Transcript Chapter 9.5 Notes: Solve Polynomial Equations in Factored Form

Chapter 9.5 Notes: Solve
Polynomial Equations in Factored
Form
Goal: You will solve polynomial equations.
• Zero-Product Property:
Let a and b be real numbers. If ab = 0, then a = 0 or
b = 0.
i.e. (x + 8)(x – 3) = 0
i.e. 2x(x – 10) = 0
Ex.1: Solve (x – 4)(x + 2) = 0
Ex.2: Solve (x – 5)(x – 1) = 0
Ex.3: Solve (2x + 5)(3x – 2) = 0
Ex.4: Solve 8x(3x – 6) = 0
Greatest Common Factor (GCF)
• The Greatest Common Factor of two or more
whole numbers is the largest whole number that
divides evenly into each of the numbers.
• The Greatest Common Factor of two or more
same variable terms with exponents is the lowest
exponent that goes into each of the exponents with
the same variable.
i.e. 14; 24
i.e. 6x5; 30x4
i.e. 45x4y; 60x5y2
Factoring
• To solve a polynomial equation using the zeroproduct property, you may need to factor the
polynomial, which involves writing it as a product
of other polynomials.
• One step in factoring is to look for the greatest
common monomial factor of the polynomial’s terms.
Ex.5: Factor out the greatest common monomial
factor.
a. 12x + 42y
b. 4x4 + 24x3
Ex.6: Factor out the greatest common monomial
factor.
a. 8x + 12y
b. 14y2 + 21y
Ex.7: Solve the equation by factoring.
a. Solve 2x2 = -8x
b. Solve 3x2 = -18x
Roots
• A root of a polynomial involving x is a value of x
for which the corresponding value of the polynomial
is 0.
– Roots means the same thing as solutions.
Ex.8: Find the roots of 6x2 – 15x.
Ex.9: Find the roots of 4s2 – 14s.
Ex.10: Solve 3s2 – 9s = 0.
Ex.11: Find the roots of a2 + 5a.
Vertical Motion
• A projectile is an object that is propelled into the air
but has no power to keep itself in the air.
– A thrown ball is a projectile, but an airplane is
not.
• The height of a projectile can be described by the
vertical motion model.
• Vertical Motion Model:
The height h (in feet) of a projectile can be modeled
by
h = -16t2 + vt + s
where t is the time (in seconds) the object has been
in the air, v is the initial vertical velocity (in feet per
second), and s is the initial height (in feet).
Ex.12: As a salmon swims upstream, it leaps into the
air with an initial vertical velocity of 10 feet per
second. After how many seconds does the salmon
return to the water?