Are these correct, can you help me with the last 3?

Question

1. Find the g.c.f. and l.c.m. of the set of numbers {11, 13, 23}
answer: g.c.f. 1
l.c.m 3,289

2. -4+/6-8/ note: / / total value signs
answer -4+2=-2

3. 2(4x^2-3x+2)-3(x^-5x-8)
Can you simplify this ??

4. 6(V-2)-4(V+3)=10-42
answer??

5. 3/√x (3 is in the numerator, and √x is in the denominator)
how do you work this problem??

Answer 1

Your first two are right. Some notes:

1. If you don't already know, you can find the GCF by factoring the numbers and taking the factors they have in common. In this case, they only have 1 as a common factor. You can find the LCM by taking the factors and multiplying the highest powers of each multiple. In this case, you are simply multiplying all three numbers together. If the GCF of two or more numbers is 1, then the LCM is the product of those numbers.

2. Yes, though you can type |6-8| by holding SHIFT and pressing the slash key (by the ENTER key).

3. Multiply through and combine like terms (assuming x squared in the second part):
2(4x^2 - 3x + 2) - 3(x^2 - 5x - 8) =
8x^2 - 6x + 4 - 3x^2 + 15x + 24 =
5x^2 + 9x + 28
This cannot be factored any more.

4. Solve for V by multiplying through and getting V by itself:
6(V - 2) - 4(V + 3) = 10-42
6V - 12 - 4V -12 = -32
2V - 24 = -32
2V = -8 (add 24 to both sides)
V = -4 (divide both sides by 2)

5. You never want to leave a radical in the denominator. So, the expression, 3/√x, is not the correct form. You can get rid of the radical by multiplying by the square root of x for both the numerator and the denominator:
3/√x * √x/√x (since √x/√x = 1)
= 3√x / √x√x
= 3√x / (√x)^2
= 3√x / x

Now, the radical is in the numerator and not the denominator.

Answer 2

Yes, the first two are correct.

3: First, multiply through the 2 and the -3: 8x^2 -6x +4 -3x^2 (I'm assuming you meant to write x^2 there; you left out the 2) +15x + 24.

Next, group factors which are multiplied by the same power of x: 8x^2 - 3x^2 -6x + 15x + 4 + 24.

Finally, add these factors: 5x^2 + 9x + 28.

4: Again, first multiply through the 6 and the -4: 6V - 12 -4V - 12 = 10 - 42. Then group factors which are multiplied by V: 6V - 4V - 12 = 10 - 42. Now add these factors together: 2V - 12 = -32. Add 12 to each side: 2V = -20. Divide by 2: V = -10.

5: I think you must have left out part of the problem, since there's no equation to solve. I will point out that it's generally considered better to have square roots in the numerator. You can multiply by root(x)/root(x) (I can't make the square root sign) to get 3root(x)/x, which gets the radical out of the denominator. That's all I can do with it.