In Exercises 44–45, divide using synthetic division. (3 x^4+11 x^3-20 x^2+7 x+35) ÷(x+5)

Name: Problem 44, Chapter 3: Precalculus
Uploaded: 2020-03-09T18:54:22-08:00
Duration: 2 min 28 s
Channel: Thomas Emment
Description: In Exercises 44–45, divide using synthetic division. (3 x^4+11 x^3-20 x^2+7 x+35) ÷(x+5)

step 1 Ok -dokey, we want to divide this long equation by x plus 5 and we're going to use synthetic div

In Exercises 44–45, divide using synthetic division. (3...

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Key Concepts

Synthetic Division

Synthetic division is a shortcut method used to divide a polynomial by a linear factor of the form x - c. It simplifies the division process by working only with the coefficients of the polynomial, making it quicker and less error-prone than traditional long division, especially when the divisor is linear.

Polynomial Division

Polynomial division is a process similar to numerical division that allows a polynomial (dividend) to be divided by another polynomial (divisor) to obtain a quotient and possibly a remainder. This method is essential for breaking down higher degree polynomials into simpler factors or for simplifying complex algebraic expressions.

Remainder Theorem

The Remainder Theorem states that when a polynomial is divided by a linear divisor of the form x - c, the remainder is equal to the value of the polynomial evaluated at x = c. This theorem is often used in conjunction with synthetic division to quickly determine the remainder without carrying out a full division process.

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