Tagged Questions
5
votes
6answers
186 views
Cubing a simple thing
I am trying to do
$$(x + 2)^3 $$
I am actually not to sure what to do from here, the rules are confusing. To square something is simple, you just foil it. It is easy to memorize and execute. Here ...
2
votes
2answers
37 views
Faulty velocity question?
If a ball is thrown vertically upward with a velocity of $160 \text{ ft/s}$, then its height after t seconds is $s = 160t − 16t^2$.
a) What is the velocity of the ball when it is $384 \text{ ...
5
votes
1answer
181 views
Find the value of $x^3-x^{-3}$ given that $x^2+x^{-2} = 83$
If $x>1$ and $x^2+\dfrac {1}{x^2}=83$, find the value of the expression$$x^3-\dfrac {1}{x^3}$$
a) $764$
b) $750$
c) $756$
d) $760$
In this question from given I tried to ...
0
votes
1answer
20 views
Relationship between 2 Dimensional Quadratic systems and roots
Given four points
$(x_1, y_1)
(x_2, y_2)
(x_3, y_3)
(x_4, y_4)$
How does one construct a system of two equations:
$a_1x + a_2x^2 + a_3y + a_4y^2 + a_5xy = c_1$
$b_1x + b_2x^2 + b_3y + b_4y^2 + ...
9
votes
5answers
73 views
Reducibility of $x^{2n} + x^{2n-2} + \cdots + x^{2} + 1$
Just for fun I am experimenting with irreducibility of certain polynomials over the integers. Since $x^4+x^2+1=(x^2-x+1)(x^2+x+1)$, I thought perhaps $x^6+x^4+x^2+1$ is also reducible. Indeed:
...
1
vote
2answers
43 views
How do I factorize equations of the form $x^2 + Bxy + Cy^2 = 0$
Given equation
$$ x^2 + Bxy + Cy^2 = 0. $$
I want to factorize it in the form
$$ (x + my)(x + ny) = 0. $$
What are the values of $m$ and $n$ in terms of $B$ and $C$?
I tried writing the ...
5
votes
4answers
85 views
In order to factor we must find its zeros?
I am self-learning precalc (Precalculus Demystified) and found the following problem on page 170 :
Completely factor the the polynomial. $P(x) = x^3 - 5x^2 + 5x + 3; c = 3$ is a zero.
Since $c = 3$ ...
1
vote
3answers
58 views
Solving quadratic equations by completing the square.
Graphing $y=ax^2+ bx + c$ by completing the square
Add and subtract the square of half the coefficent of $x$.
Group the perfect square trinomial.
Write the trinomial as a square of a ...
1
vote
4answers
69 views
I cannot find the last factor of this expression?
I'm supposed to factor $x^8-y^8$ (the exponents are 8 for both if it is too difficult to see) as completely as possible. It is easy to factor this to $(x+y)(x-y)(x^2+y^2)(x^4+y^4)$. However, the book ...
3
votes
4answers
113 views
Solving this 3-degree polynomial
I'm trying to factor the following polynomial by hand:
$-x^3 + 9x^2 - 24x + 20 = 0$
The simplest I could get is:
$-x^2(x-9) - 4(5x+5) = 0$
Any ideas on how I could go ahead and solve this by hand? ...
1
vote
1answer
35 views
Foil, greatest common factor
I had this on a test and couldn't figure it out... It was written like this:
$12p^2-75$
The answer has to be $(p+\_ ) (p-\_)$
There must be a positive and negative number when combined (addition or ...
2
votes
3answers
62 views
How can I use prime factorization to find a cube root?
This is based on a lesson at Khan Academy that I didn't understand.
In the lesson, the instructor uses the number 512 as an example and the entire prime factorization consists of three groups of ...
0
votes
2answers
51 views
Simple question on factoring derivatives with “e”
I have a very simple factoring question; I'm doing a calculus problem in which part of the question requires me to factor a derivative. The derivative in question is $e^{-x}tx^{t-1}-e^{-x}x^t$ (the ...
2
votes
4answers
58 views
How to factor $a^2+10ab+25b^2-9c^2$
This is what I got so far $a^2+10ab+(5b)^2-(3c)^2$. I think I can group $a^2+10ab$ but not sure about $(5b)^2-(3c)^2$. Can someone explain this?
1
vote
4answers
63 views
How to factor $a^2-4b^2+4ac-8bc$
I am not sure how I would factor this. Can someone explain how I would factor this?
1
vote
5answers
99 views
How to factor $x^4-7x^2-18$
I am not sure how I would factor this. The $x^4$ and $x^2$ are really throwing me off. Can someone explain how I would factor this?
7
votes
2answers
165 views
Calculate the number of real roots of $x^8-x^5+x^2-x+1 = 0$
Calculate the number of real roots of $x^8-x^5+x^2-x+1 = 0$
My try: $$\left(x^4-\frac{x}{2}\right)^2+\frac{3}{4}x^2-x+1 = ...
2
votes
2answers
67 views
How do you factor $2ab-6ac-15c^2+5bc$
$$2ab-6ac-15c^2+5bc$$
Here is what I have done:
$$(2ab-6ac)-(15c^2+5bc)$$
$$2a(b-3c)-5c(3c+b)$$
$$2a(b-3c)+5c(-3c-b)$$
$$2a(b-3c)+5c(-b-3c)$$
$$(b-3c)(2a-5c)$$
I know this isn't the correct answer ...
2
votes
2answers
47 views
Create a formula by given solutions
For my upcoming middle school exams I will need to convert a formula.
I have got the following question:
Create a formula which has the following solutions: $$ x_{1} = 5,\quad x_{2} = -3.$$
The ...
1
vote
2answers
70 views
Factoring a long expression in the form $(a+b)^3 + (c - b)^3 - (c+b)^3$
I need to factor the following:$$\left(\dfrac{2}{3}x + \dfrac{5}{3}y\right)^3 + \left(\dfrac{3}{4}z -\dfrac{5}{3}y\right)^3 - \left(\dfrac{3}{4}z + \dfrac{2}{3}x\right)^3$$A friend of mine suggested ...
3
votes
5answers
150 views
Let $r,s,t$ be the roots of the equation $ x^3 - 6x^2 + 5x + 1$. What is the value of $(2-r)(2-s)(2-t)$?
Let $r,s,t$ be the roots of the equation $ x^3 - 6x^2 + 5x + 1$. What is the value of $(2-r)(2-s)(2-t)$?
The question is mentioned in my math olympiad. Please explain how to solve the problem. I have ...
8
votes
5answers
187 views
Factor $(a^2+2a)^2-2(a^2+2a)-3$ completely
I have this question that asks to factor this expression completely:
$$(a^2+2a)^2-2(a^2+2a)-3$$
My working out:
$$a^4+4a^3+4a^2-2a^2-4a-3$$
$$=a^4+4a^3+2a^2-4a-3$$
$$=a^2(a^2+4a-2)-4a-3$$
I am ...
0
votes
3answers
58 views
How do I factor this and simplify
I just found the derivative of a function and now I'm trying to factor and simplify the expression below. I have no idea how to factor terms with fractions as exponents especially when these fractions ...
0
votes
1answer
45 views
Factorising and limits
How do I factorize this expression? $$(2^n-3^n+n4^n)^{\frac{1}{n}}$$ so far I have: $$n4^n\left(\frac{1}{n} \left(\frac{1}{2}\right)^n-\frac{1}{n}\left(\frac{3}{4}\right)^n +1\right)^{\frac{1}{n}}$$
...
0
votes
1answer
34 views
What is $q(x)$ and $r(x)$ when $(x^2-6x+9)q(x) + r(x) = x^3 -27$?
I just failed this question on a test, so I would please like to get some feedback on where my thinking was wrong.
I need help with determining $q(x)$ and $r(x)$ when: $$(x^2-6x+9)q(x) + r(x) = x^3 ...
2
votes
1answer
82 views
Help with particular solution to solving $z^4 - 2z^3 + 9z^2 - 14z + 14 = 0$.
I asked a question about how to solve: $$z^4−2z^3+9z^2−14z+14 = 0$$
When all you know is that there is a root with the real part of 1. I was given great answers and you can find the question ...
7
votes
3answers
127 views
How do I completely solve the equation $z^4 - 2z^3 + 9z^2 - 14z + 14 = 0$ where there is a root with the real part of $1$.
I would please like some help with solving the following equation:
$$z^4 - 2z^3 + 9z^2 - 14z + 14 = 0$$
All I know about the equation is that there is a root with the real part of $1$.
My approach ...
2
votes
3answers
112 views
Solve for $ x$, $-\frac{1}{2}x^2 + 2x + 5 = 0$
I'm having trouble solving this equation for $x$:
$$-\frac{1}{2}x^2 + 2x + 5 = 0$$
What's the steps to take to solve it?
Thanks.
2
votes
4answers
286 views
Factoring Polynomials with four terms and two variables
I've been working on this for hours and cannot figure it out.
When I search, I find factorization techniques that I already know but don't seem to be able to apply here, or that are for polynomials ...
9
votes
7answers
469 views
Can someone show me why this factorization is true?
$$x^n - y^n = (x - y)(x^{n-1} + x^{n-2}y + \dots + xy^{n-2} + y^{n-1})$$
Can someone perhaps even use long division to show me how this factorization works? I honestly don't see anyway to "memorize ...
1
vote
1answer
151 views
Simplifying third degree polynomials
I am trying to figure out this simple problem but I have no idea how to do it.
$\frac {2x^3 - 5x^2 -4x -3}{2x^3 + x^2 - 18x -9}$
I know that I can keep guessing at random to find a factor in the ...
1
vote
2answers
153 views
A Tri-Factorable Positive integer
Found this problem in my SAT book the other day and wanted to see if anyone could help me out.
A positive integer is said to be "tri-factorable" if it is the product of three consecutive integers. ...
4
votes
1answer
117 views
If $A,B$ are factors of $2^6 3^4 5^2,$ how many values of $|A-B|$ are possible?
Let $x=2^6 3^4 5^2$, then how many distinct values of $|A-B|$ are possible where $A, B$ are the factors of $x$?
How to approach this problem?
6
votes
4answers
456 views
Find all real solutions to $8x^3+27=0$
Find all real solutions to $8x^3+27=0$
$(a-b)^3=a^3-b^3=(a-b)(a^2+ab+b^2)$
$$(2x)^3-(-3)^3$$ $$(2x-(-3))\cdot ((2x)^2+(2x(-3))+(-3)^2)$$ $$(2x+3)(4x^2-6x+9)$$
Now, to find solutions you must set ...
1
vote
1answer
54 views
How to simplify [3a(b-c)+5][-3a(b-c)-5] by using special product?
In simplifying $$[3a(b-c)+5][-3a(b-c)-5],$$ I used $$4(au+bv)(cu+dv)=acu^2+(ad+bc)uv+bdv^2.$$
I failed to apply the formula to the equation because $a=3a$, $b=-3a$, $c=5$, $d=-5$, $u=(b-c)$, $v=?$
...
2
votes
3answers
174 views
Factoring by grouping: $x^4 - y^4 -4x^2 + 4$
Please help me factor $x^4 - y^4 -4x^2 + 4$ by grouping terms.
Thank you.
2
votes
6answers
126 views
How do I factor trinomials of the format $ax^2 + bxy + cy^2$?
Take, for example, the polynomial $15x^2 + 5xy - 12y^2$.
2
votes
4answers
68 views
Probably simple factoring problem
I came across this in a friend's 12th grade math homework and couldn't solve it. I want to factor the following trinomial:
$$3x^2 -8x + 1.$$
How to solve this is far from immediately clear to me, ...
1
vote
4answers
381 views
How to factor the quadratic polynomial $2x^2-5xy-y^2$?
How do I factor this polynomial: $2x^2-5xy-y^2$ ?
4
votes
1answer
55 views
Factoring of a fraction, possibly made a mistake
Here is the initial expression and the steps I've made so far, but from the final line I can't go on. Have I made a mistake somewhere?
...
3
votes
3answers
270 views
Factoring $ac$ to factor $ax^2+bx+c$
I was watching a first-year high-school-algebra student struggle with factoring quadratics last night. Given a quadratic $ax^2+bx+c$ (I'll give you the exact example in a moment), her method — ...
3
votes
1answer
106 views
Factoring $y$ out of $y^2 + e^y$ possible?
I'm working on solving a separable first order differential equation where I get down to:
$$.5y^2 + e^y = .5x^2 + e^{-x} + c$$
Is it possible to solve for $y$ here? I can't think of a way to factor ...
4
votes
1answer
179 views
Help with basic high school math. What happens to $j$?
I know my math is very rusty, actually, its always been that way. but I need help with this. The question below has me stumped. I've tried to show the steps I went through to get the answer. Please ...
0
votes
1answer
82 views
How to solve for x
$W(4d^2 (1-x^2)^2) = abc^3x \sqrt{(\pi^2 (i-x^2)^2 + 16 x^2) }$
I have to find x ,i have the values of all other constants ,
I tried to separate it using partial fraction but I am stuck.
a=3
b=4
c=7
...
1
vote
2answers
225 views
How do I factor a polynomial function with a degree higher than 2 without guessing numbers of $\frac{p}{q}$?
I have an equation $f(x)=x^4+4x^3+2x^22-x+6$. In the past I was taught to factor it by getting the zeros by getting $p/q$, and start guessing zeros, and plugging them into the function. Once I got one ...
6
votes
6answers
2k views
How do you factor $x^3-3x^2+3x-1$?
$$x^3-3x^2+3x-1?$$
I know this may seem trivial, but I, for the life of me, I cannot figure out how to factor this polynomial, I know that the root is $$(x-1)^3=0$$ because of wolframalpha, but I ...
36
votes
13answers
12k views
What is a real world application of polynomial factoring?
The wife and I are sitting here on a Saturday night doing some algebra homework. We are factoring polynomials and we both had the same thought at the same time: when are we going to use this?
I feel ...
2
votes
1answer
60 views
Factor the binomial $36 m^2 - \frac{25}{4} $
OK, I got a new one... it's $36 m^2 - \frac{25}4 $
and I got:
$(18m-\frac{5}2 )(18m+\frac{5}2 )$ although that is incorrect... where did I go wrong?
2
votes
1answer
112 views
How does the rational root test work?
I've doing some research in wikipedia, where appears this example:$$3x^{3} - 5x^2 + 5x - 2 = 0$$the rational solution must be among the numbers symbolically indicated by: $$±\frac{1,2}{1,3}$$
So ...
0
votes
2answers
463 views
Factor By Grouping 3rd Degree Polynomial
Just to be upfront, this is a homework question, I already know the answer, but I can't figure out how to get there or the logic behind the hint, which is really what I'm after. Please don't solve it ...
