Factorising quadratics

How do you factorise 2x^2 - 3x

I understand you factorise by taking out a common factor, will the factor be X making it x^2 - 2x?? Or am I just being silly, I feel as if it is a simple question but I am going through a mind block! And I'm guessing it's not as simple as x(2x-3)??

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2xx -3x

x(2x - 3)*

Yea it is that simple :wink:

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Reply 3

timebent

Original post by miaofcourse

You are correct just take an x out of both of them :smile:

Reply 4

miaofcourse

Original post by HFancy1997

Yea it is that simple :wink:

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Oh god

after an hour of doing hard quadratics when I saw that question I thought it must be a trick!

Reply 5

miaofcourse

Original post by timebent

You are correct just take an x out of both of them :smile:

Thank you so much!!

Reply 6

username2640523

Original post by miaofcourse

Oh god

after an hour of doing hard quadratics when I saw that question I thought it must be a trick!

What level of work is this? Curious :smile:

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Reply 7

miaofcourse

Original post by HFancy1997

What level of work is this? Curious :smile:

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A-level algebra functions (:

Reply 8

username2640523

Original post by miaofcourse

A-level algebra functions (:

Cool C1 im guessing? :smile:

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Reply 9

miaofcourse

Original post by HFancy1997

Cool C1 im guessing? :smile:

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Yes (:

Reply 10

Chittesh14

Original post by miaofcourse

Yes (:

Enjoy. Best chapters lol.

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Reply 11

B_9710

There is no common factor of x on the numerator as there is (x-1).

Reply 12

Chittesh14

Don't worry, they are separate because the X on the bottom is multiplied by 4.
The X on the numerator is within a variable so it's X-1 it's not separate or multiplied. It's a factor. I don't know how to explain it.

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Reply 13

3121

I don't know why but I factor out an X I write (X+0) just so I know it's a value of x

Reply 14

B_9710

Original post by zayn008

I don't know why but I factor out an X I write (X+0) just so I know it's a value of x

You could expand it out as follows

\displaystyle \frac{(x-1)^2}{4x}= \frac{x^2-2x+1}{4x}

. Now you could split this up into 3 separate fractions,

\displaystyle \frac{x^2}{4x} - \frac{2x}{4x} + \frac{1}{4x}

.
Now you can cancel an x on top and bottom for the first two fractions, but you cannot for the third one.
So you can only cancel a fraction, when every term on the numerator has a factor that is also on the denominator.

Reply 15

Chittesh14

No problem. I'm sorry I couldn't help much - I just forgot about this thread.

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Reply 16

RDKGames

Study Forum Helper

I'll walk you through it. So let's start with the info we are given. The first few sentences just lay out the mark gains/penalties which we can use later on.

The candidate attempts q amount of questions, therefore he does not attempt 25-q questions as there are 25 of them in total for the candidate to attempt. There is no gain for attempting questions, however we are told there is a penalty for not attempting some questions, one point per question, therefore we can see that the candidate loses (25-q) marks.

Next we are told the candidate gets c questions correct. If he attempts q questions and gets c correct out of those, then that means he gets q-c incorrect. Now there is a gain for getting the right answer, AND a penalty for getting the wrong answer. Since he got c correct, and you get 4 marks per correct answer, that means the candidate gains 4c marks. As he got (q-c) incorrect, and you lose 2 marks per incorrect answer, the candidate loses 2(q-c) marks.

Now to find the amount of marks the candidate gains in total, we will begin with 0 and add on the gains, while subtracting the losses. As we found, the only gain is 4c while the two losses are (25-q) and 2(q-c).

Therefore if you let T_m equal the total marks, you would get the following:

T_m=0+4c-(25-q)-2(q-c)=6c-q-25

which gives the required result! :smile:

Of course you can ignore the 0 but I just used it to emphasise the fact that total marks start from 0 then begin to change once you start to add and subtract.

As for future questions like these, I'd say it is important to recognise that you presented two numerical quantities; such as the marks and the questions, and you must convert between the two by means of the information given to you within the context. Once the question gives you a specific case (such as the candidate there), then use this information that there are finite amount of questions to do, so you can already form expressions such as in my working out. Remember what you need to work out, and always consider which numbers increase the wanted value, and which ones decrease it; thus add/subtract respectively. It's mostly just being able to follow the scenario they give you carefully while taking everything into account because you need to consider the opposite of what is being told in the text as well; as seen from my working out where I work with the amount of unattempted questions. It's hard to explain how to go about these questions but I'd just say think hard about the situations in order to consider everything, and it should be straightforward from there.

(edited 7 years ago)

Reply 17

HapaxOromenon3

For question 1, when you have an equation of the form x^2 = some number, x could be the positive or negative square root. For example, x^2 = 4 -> x = +/- sqrt 4 = +/- 2, since squaring a negative number gives the same result as squaring the positive (remember minus times minus makes plus!).

For question 2, Multiply the numerator and denominator of your answer by R1*R2 to see that it is equivalent to the required result. Remember that if you multiply/divide both the numerator and denominator of a fraction by the same thing, the value of the fraction stays the same.

For question 3, just multiply the numerator ad denominator of your result by -1 to again see that it is equivalent.

Reply 18

RDKGames

Study Forum Helper

1.) When you square root something, the answer is always

\pm

of whatever you get because if you take the positive and square it, obviously you will get the positive, but if you square the negative, then you will ALSO get the positive due to the 2 negatives multiplying by each other. Hence there are 2 solutions for square roots.

Example:

\sqrt4=\pm2

because

2^2=4

and

(-2)^2

2.) Your answer is exactly the same. On the denominator, from the two fractions you can make one fraction under the same denominator by the following rule:

\frac{1}{a}+\frac{1}{b}=\frac{b}{ab}+\frac{a}{ba}=\frac{a+b}{ab}

Once you have one fraction as the denominator, you can multiply the top and bottom of the overall fraction by the denominator of the smaller fraction if that makes sense: