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Today, 12:11
Yep. :D
Let's look at using the discriminant as you initially posted.
If a quadratic has only one root, then its discriminant must be zero, and...
3 replies  51 view(s)

Today, 09:06
X^2= 4Y^2
Do you see that either X= 2Y or X= 2Y?
X= 2Y+ 1
If you replace X with 2Y what do you get? If you replace X with 2Y what do...
2 replies  39 view(s)

Yesterday, 23:09
Okay...well, when I was your age, I was no fan of doing homework either...I think very few middle school students are excited about doing homework....
4 replies  66 view(s)

Yesterday, 22:51
Hello, and welcome to MHB, I hate homework! (Wave)
I moved your thread here, because our "Math Motes" forum is for threads of an...
4 replies  66 view(s)

Yesterday, 21:10
What I would do is from the given information, we know:
x^2+mx+n=(x+3)^2
Expand the RHS, and then equate coefficients to determine $m$ and $n$....
3 replies  51 view(s)

Yesterday, 19:52
Hello and welcome to MHB, ScrewedIre! (Wave)
We ask that our users show their progress (work thus far or thoughts on how to begin) when posting...
2 replies  39 view(s)

Yesterday, 19:22
Jackson got 30% of the votes, which is 3,696 votes. This means that together, Morris and Victor got the remaining 70%, which is 8,624 votes. Morris...
1 replies  37 view(s)

Yesterday, 19:05
After almost 7 years of helping with math online, I think in $\LaTeX$ now. (Nerd)
It really takes little time...and when I am posting a series of...
4 replies  103 view(s)

Yesterday, 14:55
Are you sure you've copied it correctly? It appears to me that the actual identity should be:
...
2 replies  67 view(s)

Yesterday, 10:02
That's just a placeholder to make factoring a little easier...once you get more practice you won't need it. Also, it's part of how I choose to...
4 replies  88 view(s)

Yesterday, 09:48
You've dropped one of the 1's there...:D
4 replies  60 view(s)

Yesterday, 09:38
Yes, then combine like terms. :D
4 replies  66 view(s)

Yesterday, 08:26
Here is this week's POTW:

Let $f(x)$ be a polynomial with integer coefficients. Define a sequence $a_0,a_1,\ldots$ of integers such that...
0 replies  34 view(s)

Yesterday, 08:25
Congratulations to Opalg for his correct answer, which follows:
By a translation, we can assume that one of the three points is at the origin. The...
1 replies  105 view(s)

Yesterday, 02:24
I would begin by using rational exponents in place of the radical notation:
...
4 replies  88 view(s)

Yesterday, 02:17
We are given to factor:
\left(x^2+1\right)^{\frac{2}{3}}+\left(x^2+1\right)^{\frac{5}{3}}
So, we factor out the expression with the smaller...
2 replies  58 view(s)

Yesterday, 02:08
When you factor out the expression $x^2+1$, you factor out the term having the smallest exponent (which you did), and then you subtract that exponent...
4 replies  60 view(s)

Yesterday, 02:02
What does the discriminant tell you about the roots of this quadratic polynomial?
7 replies  99 view(s)

Yesterday, 01:58
No, you are given a difference of squares...:D
4 replies  66 view(s)

Yesterday, 01:56
As a first step, I would write:
64(xa)^4x+a=64(xa)^4(xa)
Next factor out $xa$, and the other factor will be the difference of cubes. :D
2 replies  48 view(s)

May 22nd, 2017, 19:07
I get:
A_y=9.55\sin\left(48^{\circ}\right)\text{ m}=9.55\sin\left(48^{\circ}\right)\text{ m}\approx7.10\text{ m}
Your calculator is in...
1 replies  76 view(s)

May 22nd, 2017, 13:15
It will be interesting to see the OP's solution. :)
7 replies  190 view(s)

May 22nd, 2017, 12:12
Think of it like this:
...
4 replies  51 view(s)

May 22nd, 2017, 12:07
I applied the exponential property:
x^ny^n=(xy)^n
Since $8=2^3$, we can write:
8c^3=2^3c^3=(2c)^3
4 replies  64 view(s)

May 22nd, 2017, 12:02
It can be factored further, as there is both a sum and difference of cubes there. Bear in mind I only dealt with the numerator. :D
4 replies  57 view(s)

May 22nd, 2017, 00:51
Yes, in fact:
...
4 replies  57 view(s)

May 22nd, 2017, 00:45
I would write the expression as the difference of squares:
...
2 replies  30 view(s)

May 22nd, 2017, 00:40
I would begin by writing the expression as the difference of cubes:
(a+b)^38c^3=(a+b)^3(2c)^3
Now apply the difference of cubes formula...:D
4 replies  64 view(s)

May 22nd, 2017, 00:37
I would factor as follows:
8a^3+27b^3+2a+3b=(2a)^2+(3b)^3+2a+3b=(2a+3b)\left(4a^26ab+9b^2\right)+(2a+3b)=(2a+3b)\left(4a^26ab+9b^2+1\right)
...
4 replies  51 view(s)

May 22nd, 2017, 00:28
If we allow for complex factors, then we can state:
p^4+4=\left(p^2+2i\right)\left(p^22i\right)
However, over the reals, the sum of two...
5 replies  77 view(s)
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