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Polynomials and Operations flashcards
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- What does terms and coefficients mean?Polynomial Vocabulary
- The building blocks and numerical multipliers of a polynomial.
- Can a variable exponent be negative in a polynomial term?Polynomial Vocabulary
- No, polynomial variable exponents are nonnegative integers.
- How would you define degree?Polynomial Vocabulary
- The highest nonzero exponent in a polynomial.
- What happens if a leading coefficient is zero?Polynomial Vocabulary
- That term does not determine degree.
- What is meant by monomials, binomials, trinomials?Polynomial Vocabulary
- Names based on the number of polynomial terms.
- Should like terms be combined before counting?Polynomial Vocabulary
- Yes, use the simplified expression.
- What does adding like terms mean?Adding and Subtracting Polynomials
- Polynomial addition by matching powers.
- Can 3x and 4x² combine as one term?Adding and Subtracting Polynomials
- No, their powers differ.
- How would you define subtracting expressions?Adding and Subtracting Polynomials
- Adding the opposite of every term in a polynomial.
- Why use parentheses around the second polynomial?Adding and Subtracting Polynomials
- They show that subtraction affects each term.
- What is meant by standard form?Adding and Subtracting Polynomials
- An ordered form of an equivalent polynomial.
- Does reordering terms change the value?Adding and Subtracting Polynomials
- No, addition is commutative.
- What does monomial distribution mean?Multiplying Monomials and Binomials
- Distribution together with product-of-powers rules.
- What happens to x·x?Multiplying Monomials and Binomials
- It becomes x².
- How would you define binomial products?Multiplying Monomials and Binomials
- A distributive expansion of two binomials.
- Why is the middle coefficient in (x+a)(x+b) equal to a+b?Multiplying Monomials and Binomials
- It comes from the two cross-products.
- What is meant by area model?Multiplying Monomials and Binomials
- A geometric representation of polynomial multiplication.
- What does the whole area equal?Multiplying Monomials and Binomials
- The sum of all partial-product areas.
- What does square of a sum mean?Special Products
- The expansion of a binomial multiplied by itself.
- Why is (a+b)² not just a²+b²?Special Products
- The cross-products total 2ab.
- How would you define square of a difference?Special Products
- The expansion of a difference multiplied by itself.
- What sign is the b² term?Special Products
- Positive, because (−b)(−b)=b².
- What is meant by conjugate product?Special Products
- A difference-of-squares product identity.
- Why is there no ab term?Special Products
- The cross-products ab and −ab cancel.
- What does numerical common factor mean?Factoring Out a GCF
- The largest common factor of term coefficients.
- Why choose the greatest rather than a smaller factor?Factoring Out a GCF
- It fully removes the shared numerical part in one step.
- How would you define variable common factor?Factoring Out a GCF
- The common variable power present in all terms.
- What if one term has no x?Factoring Out a GCF
- No x can be factored from every term.
- What is meant by checking by distribution?Factoring Out a GCF
- Verification that a factorization is equivalent.
- Why is a GCF factorization useful?Factoring Out a GCF
- It exposes structure for further solving or simplifying.