1. explain why the product of an integer multiplied by itself can never be negative.
If an integer is positive, a positive times a positive is a positive. If the integer is negative, a negative times a negative is still a positive, thus an integer times itself is always positive and never negative.
2. The product of two integers is -144,
The sum od the integers is -7
what are the two integers?
xy= -144, x+y=-7
x(-7-x)=-144
x^2+7x = 144
(x+16)(x-9)=0 solve for the two solutions, -16 and 9
x= 9, y=-16
PS. The above is probably not part of the grade school curriculum, you could just do trial & error.
3. how many different ways can you write -36 as the product of two or more integer factors?
-2x2xx3x3=-36. There are two 2s and two 3s, thus there is 2x2=4 ways to write +36. The negative sign can be on any factor and there are two different types of factors for each combination, thus there is 4x2=8 ways to write -36 as a product of factors.
Once again, you cal also list them out.
4. suppose you divide two integers.
when is the quotient:
a) less than both integers?
If both numbers are positive and larger than one, and the divisor is larger than the square root of the dividend eg. 6/3=2, 3>root 6
b) greater than both integers?
If both integers are negative, eg. -3/-2=1.5
c) between the two integers?
If one integer is positive and another is negative, e.g -6/3=-2
or if both numbers are positive and larger than one, and the divisor is smaller than the square root of the dividend
12/3=4, 3
