# Algebra - Factorization Problems

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? 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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