5.2 Polynomials Objectives: Add and Subtract Polynomials

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Presentation transcript:

5.2 Polynomials Objectives: Add and Subtract Polynomials Multiply Polynomials

Vocabulary Binomial – a polynomial with 2 terms Trinomial – a polynomial with 3 terms. Degree of a polynomial – the highest degree of the monomials in the polynomial For 5x⁶y²+2x⁴y³, the degree for each monomial is 8 and 7. The degree of the polynomial is 8 since it is higher. Polynomial – a monomial or a sum of monomials such as 5x⁴-3y. Terms – the monomials that make up a polynomial Like terms – monomials with the same variable(s) with the same exponent on those variables.

Determine whether each expression is a polynomial Determine whether each expression is a polynomial. If it is a polynomial, state the degree. -4x⁵y²-6y³z⁸ yes, degree: 11 2. not a polynomial 7x⁴-9x+3 yes, degree: 4

Adding and Subtracting Polynomials Examples: (2x²-5x+3)+(-4x²+x-9)= -2x²-4x-6 (4a²-8a+2)-(7a²+6a-8)= (4a²-8a+2)+(-7a²-6a+8)= -3a²-14a+10 To add polynomials, add like-terms. When adding or subtracting like-terms, add or subtract the coefficients, but not the exponents. For subtraction, change signs of 2nd polynomial to opposites then use addition.

Multiplying a polynomial by a monomial Use the distributive property. (multiply coefficients and add exponents on like-bases) Example: -3x²y³(5xy⁴-7x²y⁵)= -15x³y⁷+21x⁴y⁸ ⅔ab(-6a-9b+12ab)= -4a²b-6ab²+8a²b²

Multiplying a Binomial by a Binomial Use FOIL Method or Distributive Property Examples: (FOIL) (x-8)(4x+5) 4x²+5x-32x-40 4x²-27x-40 (a³-6)(a³+3) a⁶+3a³-6a³-18 a⁶-3a³-18 Distributive Property: (x-8)(4x+5)= x(4x+5)-8(4x+5)= 4x²+5x-32x-40= 4x²-27x-40

Column Method and Box Method (3x+6)(7x-5) 3x+6 x 7x-5 -15x-30 21x²+42x+ 0 21x²+27x-30 Box Method (helpful for multiplying trinomials) (x-5)(2x+9) x -5 2x 9 2x²-x-45 2x² -10x 9x -45

Power of a Binomial To take a binomial to a power, write that binomial down that number of times and use your method of choice for multiplying binomials. Example: (2x-5)² (2x-5)(2x-5) 4x²-10x-10x+25 4x²-20x+25

Homework Page 231 16-52 even