# factoring polynomial

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Find the prime factorization for each integer.

#6. 200

Find the greatest common factor for each group.

#10. 6a2b, 9ab2, 15a2b2

Complete the factorization of each binomial.

#14. a2 - a = - a( )

Factor each polynomial by factoring out the GCF.

#20. 2a2 - 4ab2 - ab

Factor each polynomial completely.

#26. 2a2 - 4a - 2

#30. t2 - 9w2

Factor each polynomial.

#36. a2 - 2a - 35

#42. v2 - 22v - 75

Factor completely.

#46. - 3t3 + 3t2 - 6t

Factor each polynomial completely.

#54. 2x2 - x - 10

#60. 10a2 + ab - 2b2

Factor completely.

#70. 16x2 - 2x - 3

#80. 4m2 + 20m + 25

#86. z4 - 81

Factor each polynomial completely, given that the binomial following it is a factor of the polynomial.

#90. x3 - 4x2 - 3x - 10, x - 5

Solve each equation.

#98. w3 + 5w2 - w = 5

#102. t2 + 1 = 13t

6

Solve each problem.

#104. Consecutive integers. Find three consecutive integers such that the sum of their squares is 77.

#108. Racquetball. The volume of rubber (in cubic centimeters) in a hollow rubber ball used in racquetball is given by:

V = 4/3 π R3 - 4/3 π r3,

Where the inside radius is r centimeters and the outside radius is R centimeters.

a) Rewrite the formula by factoring the right-hand side completely.

b) The accompanying graph (below) shows the relationship between r and V when R = 3. Use the graph to estimate the value of r for which V = 100 cm3.

#110. Towering antenna. A guy wire of length 50 feet is attached to the ground and to the top of an antenna. The height of the antenna is 10 feet larger than the distance from the base of the antenna to the point where the guy wire is attached to the ground.

What is the height of the antenna?

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The solution is comprised of different methods for factoring the polynomials.

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