9.4 Solve Polynomial Equations in Factored Form

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Presentation transcript:

9.4 Solve Polynomial Equations in Factored Form Students will *Use the Zero Product Property to solve polynomial equations *Identify greatest common monomial factors Use the Vertical Motion Model

Zero-Product Property Let a and b be real numbers. If ab = 0, then a = 0 and b = 0. Set each factor equal to 0 and solve. Solve: (x – 3)(x + 5) = 0 x – 3 = 0 and x + 5 = 0 x = 3 and x = -5

solve (3x – 4)(x + 8) = 0 (2x + 1)(5x – 4) = 0

Greatest Common Factor “UN”Distribute – look for what is common 6x + 8y 4 𝒙 𝟐 −𝟖𝒙 9 𝒂 𝟔 +𝟑 𝒂 𝟒 −𝟏𝟐 𝒂 𝟐

Factor and solve (Remember to set = 0 first) 6 𝑥 2 - 20x = 0 12 𝑥 2 = 18x

Vertical motion model finds the height of a projectile h is the height (in feet) t is the time (in seconds) 𝑣 0 is the initial velocity (feet per second) ℎ 0 is the initial height

h = - 16 𝑡 2 + v 0 t + ℎ 0 Write an equation for the situation below. A dolphin jumped out of the water with an initial velocity of 32 feet per second. After how many seconds did the dolphin reenter the water?

A dog jumps in the air with an initial velocity of 18 feet per second to catch a flying disc. How long does the dog remain in the air?

Computer practice http://www.regentsprep.org/Regents/math/ALGEBRA/AV6/PracFact4.htm

homework Page 578-580 #7-39 odd, 46-48 all, 51-55 all, 57