From the January 2016 Common Core Algebra I Regents

We can ‘do the FOIL’ or double distributive and/or we can use the TI-84 to find the equivalence to the given. The choices look appealing as both 3 x 10 and 2 x 15 are factor pairs of 30.

To do FOIL, we do the parentheses first in each case and then multiply by x and see if it matches the given x^3 – 13x ^2 -30x

(1) FOILing (x + 3) (x – 10) gives x^2 – 10x + 3x – 30 = x^2 -7x -30 and when multiplied by x does not look like the original

(2) FOILing (x – 3) (x – 10) gives x^2 – 10x – 3x + 30 = x^2 -13x + 30 and when multiplied by x does not look like the original

(3) FOILing (x + 2) (x – 15) gives x^2 – 15x + 2x + 30 = x^2 -13x – 30 and when multiplied by x looks familiar!

(4) FOILing (x – 2) (x + 15) gives x^2 + 15x – 2x – 30 = x^2 +13x – 30 and when multiplied by x does not look like the original

Here is the TI-84 way — looking for equivalence 🙂

As you can see below answer choice (1) not a match

As you can see below answer choice (2) is also not equivalent:

Onto answer choice (3), see below: it’s a keeper –= this algebra is equivalent!!!!