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3 years ago

Factor completely 3x^2+2x-1

Mathematics

2 answers:

grandymaker [24]3 years ago

6 0

Answer:

$3x^2 + 2x - 1 = 3(x-\frac{1}{3})(x+1)$

Step-by-step explanation:

Iteru [2.4K]3 years ago

3 0

Answer:

(3x-1)(x+1)

Step-by-step explanation:

I like to factor by grouping.

a=3

b=2

c=-1

To get those values I compared 3x^2+2x-1 to ax^2+bx+c.

Now our objective to help us factor this is: Find two integers that multiply to be a*c and add up to be b.

a*c=3(-1)

b=2

Guess what? Our numbers are already visible to us; that doesn't always happen. However, a*c=3(-1) and b=2=3+(-1).

So we are going to replace our 2x with 3x+-1x or -1x+3x. Either one is fine; they are the same thing.

3x^2+2x-1

Replacing 2x with -1x+3x.

3x^2-1x+3x-1

Grouping first 2 terms together and grouping 2nd 2 terms together.

(3x^2-1x)+(3x-1)

Now we are going to factor each grouping.

x(3x-1)+1(3x-1)

Now notice we have two terms here x(3x-1) and 1(3x-1). Both of these terms have a common factor of (3x-1). We are going to now factor out (3x-1).

(3x-1)(x+1)

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The mean of three numbers x1,x2,x3 can be obtained by a calculus. The first step of the algorithm is

1) $mean(x1,x2,x3) = \frac{x1+x2+x3}{3}$

In order to obtain the median, maximun and minumun of x1, x2 and x3, we can compare x1 and x2. The smaller of those numbers will be compared to x3 and, if x3 is even smaller, then x3 is the minimun, the other small number is the median, and the remaining number is the maximun. Otherwise, we compare x3 with the bigger number to find median and maximun. To summarize:

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