I’m tutoring a high school pre-calc student who has to find the roots of a 3rd degree polynomial equation for homework, and I’m struggling to figure out what they are without using an online calculator or the cubic formula. Her teacher seems to suggest that there is another way to do it. Any thoughts?
$$525=(2t+3)(2t+5)(2t+7)$$
EDIT: New Age Special Effects, Inc., prepares computer software based on specifications by film directors. To simulate an approaching vehicle, they begin with a computer image of a 5cm by 7cm by 3cm box. The program increases each dimension at a rate of 2cm/sec. How long does it take for the volume V of the box to be at least 5 times its original size?