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Questions and Answers
A polynomial that cannot be factored further is called a reducible polynomial.
A polynomial that cannot be factored further is called a reducible polynomial.
False (B)
The method of factoring by grouping involves finding the greatest common factor (GCF) of all terms in the polynomial.
The method of factoring by grouping involves finding the greatest common factor (GCF) of all terms in the polynomial.
False (B)
The distributive property can be used to factor polynomials.
The distributive property can be used to factor polynomials.
True (A)
Factoring a polynomial always results in a product of binomials.
Factoring a polynomial always results in a product of binomials.
To check if a factored form is correct, you should multiply the factors to ensure they equal the original polynomial.
To check if a factored form is correct, you should multiply the factors to ensure they equal the original polynomial.
Prime polynomials are reducible polynomials that can be expressed as a product of simpler polynomials.
Prime polynomials are reducible polynomials that can be expressed as a product of simpler polynomials.
Flashcards
Irreducible polynomial
Irreducible polynomial
A polynomial that cannot be factored further is called an irreducible polynomial.
Factoring by grouping
Factoring by grouping
Factoring by grouping involves pairing terms with common factors and then factoring out the GCF from each pair.
Distributive property for factoring
Distributive property for factoring
The distributive property can be used to multiply factors and expand polynomials.
Factors of a polynomial
Factors of a polynomial
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Checking factored forms
Checking factored forms
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Prime polynomials
Prime polynomials
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Study Notes
Factoring Polynomials
Definition
- Factoring a polynomial means expressing it as a product of simpler expressions, called factors.
- Factoring is the reverse operation of multiplying polynomials.
Methods of Factoring
- Factoring out the greatest common factor (GCF)
- Find the GCF of all terms in the polynomial.
- Divide each term by the GCF.
- Factoring by grouping
- Group terms with common factors.
- Factor out the common factor from each group.
- Factoring quadratic expressions
- Look for two binomials that multiply to the original quadratic expression.
- Use the ac method or the reverse FOIL method to factor quadratic expressions.
Factoring Types
- Monomial factors
- Factoring out the GCF of a polynomial.
- Binomial factors
- Factoring a quadratic expression into two binomials.
- Trinomial factors
- Factoring a cubic expression into three binomials.
Key Concepts
- Factoring by decomposition
- Express a polynomial as a product of simpler polynomials.
- Irreducible polynomials
- Polynomials that cannot be factored further.
- Prime polynomials
- Irreducible polynomials that cannot be expressed as a product of simpler polynomials.
Tips and Tricks
- Look for common factors
- Factor out the GCF of all terms in the polynomial.
- Use the distributive property
- Expand and simplify the polynomial to reveal hidden factors.
- Check your work
- Multiply the factors to ensure they equal the original polynomial.
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