Assignment:
Q1. A rectangular painting with a width of x centimeters has an area of x^2 + 50x square centimeters. Find a binomial that represents the length.
Q2. The amount of an investment of P dollars for t years at simple interest rate r is given by A= P +Prt.
A. rewrite this formula by factoring out the greatest common factor on the right-hand side.
B. Find A if $8300 is invested for 3 years at a simple rate of 15%
Q3. Factor each polynomial. If it is prime say so.
a. 18z+45+z^2
b. x^2-5xs-24s^2
c. –4w^3-16w^2+20w
Q4. A triangular sail has an area of x^2+5x+6 square meters and a height of x+3 meters. Find the length of the sail’s base.
Q5. Factor trinomial using the ac method.
15x^2-7x-2
Q6. Factor polynomial
-36a^2b+21ab^2-3b^3
Q7. Factor each polynomial completely, given that the binomial following it is a factor of the polynomial.
x^3+2x^2-5x-6, x+3
Q8. Factor each difference or sum of cubes.
u^3-125v^3
Q9. Factor polynomial tell if its prime.
32a^2+4a-6
Q10. Solve equation
a. 2h^2-h-3=0
b. 2w(4w+1)=1
c. 1/18h^2 – 1/2h + 1=0
Q11. One side of a rectangular stage is 2 meters long than the other. If the diagonal is 10 meters, then what are the lengths of the sides?
Q12. 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 heading toward the same crossing. How far is the train form the crossing?
Provide complete and step by step solution for the question and show calculations and use formulas.