AIM: How do we multiply and divide polynomials? Do Now: 1) Put in standard form and find degree: 12y⁵ + 7y⁸ - 4y³ - 9y⁴ + 3y² - 18 +4y 2) Subtract 4a³ + 5a² - 3a + 8 from 2a³ - 4a² + 3a - 17

HW # 2 – Chapter 1 pg 21 #2,12,17,18 and divide 8r⁵ + 4r³s – 20r⁴t³ by 2r² Multiplying Polynomials First, how do we multiply monomials? Example 1 : Multiply 5a³ by 4a⁵ RULE : Multiply the coefficients and add the exponents for the variable

Multiply ¾p²q⁵ by ⅔q²r⁴ What if the variables are not the same or if there is more than one variable? Example 2: Multiply ¾p²q⁵ by ⅔q²r⁴ RULE – Still multiply coefficients , but add the exponents only on like variables.

Now that we can multiply monomials, how about polynomials Now that we can multiply monomials, how about polynomials? Anybody remember FOIL? The FOIL method is ONLY used when you multiply 2 binomials. Use the FOIL method to multiply the following binomials: (y + 3)(y + 7).

(y + 3)(y + 7). F tells you to multiply the FIRST terms of each binomial.

(y + 3)(y + 7). O tells you to multiply the OUTER terms of each binomial.

(y + 3)(y + 7). I tells you to multiply the INNER terms of each binomial. y2 + 7y + 3y

(y + 3)(y + 7). L tells you to multiply the LAST terms of each binomial. y2 + 7y + 3y + 21 Combine like terms. y2 + 10y + 21

Remember, FOIL reminds you to multiply the: First terms Outer terms Inner terms Last terms

Example 3 :Multiply (y + 4)(y – 3)

Example 4: Multiply (2a – 3b)(2a + 4b) 4a2 + 14ab – 12b2 4a2 – 14ab – 12b2 4a2 + 8ab – 6ba – 12b2 4a2 + 2ab – 12b2 4a2 – 2ab – 12b2

Group and combine like terms. Multiply (2x - 5)(x2 - 5x + 4) You cannot use FOIL because they are not BOTH binomials. You must use the distributive property. 2x(x2 - 5x + 4) - 5(x2 - 5x + 4) 2x3 - 10x2 + 8x - 5x2 + 25x - 20 Group and combine like terms. 2x3 - 10x2 - 5x2 + 8x + 25x - 20 2x3 - 15x2 + 33x - 20

Example 5 :Multiply (2p + 1)(p2 – 3p + 4) Example 6: Multiple (7c – 7)(3c² - 2c + 3)

Dividing Polynomial Expressions Example 7: Divide 12x²y³ + 15x⁴y⁵ by 3xy RULE : Divide each term of the polynomial by the monomial - * hint – when dividing like variables subtract the exponents

Example 8: Divide 54a³b⁵c² -30a⁴b⁴ + 42a⁶b⁷c⁵ by 6ab³