Math Problem Statement
The degree of the polynomial is 3. What is the value of m?
Solution
To find the value of for which the degree of the polynomial is 3, let's analyze the polynomial given in the image:
Degree of the Polynomial
The degree of a polynomial is determined by the highest sum of the exponents in any single term.
- First term: has a degree of (since ).
- Second term: has a degree of (since the exponent of is and the exponent of is ).
- Third term: has a degree of (since the exponent of is ).
Since the degree of the polynomial is given as , the term with the highest degree must equal 3. The highest degree is from the term , which is .
Equation:
Solving for :
Thus, the value of is .
Would you like further details or have any questions?
Related Questions:
- What happens to the degree if is greater than 2?
- How does the presence of affect the degree of each term?
- What is the degree of the polynomial if is less than 2?
- How do coefficients affect the degree of a polynomial?
- Can you find a value of that would make the polynomial's degree equal to 4?
Tip:
Always remember that the degree of a polynomial is determined by the term with the highest sum of exponents, not just the highest exponent of a single variable.
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Math Problem Analysis
Mathematical Concepts
Polynomials
Degree of a Polynomial
Formulas
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Theorems
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Suitable Grade Level
Grades 9-12
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