Question

The profit for a certain company can be modeled by P(t) = t3 + 5t2 - 4t - 20, where t is the time in days. Use factoring to determine the values of t for which P(t) = 0.

Answer 1

as the last term is 20 the roots of the equation will be factors of 20
us the factor theorem to find one root
P(2) = 8 +20 - 8 - 20 = 0

so t - 2 is one factor

now you can use long division or synthetic division to find the other factors

Answer 2

the other one is t-5?

Answer 3

i mean 4

Answer 4

sorry i was wrong to say all the roots would be factors of 20
2 certainly is but the otrhers may not be whole numbers

Answer 5

its best to do the division at this stage

Answer 6

the quotient is t^2 + 7t +10

can you factor this?

Answer 7

do you agree with that result ?

Answer 8

yes (t+5)(t+2)

Answer 9

ok so now you have your values of t from
P(t) = (t -2)(t + 2)(t + 5) = 0

Answer 10

and those are all the roots?

Answer 11

roots are 2, -5 and -2

Answer 12

ok thansk

Answer 13

yw