Fill in the blank to correctly complete each sentence. In the term -6x2y, -6 is the ______.
목차
- 0. Review of Algebra4h 18m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations1h 43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 5m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 22m
- 10. Combinatorics & Probability1h 45m
0. Review of Algebra
Multiplying Polynomials
Problem 13
교과서 질문
In Exercises 9–22, multiply the monomial and the polynomial.5x³ (2x⁵−4x²+9)
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Identify the expression to be multiplied: \(5x^3\) is the monomial and \((2x^5 - 4x^2 + 9)\) is the polynomial.
Apply the distributive property: Multiply the monomial \(5x^3\) by each term in the polynomial separately.
Multiply \(5x^3\) by the first term \(2x^5\): Use the rule \(a^m \cdot a^n = a^{m+n}\) to combine the exponents.
Multiply \(5x^3\) by the second term \(-4x^2\): Again, use the exponent rule to combine the exponents.
Multiply \(5x^3\) by the constant term \(9\): Remember that multiplying by a constant does not change the variable part.
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TextbookSolutions.keyConceptsTitle
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Monomials
A monomial is a single term algebraic expression that consists of a coefficient and one or more variables raised to non-negative integer powers. For example, in the expression 5x³, 5 is the coefficient and x is the variable raised to the power of 3. Understanding monomials is essential for performing operations like multiplication with polynomials.
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Introduction to Polynomials
Polynomials
A polynomial is an algebraic expression that consists of multiple terms, each of which is a monomial. Polynomials can be classified by their degree, which is the highest power of the variable in the expression. In the given example, 2x⁵ - 4x² + 9 is a polynomial with three terms, and recognizing its structure is crucial for correctly applying multiplication with a monomial.
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Distributive Property
The distributive property states that a(b + c) = ab + ac, allowing us to multiply a single term by each term in a polynomial. This property is fundamental when multiplying a monomial by a polynomial, as it ensures that each term in the polynomial is multiplied by the monomial separately, leading to the correct expansion of the expression.
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Multiply Polynomials Using the Distributive Property
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