - c. This technique streamlines the process by focusing on the coefficients and reducing the amount of written work compared to traditional long division. Although it is most straightforward when the divisor is monic (leading coefficient of one), synthetic division can sometimes be adapted for divisors with different leading coefficients.

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