# Tagged Questions

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### Nonlinear system of equations / factoring two-variable cubic over $\mathbb{R}$

About halfway through a homework problem, I end up with a three-way identity: $$\frac{uw}{v+w} = \frac{uv}{u+w} = \frac{vw}{u+v}$$ (I say I end up with..., but this is the method suggested by my ...
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### $a,b,c$ are three distinct natural numbers. Then how many ordered triplets $(a,b,c)$ will exist such that L.C.M (a,b,c) = 144.

Let $a,b,c$ be three distinct natural numbers. Then how many ordered triplets $(a,b,c)$ will exist such that L.C.M (a,b,c) = 144. Here's how I proceeded, 144=$(2^4)(3^2)$, so 144 has 15 factors(1 ...
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### Factoring and Simplifying

I'm trying to do this problem, $$(4x + 1)^{15}\cdot\frac{1}{3}(12x - 5)^{-\frac{2}{3}}\cdot 12 + (12x - 5)^{\frac{1}{3}}\cdot15(4x + 1)^{14}\cdot 4$$ I've gotten down to, ...
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### Show that a Polynomial has certain factorization

$P(x)$ is a polynomial in $x$ of degree $\leq n-1$. Show that $P(x)$ has $n-1$ distinct roots and thus has the factorization $$k\Pi_{i=2}^n(x-a_i)$$, where the constant $k$ is the coefficient of ...
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### factor to find an algebraic expression for the length and width of the rectangle

the area of the rectangle is defined by $$6x^2+13x-28$$ so far, i have decomposed the expression to get $$(3x-4)(2x+7)$$ but, now i need to find the length and width and that's where I have a bit of ...
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### How to factor cubics having no rational roots

$$-8x^3 +8x -3 = 0$$ I've already tried the possible roots of $\pm 1$ and $3$ using the rational roots test, but none of these help break it down into something more workable. How do I solve this ...
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### Factoring with rational exponents

I'm not quite sure how to do this question. Every way that I tried doing it didn't yield an answer that is equivalent to the original question. $$(2x+1)^{2/3}-4(2x+1)^{-1/3}$$ When I tried doing ...
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### How to factor $x^3-x^2+x+3$ [closed]

I have a partial fractions integral with $x^3-x^2+x+3$ in the denominator. How do I factor this?
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### Showing $(a+b+c)(x+y+z)=ax+by+cz$ given other facts

$$x^2-yz/a=y^2-zx/b=z^2-xy/c$$ None of these fractions are equal to 0.We need to show that, $(a+b+c)(x+y+z)=ax+by+cz$ This question comes from a chapter that wholly deals with factoring ...
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Is it possible to write $$64x^6-112x^4+56x^2-7$$ in linear factors? If so, what are they? (Finding it really difficult to ask this question!!)
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### Factorizing $(x-1)(x-3)(x-5)(x-7)-64$

We need to factorize: $$(x-1)(x-3)(x-5)(x-7)-64$$ We can, by the rational root theorem, see that there are no roots of this polynomial.Next observation is that $64=(8)^2$. So this means that if the ...
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### Computations question

a) Determine the prime factorizations of 3850 and 4125 b) Find the value of d = gcd(3850,4125) c) List all the positive divisors of d This is what I have so far. a) 3850: 11, 5, 5, 7, 2 4125: ...