1
vote
3answers
26 views

Basic Algebraic Manipulation

How would I solve for $X$ in this instance? I can't figure out how to get the $X$ variables by themselves and the known values on the other side by themselves. $2(4-X)(4-X)+X = 3$
0
votes
1answer
42 views

Factor this equation [closed]

Can someone factor this for me? $(x^{\frac{n}3}-a^{\frac{n}3})$ I am stuck on it. Let n be any natural number.
0
votes
0answers
30 views

Is this factorization true for all $n$ in the natural numbers

I need to know if $x-a=(x^{\frac{n}3}-a^{\frac{n}3})(x^{\frac{n+1}3}+a^{\frac{n}3} x^{\frac{n}3}+a^{\frac{n+1}3})$ Is true. I know its true for $n=1$, is it true for all natural numbers though?
0
votes
4answers
21 views

What formula do I use for factoring these?

An elementary question, but I am having a lot of discrepancies identifying the correct formula to use, I can do more complex ones but not the simple ones if that makes sense. a) $8x^3 + 1$ b) $m^2 - ...
1
vote
5answers
49 views

Factor fully $98g^2+112g+32$ by decomposition

By looking at this question I understand it is a complex trinomial so do I just decompose it??I have multiplied 98 by 32 getting 3136, but I'm not quite sure what comes next.
-2
votes
2answers
62 views

Factor fully $625-(y-2)^2$

So far, I have used $(y-2)$ twice (multiplying both) because of the exponent being $2$. But, I need to factor and that's when I get confused. Please help!
2
votes
1answer
28 views

Determine 2 values of $k$ so that $36m^2+8m+k$ can be factored over the integers

So, I really need help with this, thank you very much for helping me. Anyway, I understand that $36m^2+8m+k$ is a complex trinomial and when factoring I should use $a^2+2ab+b^2=(a+b)^2$, but this is ...
1
vote
3answers
96 views

how do you factor $x^2 +kx+40$ over the integer

please please help me, I'm having a lot of troubles. I tried to use a^2+2ab+b^2 formula (like i was told) but that's where get lost. I understand that Factoring uses the opposite operation, but 40 ...
2
votes
5answers
98 views

Derivation of factorization of $a^n-b^n$

How does one prove that: $$a^n-b^n=(a-b)\left(a^{n-1}+a^{n-2}b+a^{n-3}b^2+\dots+a^2b^{n-3}+ab^{n-2}+b^{n-1}\right)$$ Better yet, why is $a^n-b^n$ divisible by $a-b$? I would very much appreciate some ...
1
vote
1answer
164 views

Factoring using the 'Criss-Cross' method

my teacher taught our class how to factorize using the criss cross method, and I did not understand what she tried to communicate to the class. The equation I am trying to solve as an example is $7x^2 ...
2
votes
1answer
51 views

What is the solution? Factoring and computing the equation.

If you will be gracious enough to answer, the equation is currently: $$10^x + 15^{x-1}= 20,$$ What is the value of $2x^2$? Please list all steps, if you don't mind. To follow up, what is the name of ...
0
votes
5answers
62 views

Factorization of a degree three polynomial

So I was doing some Vector Calculus homework and was working with Lagrange Multipliers, but then I came across a polynomial that I either forgot how to factor or never learned. I plugged it into ...
1
vote
1answer
46 views

Factorise: $a^4-b^4+c^4-d^4-2(a^2c^2-b^2d^2)+4ac(b^2+d^2)-4bd(a^2+c^2)$

Factorise: $a^4-b^4+c^4-d^4-2(a^2c^2-b^2d^2)+4ac(b^2+d^2)-4bd(a^2+c^2)$. My working: $(a^4-2a^2c^2+c^4)-(b^4-2b^2d^2+d^4)+4ac(b^2+d^2)-4bd(a^2+c^2)$ ...
3
votes
3answers
128 views

Solve $t^4+4 t^3+6 t^2+4 t-32 t^{1/4}+1 = -16 $

I'm trying to solve the following equation: $$(t+1)^4 - 32 t^{\frac{1}{4}}=-16 $$ where t $\geq 0$, which is equivalent to $$t^4+4 t^3+6 t^2+4 t-32 t^{\frac{1}{4}}+1 = -16 $$ Wolfram Alpha tells that ...
2
votes
0answers
66 views

What is the line of thinking to get $[(n^2+3n+1)^2-5n(n+1)^2]$ from $(n^4+n^3+n^2+n+1)$?

There is this one little tiny step along the working that I don't quite understand, but I think it is better if I write the whole problem and solution for clarity. Problem: Factorise $5^{1995}-1$ ...
0
votes
1answer
56 views

Substitution to linear + nth power form

Given an arbitrary polynomial: $$a_0 + a_1x + a_2x^2 ... a_nx^n$$ Does there exist a series of substitutions (or single substitution if you choose to combine them) that leaves this function in the ...
1
vote
6answers
151 views

How to factorize $2x^2+5x+3$?

I'm doing pre-calculus course at coursera.org and I'm in trouble with this solution $$2x^2 +5x +3 = (2x+3)(x+1)$$ By trial, using ac-method I got stuck: $$ ac = (2)(3) = 6\\ 6 + ? = 5 \Rightarrow~ ? ...
0
votes
4answers
56 views

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 ...
2
votes
4answers
118 views

How to determine if $2+x+y$ is a factor of $4-(x+y)^2$?

I know it is a factor but how could have I determined that it was? Feel free to link whatever concept is needed than solve it. Studying for clep and it's one of the practice problems. When I expand it ...
1
vote
2answers
54 views

Question about Polynomial Factor Theorem

I was reading the solution to an algebra problem but got stuck at one part. Problem is here: (http://math.la.asu.edu/~ifulman/mat194/problem-solving.pdf) Example 4.2.6 -- page 140 of the PDF (the book ...
0
votes
3answers
80 views

Prove that $ x^n - y^n = (x-y). (x^{n-1}+x^{n-2}y\,+ \,\,…\,\,+ y^{n-1})$ [closed]

Prove that $ x^n - y^n = (x-y). (x^{n-1}+x^{n-2}y\,+ \,\,...\,\,+ y^{n-1}) $; $\,\,\,\,\,$$x,y \in \mathbb{R}$
2
votes
2answers
31 views

Polynomial With Imaginary Roots

Working on question 1 here http://www.sosmath.com/cyberexam/precalc/EA2002/EA2002.html Find a polynomial with integer coefficients that has the following zeros: ...
0
votes
3answers
52 views

Can someone please explain how this was factored?

How was $x^2(x+1)-4(x+1)$ factored into $$(x^2-4)(x+1)?$$ I know this seems very basic but can someone please explain this?
2
votes
1answer
49 views

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 ...
0
votes
1answer
56 views

Please help me with factorisation

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!!)
2
votes
1answer
148 views

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 ...
0
votes
1answer
65 views

How long is an arrow in the air?

The height $h$ of an arrow in feet is modeled by $h(t) = -16t^2 + 63t + 4$, where $t$ is the time in seconds since the arrow was shot. How long is the arrow in the air? Could someone explain where to ...
2
votes
3answers
133 views

Factoring out an exponential?

I have the following expression $$\frac{2^{k+1}(k+1)!}{(k+1)^{k+1}}\cdot\frac{k^k}{2^k k!}$$ I get $$\frac{2(k+1)(k^k)}{(k+1)^{k+1}}$$ But how do I factor out the ${(k+1)}^{k+1}$
1
vote
3answers
67 views

How do you factor $(10x+24)^2-x^4$?

I tried expanding then decomposition but couldn't find a common factor between two terms
1
vote
2answers
107 views

Factoring Complex Trinomials

What is the answer for factoring: $$10r^2 - 31r + 15$$ I have tried to solve it. This was my prior attempt: $$10r^2 - 31r + 15\\ = (10r^2 - 25r) (-6r + 15)\\ = -5r(-2r+5) -3 (2r-5) $$
0
votes
1answer
44 views

Polynomial (third degree)

A third degree polynomial $p(x)=0$ when $x=1$ and $x=3$. We also learn that $p(x) \geq 0 $ when $x \geq 1$ and $p(2) =2$. Determine $p(x)$. How should I proceed? I presume no calculus is needed.
1
vote
0answers
37 views

Given a cubic $f(x)$ with specified negative real roots $-a,-b,-c$, what happens when we search for solutions to $f(x)=d$?

Noting Roots of a Certain type of Cubic Equation, what if we have the following simpler form for real $d$: $$(x+a)(x+b)(x+c)=d\tag{1}$$ (With $a,b,c\in \mathbb R^+$.) Clearly, depending on $d$, the ...
1
vote
1answer
74 views

Why does completing the square give you the minimum point?

Say we have an equation:$y=$ ${x^2} + 2x + 1$ Completing the square we get: $\eqalign{ & y={x^2} + 2x + 1 \cr & = {(x + 1)^2} - {(1)^2} + 1 \cr & = {(x + 1)^2} \cr} $ The ...
3
votes
2answers
61 views

How do you factor this? $x^3 + x - 2$

How do you factor $x^3 + x - 2$? $(x-1)(x^2 + x + 2)$ Note the factored form here. Thanks!
-2
votes
3answers
111 views

How do I factor this polynomial $x^5-4x^3+8x^2-32$? [closed]

How do I factor this polynomial? $p(x) = x^5-4x^3+8x^2-32$
2
votes
3answers
95 views

Factor $(x+y)^7-(x^7+y^7)$

So I was doing some practice problems to prepare upcoming math contests. This is one of the problems: Factor $(x+y)^7-(x^7+y^7)$ I got zero for $(x+y)^7-(x^7+y^7)$, however, the solutions ...
1
vote
2answers
251 views

Find the square root of $(x^2 + 3x + 7)(x^2 + 5x + 3) + (x − 2)^2$

I want to find the square root of $$(x^2+3x + 7)(x^2+5x+3)+ (x −2)^2$$ First , I would like to know if it is really necessary to expand everything , because I think it is in the given form for a ...
3
votes
4answers
206 views

Factorize : $x^6 − 10x^3 + 27$

I want to factorize $$x^6 − 10x^3 + 27$$ I tried two methods , first I let $y=x^3 $ and converted it into a quadratic but the solutions are not real . The second method I tried was getting it to ...
1
vote
4answers
81 views

Help in factoring polynomials

Please help in factoring: $x^3 - 13x + 12$ $x^5 - 3x^3 - 4x$ $x^3 - 6x^2 + 5x + 12$ Thank you in advance.
-1
votes
3answers
223 views

Factoring Pre calculus Question

Please help me factor $6x^3-9x^2+2x-3$ by grouping terms.
1
vote
1answer
237 views

Solving inequalities, simplifying radicals, and factoring. (Pre calculus)

(Q.1) Solve for $x$ in $x^3 - 5x > 4x^2$ its a question in pre calculus for dummies workbook, chapter 2. The answer says: then factor the quadratic: $x(x-5)(x+1)>0$. Set your factors equal to ...
6
votes
6answers
834 views

How to factor $2x^2-x-3$?

I know its: $$(x+1)(2x-3)$$ But how do you come to that conclusion?
0
votes
0answers
60 views

Factoring: solving for 'x' in a power equation.

Is it possible to solve for b in the following? $$g={t(b-1)\over(b^k-1)}$$ I have attempted this by hand and on a leading online calculator, but have been unable ...
25
votes
2answers
1k views

Factorize $(x+1)(x+2)(x+3)(x+6)- 3x^2$

I'm preparing for an exam and was solving a few sample questions when I got this question - Factorize : $$(x+1)(x+2)(x+3)(x+6)- 3x^2$$ I don't really know where to start, but I expanded everything to ...
1
vote
1answer
126 views

Simplifying the expression $(\sqrt{5}+\sqrt{7})/(\sqrt{10}+\sqrt{14}+\sqrt{15}+\sqrt{21})$

Alrite guys, this question might sound stupid, but I can't find a way to simplify this complicated expression: $$\frac{\sqrt{5}+\sqrt{7}}{\sqrt{10}+\sqrt{14}+\sqrt{15}+\sqrt{21}}$$ I can't take the ...
-2
votes
1answer
50 views

Suppose that $x > y > 0$. Which of the following is equivalent to $\dfrac{x^y y^x}{y^y x^x}$? [closed]

Suppose that $x > y > 0$. Which of the following is equivalent to $\large\dfrac{x^y y^x}{y^y x^x}$? $(x-y)^\dfrac{y}{x}$ $\left(\dfrac{x}{y}\right)^{\large x-y}$ $1$ ...
15
votes
4answers
677 views

Factor $x^4 - 11x^2y^2 + y^4$

This is an exercise from Schaum's Outline of Precalculus. It doesn't give a worked solution, just the answer. The question is: Factor $x^4 - 11x^2y^2 + y^4$ The answer is: $(x^2 - 3xy -y^2)(x^2 + ...
0
votes
1answer
55 views

how do you find the highest common factor of two multivariate polynomials?

How do you find the highest common factor of two multivariate polynomials? I am happy to get answers that are only useful for polynomials over the real numbers, as that is what I am dealing with.
5
votes
6answers
168 views

Factoring Quadratic Trinomials

I'm currently doing some homework, but I'm COMPLETELY stuck on one problem. I need to factor the following trinomial: $$5x^2+7xy+2y^2$$ How can I solve this problem? I have no idea what to do ...
1
vote
1answer
59 views

How to isolate j?

can anyone explain me how to isolate the j variable please? $$q = \frac{1 - (1 + j)^{-n}}{j} p $$ TIA