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Questions and Answers
Which of the following is the process of factoring a monomial from a polynomial?
Which of the following is the process of factoring a monomial from a polynomial?
- Finding the greatest common factor for the constants and the variable terms
- Identifying the factors of the monomial
- Checking for common factors in two constants
- Using the distributive property to factor out the greatest common factor (correct)
What are the factors of the monomial 10x^4?
What are the factors of the monomial 10x^4?
- 10x, 10x^2, 10x^3, 10x^4
- 1, 10, 5, 2
- x, x^2, x^3, x^4
- 10, x, 10x, x^2, 10x^2, x^3, 10x^3, x^4 (correct)
What is the greatest common factor of the constants 30 and 42?
What is the greatest common factor of the constants 30 and 42?
- 2 (correct)
- 6
- 5
- 3
What is the greatest common factor of the variable terms x^3 and x^4?
What is the greatest common factor of the variable terms x^3 and x^4?
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What is the result of factoring out the greatest common factor from the polynomial 10x^3 + 15x^2?
What is the result of factoring out the greatest common factor from the polynomial 10x^3 + 15x^2?
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Study Notes
Factoring Monomials from Polynomials
- Factoring a monomial from a polynomial involves identifying a common factor and rewriting the polynomial as a product of that factor and a simplified polynomial.
Factors of the Monomial 10x^4
- The factors include 1, 2, 5, 10 (numerical factors) and x, x^2, x^3, x^4 (variable factors).
- The full factorization of 10x^4 is 10 * x * x * x * x.
Greatest Common Factor of 30 and 42
- The greatest common factor (GCF) for 30 and 42 is 6.
- GCF is determined by identifying the largest number that divides both constants without leaving a remainder.
Greatest Common Factor of x^3 and x^4
- The GCF of the variable terms x^3 and x^4 is x^3.
- This is because x^3 is the lowest power of the variable common to both terms.
Factoring Out the Greatest Common Factor from 10x^3 + 15x^2
- The GCF of the terms 10x^3 and 15x^2 is 5x^2.
- Factoring 5x^2 out of the polynomial gives the result: 5x^2(2x + 3).
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