2
votes
1answer
61 views

Expanding Square Roots, Why No Negative?

I haven't thought through algebra in a while and the last explanation I received of this seemed arbitrary. I hope I can get some clarification here. I understand that $\sqrt{+a} = \pm b$. Here's ...
0
votes
2answers
42 views

How factor with square root

I have the following equation that I'm trying to factor, but I'm stuck at the end. $$\frac{zx^{-4}\sqrt{x}(yz^4)^3}{z^7xy}$$ $$\frac{\frac{1}{x^4}\sqrt{x}(yz^4)^3}{z^6xy}$$ ...
1
vote
3answers
26 views

Need help with basic factoring equation

I'm just trying to brush up on my factoring of quadratic equations. $$\frac1{x+3} + \frac1{x^2 + 5x +6}$$ $$\frac1{x+3} + \frac1{(x+2)(x+3)}$$ $$\frac{(x+2)(x+3) + (x+3)}{(x+2)(x+2)(x+3)}$$ Then ...
3
votes
1answer
73 views

Factors of integers of the form $k^2-k+1$

Factorisation of arbitrary integers is of course a computationally hard problem. But what if the integers I'm interested in factorising are all of the form $k^2-k+1$ ? Is there some way to compute ...
5
votes
2answers
333 views

Factoring Quadratics: Asterisk Method

I'm teaching my students about factoring quadratics. We've done GCF, difference of two squares, squared binomials, and grouping. One of my colleagues then found this asterisk method on line. It's ...
1
vote
1answer
87 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 ...
1
vote
2answers
268 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 ...
2
votes
3answers
121 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 ...
3
votes
1answer
58 views

Factorising a quadratic equation

I've just started studying for an A-Level in Mathematics. This is probably a simple question but when I factorized the quadratic equation $15x^2+42x-9$ I took out the common factor $3$ to get ...
2
votes
6answers
259 views

Factoring Quadratics

Is there a method to find which numbers to use when simplifying quadratics? For example $x^2 + 5x + 6$ is easy enough to find, but what if I have bigger numbers, or I have this quadratic expression: ...