what are the binomial factors of t squared minus 12t minus 45?

Question

The choices are

a) (t-9)(t-5)

b) (t+3)(t-15)

c) (t-15)(t-3)

d) (t-3)(t+15)

Answer 1

t²-12t-45. In (a)-(d) the product of the constants in each case is 45.

The sign of 45 is negative which means that we must have a plus sign in one binomial and a minus in the other. So we can eliminate (a) and (c). That leaves (b) and (d). The difference between the absolute values of the constants has to be 12, and to get -12 we need -15 and +3, so option (b) is the correct answer.