Exam 5: Polynomials: Factoring

Solve the problem. -Two cars leave an intersection. One car travels north; the other east. When the car traveling north had gone 12 miles, the distance between the cars was 4 miles more than the distance traveled by the car heading east. How far had the eastbound car traveled?

Factor. - $x^{2}+3 x y-18 y^{2}$

Factor. - $12 y^{2}+17 y+6$

Factor. - $20 z^{2}-3 z-9$

Factor. - $7 x^{2}-7 x-42$

Solve by factoring and using the principle of zero products. - $12 d^{2}+18 d+6=0$

Solve by factoring and using the principle of zero products. - $15 y^{2}+16 y+4=0$

Factor completely. - $\mathrm{x}^{2}-30 \mathrm{x}+225$

Determine whether the following is a difference of squares. - $t^{3}-25$

Determine whether the following is a trinomial square. - $x^{2}-4 x y+4 y^{2}$

Factor. - $21 m^{2}-17 r^{3}$

Factor. - $9 x^{2}-9 x-54$

Solve the problem. -In a sports league of $n$ teams in which each team plays every other team twice, the total number $N$ of games to be played is given by $\mathrm{N}=\mathrm{n}^{2}-\mathrm{n}$ . What is the total number of games to be played in a football league having 8 teams?

Factor. - $4 x^{2}-12 x y-16 y^{2}$

Solve the problem. -If an object is thrown upward with an initial velocity of $16 \mathrm{ft} / \mathrm{sec}$ , its height after $\mathrm{t}$ sec is given by $\mathrm{h}=16 \mathrm{t}-16 \mathrm{t}^{2}$ . Find the number of seconds before the object hits the ground.

Find the $x$ -intercepts of the graph of the equation. (The grids are intentionally not included.) - $y=x^{2}+2x-8$

Factor. - $10 \mathrm{z}^{2}+7 \mathrm{z}-12$

Provide an appropriate response. -A student was trying to solve the problem $2 x(6 x-8)=0$ . The student knew that he or she should set $6 \mathrm{x}-8=0$ but was confused about whether or not he or she should set $2 \mathrm{x}=0$ , or $2=0$ and $\mathrm{x}=0$ . How would you advise this student?

Determine whether the following is a difference of squares. - $\mathrm{x}^{2}-41$

Solve using the principle of zero products. - $(9 y+7)(2 y+5)=0$