The easiest way is to set the expressions equal to 0 then find the roots using the quadratic equation.
Do you know the quadratic equation?
Hi all, I started this subject today and I have many questions of a similar nature. It would be much appreciated if someone could give me a step-by-step tutorial on how to answer a question such as this:
Factorize these quadratic expressions:
3x^2 - 7x + 2
or
9x^2 + 30x + 25
I've never used this forum before so I'm sorry if I did anything wrong.
Thanks heaps!
Sam
I learned this 2 semesters ago, so forgive me if I err (someone feel free to correct any misconceptions I have, I tried to look it up but didn't find anything)
Look at the polynomial 3x^2 - 7x + 2
The first coefficient is 3, and the last is 2. There is a property that if you can remove a factor, it will take the form of (x+p/q) or (x+q/p) where p is a factor of the first coefficient, and q is a factor of the second coefficient. So potential factors are , , , , , , , , , , , , ,
In this case, I found that works.
To pull it out, I used division:
Perform the division:
So 3x^2 - 7x + 2 can be factored into (x-2)(3x-1)
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The second one is pretty easy, because it's obvious. The first and last coefficients are perfect squares, so you could look at it like this:
From here it should be rather clear you are looking at a perfect square, if it is not, try playing around with perfect squares a bit so that you can learn to recognize them.