Math Problem Statement
Solution
Let's go through each question one at a time.
Question 1
To find the remainder when is divided by each of the expressions, we can use the Remainder Theorem. According to this theorem, if we want to find the remainder of a polynomial when divided by , we evaluate .
Given :
a)
To find the remainder when is divided by , we substitute : So, the remainder is 23.
b)
To find the remainder when is divided by , we substitute : The remainder is -92.
c)
When dividing by , we substitute : The remainder is -1.
Question 2
We need to determine the value of such that the expression leaves a remainder of when divided by .
Using the Remainder Theorem, we substitute and set the result equal to : So, the value of is 15.
Would you like more details or have any further questions?
Related Questions:
- How does the Remainder Theorem apply to polynomials of higher degrees?
- What is the difference between the Remainder Theorem and Synthetic Division?
- How would we find the quotient in addition to the remainder?
- What changes when dividing by a binomial like instead of ?
- How would we determine the remainder if the divisor was ?
Tip: When using the Remainder Theorem, always check if the divisor is of the form for straightforward substitution.
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Math Problem Analysis
Mathematical Concepts
Algebra
Polynomials
Remainder Theorem
Formulas
Remainder Theorem: f(a) when dividing by (x - a)
Theorems
Remainder Theorem
Suitable Grade Level
Grade 10-12