Question

14x^2 + 37x + 5....Richard is designing a new website for students to create study groups and collaborate with other students.

The site will launch with five study groups, each with its creator as its only member, and Richard anticipates that two study groups will be added every month. He also estimates that seven new members will be added to each study group every month.

Answer 1

Answers:
1) The constant of the polynomial expression represents the:
number of group members when the site launches

2) The binomial (1+7x) is a factor of the polynomial expression and represents the:
number of members per group after x months

Solution:
1) The estimate for the total number of groups members (y) is given by the polynomial expression:
y=14x^2+37x+5
where x is the number of months since the site's launch.

When the site launchs:
x=0→y=14(0)^2+37(0)+5=14(0)+0+5=0+0+5→y=5
The number of group members when the site launches is 5
And the problem says: "The site will launch with five study groups"

2) The site will launch with five study groups, each with its creator as its only member, then the number of members per group is 1.
Richard estimates that seven new members will be added to each study group every month (x), then:
The number of members per group after x months will be: 1+7x