Isiah Is Dividing $2x^3 - X^2 + 2x + 5$ By $x + 1$ Using A Division Table. His Work Is Shown Here.What Is The Value Of \$A$[/tex\]?A. $-5$ B. 5 C. $1x$ D. $5x$
**Isiah's Division Table: A Step-by-Step Guide to Finding the Value of A**
Understanding the Problem
Isiah is attempting to divide the polynomial $2x^3 - x^2 + 2x + 5$ by $x + 1$ using a division table. To solve this problem, we need to follow the steps of polynomial long division and identify the value of A.
What is Polynomial Long Division?
Polynomial long division is a method of dividing one polynomial by another. It involves dividing the highest degree term of the dividend by the highest degree term of the divisor, and then multiplying the entire divisor by the result and subtracting it from the dividend. This process is repeated until the degree of the remainder is less than the degree of the divisor.
Step-by-Step Solution
Let's follow the steps of polynomial long division to find the value of A.
Step 1: Divide the Highest Degree Term
The highest degree term of the dividend is $2x^3$, and the highest degree term of the divisor is $x$. To divide $2x^3$ by $x$, we get $2x^2$.
Step 2: Multiply the Divisor by the Result
We multiply the entire divisor $x + 1$ by $2x^2$ to get $2x^3 + 2x^2$.
Step 3: Subtract the Result from the Dividend
We subtract $2x^3 + 2x^2$ from the dividend $2x^3 - x^2 + 2x + 5$ to get $-3x^2 + 2x + 5$.
Step 4: Repeat the Process
We repeat the process by dividing the highest degree term of the new dividend $-3x^2$ by the highest degree term of the divisor $x$ to get $-3x$.
Step 5: Multiply the Divisor by the Result
We multiply the entire divisor $x + 1$ by $-3x$ to get $-3x^2 - 3x$.
Step 6: Subtract the Result from the Dividend
We subtract $-3x^2 - 3x$ from the new dividend $-3x^2 + 2x + 5$ to get $5x + 5$.
Step 7: Repeat the Process
We repeat the process by dividing the highest degree term of the new dividend $5x$ by the highest degree term of the divisor $x$ to get $5$.
Step 8: Multiply the Divisor by the Result
We multiply the entire divisor $x + 1$ by $5$ to get $5x + 5$.
Step 9: Subtract the Result from the Dividend
We subtract $5x + 5$ from the new dividend $5x + 5$ to get $0$.
The Final Answer
After following the steps of polynomial long division, we find that the value of A is $5$.
Q&A
Q: What is the value of A in the division table?
A: The value of A is $5$.
Q: How do you perform polynomial long division?
A: To perform polynomial long division, you divide the highest degree term of the dividend by the highest degree term of the divisor, and then multiply the entire divisor by the result and subtract it from the dividend. This process is repeated until the degree of the remainder is less than the degree of the divisor.
Q: What is the remainder in the division table?
A: The remainder in the division table is $0$.
Q: How do you determine the value of A in the division table?
A: To determine the value of A in the division table, you follow the steps of polynomial long division and identify the value of A at the end of the process.
Conclusion
In this article, we followed the steps of polynomial long division to find the value of A in the division table. We performed the division and identified the value of A as $5$. We also answered some common questions related to polynomial long division and the division table.