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Algebra - Factorization Problems

? Demonstrate that factoring a polynomial is the reverse of multiplying a polynomial.
? Use greatest common factor (GCF) to factor monomials out of quadratic trinomials.
? Factor single-variable polynomials by grouping.
? Factor quadratic trinomials.
? Factor multivariate polynomials by grouping.
? Factor differences of squares.
? Factor complete squares.
? Solve quadratic equations using the zero factor property.
? Apply the Pythagorean Theorem to real-life problems.

40. 16x2Z, 40xz2, 72z3

68. 15x2y2 -9xy2 + 6x2y

72. a(a + 1) -3(a +1)

16. 9a2 - 64b2

62. x3y + 2x2y2 + xy3

64. h2 - 9hs + 9s2

102. 3x3y2 - 3x2y2 + 3xy2

18. 2x2 + 11x + 5

26. 21x2 + 2x - 3

88. a2b + 2ab - 15b

36. m4 - n4

66. 8b2 + 24b + 18

72. 3x2 -18x - 48

82. 9x2 +4y2

18. 2h2 - h - 3 = 0

32. 2w(4w + 1) = 1

98. Avoiding a collision. A car is traveling on a road that
is perpendicular to a railroad track. When the car is
30 meters from the crossing, the car's new collision
detector warns the driver that there is a train 50 meters
from the car and heading toward the same crossing. How
far is the train from the crossing?

104. Venture capital. Henry invested $12,000 in a new
restaurant. When the restaurant was sold two years
later, he received $27,000. Find his average annual
return by solving the equation 12,000(1 _ r)2 _
27,000.

Team :

100. Demand for pools. Tropical Pools sells an aboveground
model for p dollars each. The monthly revenue for this
model is given by the formula

R(p)=0.08p2 +300p.
Revenue is the product of the price p and the demand
(quantity sold).
a) Factor out the price on the right-hand side of the
formula.
b) Write a formula D(p) for the monthly demand.
c) Find D(3000).
d) Use the accompanying graph to estimate the price at
which the revenue is maximized. Approximately how
many pools will be sold monthly at this price?

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