-divided-by-(x-4).jpeg "(x^2+x-17) Divided By (x-4)")
Division of Polynomials: (x^2 + x - 17) ÷ (x - 4)
Introduction
In this article, we will perform the division of two polynomials: (x^2 + x - 17) divided by (x - 4). Polynomial division is a fundamental concept in algebra and is used to simplify expressions and solve equations.
The Problem
Given the polynomials:
Dividend: x^2 + x - 17 Divisor: x - 4
Our goal is to find the quotient and remainder when dividing the dividend by the divisor.
The Process
To perform the division, we will use the long division method. Here are the steps:
Step 1: Write the dividend and divisor
____________________
x - 4 | x^2 + x - 17
Step 2: Divide the leading term of the dividend by the divisor
x^2 ÷ x = x
Step 3: Multiply the divisor by the result and subtract
____________________
x - 4 | x^2 + x - 17
- (x^2 - 4x)
5x - 17
Step 4: Divide the new leading term by the divisor
5x ÷ x = 5
Step 5: Multiply the divisor by the result and subtract
____________________
x - 4 | x^2 + x - 17
- (x^2 - 4x)
5x - 17
- (5x - 20)
3
The Result
The quotient is x + 5, and the remainder is 3.
(x^2 + x - 17) ÷ (x - 4) = x + 5 + (3)/(x - 4)
Conclusion
In this article, we have performed the division of two polynomials using the long division method. The result shows that the quotient is x + 5, and the remainder is 3. This process is essential in algebra and is used to simplify expressions and solve equations.
