Math Problem Statement
Solution
To solve each part of question 9, we need to use polynomial long division or reverse the division process by finding the divisor, given the dividend, quotient, and remainder.
The relationship is based on:
We can rearrange this to solve for the divisor:
Let's go through each part.
(a)
- Dividend:
- Quotient:
- Remainder:
Substitute the values into the formula:
Solve for the divisor by dividing:
Perform polynomial division to find the divisor.
(b)
- Dividend:
- Quotient:
- Remainder:
Substitute into the relationship:
Solve for the divisor:
Simplify and perform polynomial division to find the divisor.
(c)
- Dividend:
- Quotient:
- Remainder: 31
Solve for the divisor:
Perform polynomial division to find the divisor.
(d)
- Dividend:
- Quotient:
- Remainder: 19
Solve for the divisor:
Simplify and perform polynomial division to find the divisor.
Would you like a detailed step-by-step breakdown for any specific part of this solution?
Here are five related questions for further exploration:
- How do you perform polynomial long division step-by-step?
- What are the key differences between polynomial division and synthetic division?
- How can you verify the result of a polynomial division problem?
- What is the remainder theorem and how does it apply to these problems?
- How can you factor polynomials efficiently when solving division problems?
Tip: In polynomial division, always ensure the degrees of both the dividend and divisor are in descending order to avoid confusion.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Polynomial Division
Algebra
Remainder Theorem
Formulas
Dividend = (Divisor × Quotient) + Remainder
Divisor = (Dividend - Remainder) / Quotient
Theorems
Polynomial Long Division
Remainder Theorem
Suitable Grade Level
Grades 10-12
Related Recommendation
Solve Polynomial Division Problem: Quotient and Remainder
Polynomial Division: Quotient and Remainder Calculation
Polynomial Division Table Completion with Given Dividend, Quotient, and Remainder
Polynomial Division and Remainder Theorem: Step-by-Step Solution
Cubic Polynomial Remainder with Quadratic Divisors