Lesson 8-6 Multiplying a Polynomial by a Monomial

Multiply a Polynomial by a Monomial Ex. 1 Use the Distributive Property to multiply a polynomial by a monomial. Find -2x 2 (3x 2 - 7x + 10). 3x 2 - 7x + 10 (x) -2x 2

Multiply a Polynomial by a Monomial Use the Distributive Property to multiply a polynomial by a monomial. Find 6y(4y 2 - 9y + 7).

Simplify Expressions Ex. 2 When expressions contain like terms, simplify by combining the like terms. Simplify 4(3d 2 + 5d) - d(d 2 - 7d + 12) = 4(3d 2 ) +4( 5d) +(-d)(d 2 ) -(-d)(7d) +(-d)( 12)Distributive Property = 12d d + (-d 3 ) - (-7d 2 ) + (-12d) Product of Powers = 12d d -d 3 + 7d 2 -12dSimplify = -d 3 + (12d 2 + 7d 2 ) + (20d - 12d)Commutative and Associative Properties = -d d 2 + 8dCombine like terms

Simplify Expressions When expressions contain like terms, simplify by combining the like terms. Simplify 3(2t 2 - 4t -15) + 6t(5t + 2)

Ex. 3 Greg pays a fee of $20 a month for local calls. Long-distance rates are 6 ¢ per minute for in-state calls and 5¢ per minute for out-of-state calls. Suppose Greg makes 300 minutes of long-distance phone calls in January and m of those minutes are for in-state calls. Use Polynomial Models = service fee + in-state minutes B+20=m 6 ¢ per minute + out-of-state minutes  .06  +(300-m) Bill Find an expression for Greg’s phone bill in January. Let B = the phone bill in January. 5 ¢ per minute.05 = m + 300(.05) - m(.05) = m m = m Evaluate the expression to find the cost if Greg had 37 minutes of in- state calls in January. = m = (37) = Greg’s bill was $35.37

Entertainment: Admission to the Super Fun Amusement Park is $10. Once in the park, super rides are an additional $3 each and regular rides are an additional $2. Sarita goes to the park and rides 15 rides, of which s of those 15 are super rides. A.Find an expression for how much money Sarita spent at the park. B. Evaluate the expression to find the cost if Sarita rode 9 super rides.

Ex. 4 Polynomials on Both Sides Solve y(y - 12) + y(y + 2) + 25 = 2y (y + 5) - 15 y 2 -12y + y 2 + 2y + 25 = 2y y y 2 -10y + 25 = 2y y y + 25 = 10y y = -40 y = 2