Math Problem Statement
Solution
We are given that is a factor of the polynomial , and we are asked to find the value of .
Since is a factor, by the Factor Theorem, the polynomial should equal zero when . Therefore, we substitute into the polynomial and set it equal to zero:
Now, let's compute each term:
Now substitute these values into the equation:
Simplify the constant terms:
So the equation becomes:
Now, solve for :
Thus, the value of is .
Would you like further details on any step, or have any other questions? Here are some related questions to expand on this concept:
- What is the Factor Theorem and how is it used to solve polynomial equations?
- How do you perform polynomial division when factoring higher-degree polynomials?
- How can the Remainder Theorem be applied to polynomials?
- What are synthetic division and its benefits over long division in polynomial problems?
- How would the approach change if were a factor instead?
Tip: Whenever you're working with polynomials and factors, using the Factor Theorem is a quick and efficient method to find unknown constants like .
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Math Problem Analysis
Mathematical Concepts
Algebra
Polynomials
Factor Theorem
Formulas
Substitution of x to verify factor
Factor Theorem
Theorems
Factor Theorem
Suitable Grade Level
Grades 9-11