Since we know one root, which is -3, we can use synthetic division to find (x+3) would need to be multiplied by to get the original polynomial. Then, we factor the quadratic to find the other two factors, which are 1/2 and -2
Let's split the problem in non-intersecting subsets: we have good wood racquets, defective wood rackets, good graphite racquets, defective graphite rackets.
The probability that the racket is wood or defective covers the following subsets: good wood, defective wood and defective graphite, which have, respectively, , and elements.