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12.1/12.2 Polynomials, p590/596 Warm Up Identify the base and exponent of each power.

12.1/12.2 Polynomials, p590/596 Warm Up Identify the base and exponent of each power. 1. 3 4 2. 2 a 3. x 5 Identify the coefficient (number in front) of each term. 4. 3 x ⁴ 5. ab 6. - ab Use the Distributive Property (pass out) to simplify. 7. 9(6x + 7) 8. 4(10x – 2).

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12.1/12.2 Polynomials, p590/596 Warm Up Identify the base and exponent of each power.

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  1. 12.1/12.2 Polynomials,p590/596 Warm Up Identify the base and exponent of each power. 1. 34 2. 2a 3. x5 Identify the coefficient (number in front) of each term. 4. 3x⁴ 5. ab 6. - ab Use the Distributive Property (pass out) to simplify. 7. 9(6x + 7) 8. 4(10x – 2) Preview of Algebra 1 Prep. for 10.0 Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques. Also 7AF1.2 LO: I willsimplifypolynomialsby identifying & combining like terms. 1st Identify the like terms 2nd Combine the Coefficients 3rd Combine the Constants

  2. Remember: Terms are separated by addition or subtraction signs • Monomial- __ term • Binomial- __ terms • Trinomial- __ terms • Polynomial- ___ terms 4x2+2x5-xy+5 Simplify polynomials-add or subtract LIKE TERMS. LIKE TERMS- Same Variable, Same Exponent Like terms 4a3b2 + 3a2b3 – 2a3b2 The variables have different powers. Not like terms

  3. LIKE TERMS- Same Variable, Same Exponent • Identify the like terms in each polynomial. • 5x3 + y2 + 2 – 6y2 + 4x3 • 3a3b2 + 3a2b3 + 2a3b2– a3b2 • C. 7pq + 7p q + 7pq 2 2 3 3 2

  4. 1st Identify the like terms 2nd Combine the Coefficients 3rd Combine the Constants • Simplify the polynomials. • 4x2 + 2x2 + 7 – 6x + 9 • B. 3n m –6nm + nm – 8nm • C. 2x + 5x + 6 – 4x + 9 • D. 2np–7np + n p – 9n p 5 4 3 5 4 3 3 3 5 4 6 5 4 6 12.1/12. Day 1 AYR? p587even

  5. 12.2 Day 2 You may need to use the DISTRIBUTIVE PROPERTY to simplify. YOUR PARENTHESES GOODBYE. To remove the parentheses: multiply 1st, the add or subtract. - ___ Before: Now: 1st Identify the like terms 2nd Combine the Coefficients 3rd Combine the Constants

  6. Simplify. • 2(x3 + 5x2) • B. –2(6m p + 8mp) + m p • C. –4(3m n + 7mn) + m n YOUR PARENTHESES GOODBYE. To remove the parentheses: multiply 1st, the add or subtract. 3 2 2 1st Identify the like terms 2nd Combine the Coefficients 3rd Combine the Constants 3 2 2

  7. 2(r2 + rh) = 3a(b2 + c) = A. The surface area of a right cylinder can be found by using the expression 2(r2 + rh), where r is the radius and h is the height. Use the Distributive Property to write an equivalent expression. YOUR PARENTHESES GOODBYE. To remove the parentheses: multiply 1st, the add or subtract. B. Use the Distributive Property to write an equivalent expression for 3a(b2+ c). 1st Identify the like terms 2nd Combine the Coefficients 3rd Combine the Constants

  8. 12.2 RM & SRe p593 & p599 Identify the like terms in each polynomial. 1. 2x2 – 3z + 5x2 + z + 8z2 2. 2ab2 + 4a2b – 5ab2 – 4 + a2b Simplify. 3. 5(3x2 + 2) 4. –2k2 + 10 + 8k2 + 8k – 2 5. 3(2mn2 + 3n) + 6mn2

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