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If x is an integer divisible by 3, is x squared divisible by 3?

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Q: If x is an integer divisible by 3 then is x2 divisible by 3?
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What is a counter example to falsify If x is an integer divisible by 3 then x2 is an integer divisible by 3?

Suppose x = sqrt(3*a) where a is an integer that is not divisible by 3. then x2 = 3*a which is divisible by 3. but x is not even rational and so is not an integer and is certainly not divisible by 3.

If x is an integer that is divisible by three then is x2 always divisible by 3?


If the domain of f(x)-x2 is integer values of x such that -3-x?


If x2 is an integer divisible by 3 then x is divisible by 3?

Yes. If x is not divisible by 3 then x leaves a remainder of 1 or 2 when it is divided by 3. That is, x is of the form 3y+z where z = 1 or 2. Then x2 = (3y+z)2 = 9y2 + 6yz + z2 = 3(3y2 + 2yz) + z2 The first part of this expression is clearly a multiple of 3, but z2 is not. Whether z = 1 or 2, z2 leaves a remainder of 1 when divided by 3.

An integer minus three times its reciprocal equals twenty six thirds What is the integer?

Call the unknown integer x. Then, from the problem statement, x - 3/x = 26/3, or:x2 - 3 = 26x/3; or x2 - (26/3)x - 3 = 0x = 9

What is The square of a positive integer is 4 more than 3 times the integer?

x2=3x+4 x2-3x-4=0 (x-4)(x+1)=0 x=4 or x=-1 Since you specified a positive integer, the number in question is 4.

Which of the following is divisible by 3 and 6 but is not divisible by 4?

All numbers of the form 6+12x are, for all integer x.

Can a number be divisible by 9 but not 3?

yes * * * * * Absolutely not! If it is divisible by 9 it must be divisible by 3. Here, if you want it, is a proof: x is divisible by 9 implies that x = 9*y for some integer y. Now 9 = 3*3, so writing 3*3 instead of 9 gives x = (3*3)*y so, by the associative property of multiplication, x = 3*(3*y) and then, by the closure of multiplication of integers, 3*y is also an integer. Say, z, for example. That is to say, x = 3*z which is equivalent to saying that x is divisible by 3.

What does divisible meabn?

For an integer x to be evenly divisible by another integer y, x/y must also be an integer. Here are some examples: 4/2=2. 15/3=5. 18/6=3. From these examples, you can see that 4 is divisible by 2, 15 is divisible by 3, and 18 is divisible by 6. When two numbers are not evenly divisible by each other, you end up with a remainder, or fractional/decimal answer. Here is an example: 25/2 =12.5

What is a grouping factor for polynomial x3 ax 3a 3x2?

x3 + ax + 3a + 3x2 = x (x2 + a) + 3 (a + x2) = x (x2 + a) + 3 (x2 + a) = (x2 + a)(x + 3) Checking the work: x3 + ax + 3x2 + 3a or x3 + 3x2 + 3a + ax = x2 (x + 3) + a (3 + x) = x2 (x + 3) + a (x + 3) = (x + 3)(x2 + a)

Find all integer values of x that make the equation or inequality true x2 equals 9?

that would be limited to 3 and -3 for values of x

What is the factor of x2 - 9?

(x + 3)(x - 3)

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