Factor:
12x2 - 21

a) (6x + 3)(2x + 7)
b) (12x + 7)(x + 3)
c) (3x + 7)(4x - 3)
d ) prime

When you factor this, the easiest way to do it is to set the expression equal to 0 and then factor out anything common to get it into a simpler form. 3 goes into both 12 and 21. . Now of course, , so that means that . We solve for x to get and and finally that . 4 is a perfect square that can be simplified, so that leaves us with . If we expand that back out we have the 2 factors as . Obviously, that is not one of your choices, so your choice is the last one: prime.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for