13
votes
10answers
4k views

Taking Calculus in a few days and I still don't know how to factorize quadratics

Taking Calculus in a few days and I still don't know how to factorize quadratics with a coefficient in front of the 'x' term. I just don't understand any explanation. My teacher gave up and said just ...
2
votes
2answers
59 views

Using factoring to solve the equation $(r^2 + 5r - 24)(r^2 - 3r + 2) = (4r - 10)(r^2 + 5r - 24)$

Solve for all values of $r$: $$(r^2 + 5r - 24)(r^2 - 3r + 2) = (4r - 10)(r^2 + 5r - 24)$$ I'm not sure how my thinking isn't really correct here. I know this all seems very elementary and such, ...
2
votes
5answers
203 views

Show that this expression is a perfect square?

Show that this expression is a perfect square? $(b^2 + 3a^2 )^2 - 4 ab*(2b^2 - ab - 6a^2)$
2
votes
1answer
69 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
87 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
27 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
78 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
388 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
111 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
323 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 ...
3
votes
3answers
135 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
271 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: ...
11
votes
8answers
600 views

How to factor quadratic $ax^2+bx+c$?

How do I shorten this? How do I have to think? $$ x^2 + x - 2$$ The answer is $$(x+2)(x-1)$$ I don't know how to get to the answer systematically. Could someone explain? Does anyone have a link to ...