Use the ac test to determine which of the following trinomials can be factored.
Find the values of m and n for each trinomial that can be factored. 
x(squared) - 3x +7 
thanks

Example 1 (your example):
1x² - 3x + 7

Multiply the 1 by the 7
That gives 7.
Now ask "Can you think of two positive integers that have product 7 and
SUM 3?"  (It's "SUM" because the last sign is +)
The answer is no.
So it CANNOT be factored.

Example 2:
1x² + 4x - 21

Multiply the 1 by the 21
That gives 21.
Now ask "Can you think of two positive integers that have product 21 and
DIFFERENCE 4?"  (It's "DIFFERENCE" because the last sign is -)
The answer is yes, because 7·3 = 21 and 7-3=4
So it CAN be factored.

Example 3:

2x² - 7x + 6

Multiply the 2 by the 6
That gives 12.
Now ask "Can you think of two positive integers that have product 12 and
SUM 7?"  (It's "SUM" because the last sign is +)
The answer is yes, because 4×3=12 and 4+3=7
So it CAN be factored.

Example 4

16x² - 8x + 1

Multiply the 16 by the 1
That gives 16.
Now ask "Can you think of two positive integers that have product 16 and
SUM 8?"  (It's "SUM" because the last sign is +)
The answer is yes, because 4·4 = 21 and 4+4=8
So it CAN be factored.


Example 5

16x² - 8x - 1

Multiply the 16 by the 1
That gives 16.
Now ask "Can you think of two positive integers that have product 16 and
DIFFERENCE 8?"  (It's "DIFFERENCE" because the last sign is +)
The answer is no.
So it CANNOT be factored.

Edwin