Fill in the blank for remainder therom

x 3 + x 2 - 21x - 45 = (x + 3)(x - 5)(x+? )

Not sure about remainder theorem but I'm sure that the last terms should all multiply tho the last term

see the expanded form is -45

so the last terms of each binomial should multiply to -45

3 times -5 times ?=-45
-15 times ?=-45
divide by -15
?=3

the question mark is 3

(3x+2)(2x+5) , (x-3)(x-1), (2x-3)(5x+1), (3x-1)^2? (3x+2)(2x+5) ,
(x-3)(x-1),
(2x-3)(5x+1),
(3x-1)^2

Expressions A, B, and D

Step-by-step explanation:

Expression A works because anything to the power of 0 is equal to one. Therefore, 1/1 = 1.

Expression B works because a negative number that is put to an even-numbered power will end up being positive. Therefore, -1*-1*-1*-1 = 1.

Expression C does NOT work because a negative number that is put to an odd-numbered power will end up being negative (-1*-1*-1*-1*-1*-1*-1 = -1).

Expression D works because positive 1 put to any power will end up being 1, for 1 times itself will end up being 1. Therefore, (you get the idea).

Expression E does NOT work because a number put to a negative power will end up becoming a fraction. 13^-1 is the same thing as writing 1/13. Therefore, 1/(1/13) will equal 13.

Hope this helps!