Algebra I Distributive Property Worksheet



CC Algebra IName_________________________Polynomials Combining Like TermsDate_________ Aim: What are Polynomials and how do we get them in standard form?Do Now:Distribute2(x+3)2. 3(2x+3)3. -2(4x-5)*Distributive Property Multiply the term being distributed to all terms inside of ____________________Always stop arrows when the parentheses endBe careful of negative signs for multiplication*Combine Like TermsTerms must have the exact same __________________and __________________ Add or Subtract the coefficients of like termsPolynomialsMonomialBinomialTrinomialWhat is the classification of the following polynomial by its degree? By its number of terms? 5x4 ? 3x + 4x6 + 9x3 ? 12 ? x6 + 3x4Step 1Write the polynomial in standard form. First, combine any like terms. Then, place the terms of the polynomial in descending order from greatest exponent value to least exponent value.5x4 ? 3x + 4x6 + 9x3 ? 12 ? x6 + 3x4Combine like terms.Place terms in descending order.Step 2The degree of the polynomial is equal to the value of the greatest exponent. This will be the exponent of the first term when the polynomial is written in standard form.What is the degree of the polynomial?What is the leading term?What is the leading coefficient? -23082258763000 ExampleProblems: Simplify each expressionReminder: DISTRIBUTE BEFORE COMBINING LIKE TERMS & STANDARD FORMx + 3 – 5x + 7 + 4x2 – 4 (3a – 7) + 4a29ab + 3b2 – 7b2 + 8ab – 12 9 (x2 – 3) - 5x2x + 7x2 – 9x + 21x3 + 5x 5 (2r + 6) – 12r -7 (3m – 4) + 2x (2x + 7) + x (9 + 5x3)3t + 6 + 2t(3t - 6)8(2z + 4) – 3z(3z – 6)Vocabulary with PolynomialsRewrite the following polynomial in standard form: What is the constant term in the previous polynomial?What is the leading coefficient of each of the following polynomials? What is the degree of the following polynomial: Classify the polynomial by number of terms (give the word):Classify the polynomial by degree (give the word):_____ binomial_____ standard form_____ leading coefficient_____ monomial11. _____ degree12. _____ constant term13. _____ trinomiala. A polynomial with only one term.b. The number that does not multiply any power of x.c. A polynomial with two terms.d. Written with terms in descending order, from largest degree to smallest degree.e. A polynomial with four terms.f. The value of the exponent in a polynomial.g. The number in front of the first term of a polynomial.h. A polynomial with three terms.i. The first term of a polynomial. ................
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