Assignment:
Find the greatest common factor for each group of monomials.
Q1.) 16x^2z, 40xz^2, 72z^3
Factor out the GCF in each expression.
Q2.)15x^2y^2 – 9xy^2 + 6x^2y
Factor out the GCF in each expression.
Q3.) a (a+1) -3 (a+1)
Factor each polynomial.
Q4.) 9a^2 – 64b^2
Factor each polynomial completely.
Q5.) x^3y + 2x^2y^2 + xy^3
Use grouping to factor each polynomial completely.
Q6.) x^3+ax+3a+3x^2
Factor each polynomial. If the polynomial is prime, say so.
Q7.) 18z+45+z^2
Factor each polynomial.
Q8.) h^2 - 9hs + 9s^2
Factor each polynomial completely.
Q9.) 3x^3y^2 - 3x^2y^2 + 3xy^2
Factor each trinomial using the ac method.
Q10.) 2x^2+11x+5
Q11.) 21x^2+2x-3
Q12.) 8x^2-10x-3
Factor each polynomial completely.
Q13.) a^2b+2ab-15b
Factor each polynomial completely.
Q14.) m^4 – n^4
Factor each polynomial completely. If a polynomial is prime, say so.
Q15.) 3x^3 – 12x
Q16.) 8b^2+24b+18
Q17.) 3x^2-18x-48
Q18.) 9x^2 + 4y^2
Solve by factoring.
Q19.) 2h^2-h-3=0
Solve each equation.
Q20.) 2w(4w+1)=1
Solve each equation.
Q21.) x^2-36=0
Q22.) x^3=4x
Q23.) (x-3)^2 + (x+2)^2=17
Q24.)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?
Q25.)Winter wheat. While finding the amount of seed needed to plant his three square wheat fields, Hank observed that the side of one field was 1 kilometer longer than the side of the smallest field and that the side of the largest field was 3 kilometers longer than the side of the smallest field. If the total area of the three fields is 38 square kilometers, then what is the area of each field?
Q26.)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.
Q27.)Rectangular stage. One side of a rectangular stage is 2 meters longer than the other. If the diagonal is 10 meters, then what are the lengths of the sides?
Q28.)Throwing a wrench. An angry construction worker throws his wrench downward from a height of 128 feet with an initial velocity of 32 feet per second. The height of the wrench above the ground after t seconds is given by s(t)= -16t^2 - 32t + 128.
a) What is the height of the wrench after 1 second?
b) How long does it take for the wrench to reach the ground?
Provide complete and step by step solution for the question and show calculations and use formulas.