# Tagged Questions

For questions about finding factors of e.g. integers or polynomials

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### Factoring under a 4th power

Show that $$\left( a + b \right) ^ 4 = b^4 \left( \frac{a}{b} + 1 \right) ^4$$ Its clear without an exponent $$\left( a + b \right) = b \left( \frac{a}{b} + 1 \right)$$ but I'm not sure why ...
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### Factor Transition Issue

$$F'(x)=(2ax+b)e^x+(ax^2+bx+c)e^x=(ax^2+(b+2a)x+c+b)e^x$$ Can someone explain this? I can't understand the transition. What method is this?
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### Factorise Algebraic Expression

Background: I came across the following problem in class and my teacher was unable to help. The problem was factorise $x^6 - 1$, if you used the difference of 2 squares then used the sum and ...
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### factors in polynomial rings with field coefficients

I'm reading through Dummit and Foote Abstract Algebra, and I was looking for an explanation of the following: Proposition 9: $F$ a field and $p(x)\in F[x]$. Then $p(x)$ has a factor of degree one if ...
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### The appearance of complex numbers when factoring quadratics [closed]

Why does $i$ only get involved in factoring quadratics like $x^2+9$, but not $x^2-9$? Why does the $+$ sign lead to complex numbers?
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### How many factors does $36^2$ have

How many factors does $36^2$ have $(A)2 \\ (B)8 \\ (C)24 \\ (D)25 \\ (E)26$ $36^2=2^4\times3^4$ How do i count the number of factors?I don't know.
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### What is meant by “maximal proper factors” of a integer?

I understand what is meant by proper factors, e.g. the proper factors of 36 are 2, 3, 4, 6, 9, 12, & 18. However I've just seen the phrase "maximal proper factors" used in the context of ...
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### Prime factorization of Gaussian integers

I want to find $a, b\in\mathbb{Z}[i]$ such that $a(2+3i)+b(5+5i)=1$. I don't know how to do this, but my first thought was to do something with the norm or otherwise factoring $5+5i=(2+i)(2-i)(1+i)$,...
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### Irreducible polynomials in $\mathbb{C}[X,Y]$

I have the polynomial $X^2+Y^2-1$ in $\mathbb{C}[X,Y]$. Is this irreducible? If not, how do I factorize it? Should I handle this the same as if it were $\mathbb{R}[X,Y]$, or should I do it ...
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### How can I find the point of intersection between these functions?

Find the point of intersection between $f(x) = x^3$ and $g(x) = x^{1/3}$ Once I equal each equation to each other, I could factor out the $x$ but the exponent 1/3 is confusing me. Thank you!
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### Solve for $A,B$: $\mathrm{LCM}(A,B)=168$, $\mathrm{HCF(A,B)}=12$

The highest common factor and the lowest common multiple of two numbers $A$ and $B$ are $12$ and $168$ respectively. Find the possible values of $A$ and $B$ with the exception of $12$ and $168$. ...
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### A ball is thrown upward from the top of a tower.If its height is described by $-t ^2+60t+700$,what is the greatest height the ball attains?

A ball is thrown upward from the top of a tower.If its height is described by $-t ^2+60t+700$,what is the greatest height the ball attains ? I've managed to get a solution by realizing that the ...