factoring?

Question

I have no clue how to factor. So please Show me the Way you did it.

x^2+5x+6 = ???

Answer 1

well you setup a brackets like this
(x + _) (x +_)

now look at the number in front of the single x. it is 5
look at the number without a variable (an x) . it is 6
so now you have to find 2 number that will add up to 5 but when multiplied together will give you 6,,,you can do this by trial and error until you get the hang of it...so in this case the answer is 2 and 3

therefore (x +2) (x+3)...to double check just multiple it out....
x^2 +3x +2x +6 ... you get the point
i hopethis helps

Answer 2

Joketoad's answer is correct (x+3)(x+2)

In factoring quadratics (of the form you have given) you want to look for factors (numbers multiplied together) of the last term to add up to the middle term.

If I asked you to factor x^2 + 8x + 15 you would say to yourself, "what numbers multiplied together to make 15 also add up to equal 8?" It's either 15 x 1 or 5 x 3. Now which of these adds up to the middle term, 8?

So it factors (x+3)(x+5) you can FOIL to verify. Hope this helps.

Answer 3

The general formula for such binomial expression is:

(x+a) * (x+b) = x^2 + (a+b)*x + (a*b)

Now in the equation you put here:

x^2 + 5x + 6 = ??
Now you have to find two values that when MULTIPLIED yield +6 and when ADDED yield 5. Those numbers are +3 and +2 so we will get:

(x+2) * (x+3)

And finally:

x^2 + 5x + 6 = (x+2) * (x+3)

Good luck.

Answer 4

since there's no coefficient in front of x^2 you just have to worry about 5x and 6. FInd 2 numbers that add up to 6 and multiply out to 5: 5 and 1. Now plug them into this basic setup:
(x+__) *(x+__)

Answer 5

x²+5x+6=(x+3)(x+2)

all you need to do is find factors of 6 that add up to 5. 2 & 3 fit the bill.

Answer 6

x^2+5x+6

Factors of 6 that add up to positive 5 = 2,3

(x+2)(x+3)

Answer 7

A quadratic that can be factored will normally look like this:

(x+a)(x+b) = x^2 + (a+b)x + (a*b)

So you need to find two numbers (a and b) such that a times b is 6 and (a+b)=5

This sounds like 2 and 3 to me.

You can check by muliplying them out:
(x+2)(x+3) =


(quadratic is just a name for a second degree equation)

Answer 8

(x+3)(x+2)

Answer 9

There are two ways to do this.

Find the factors:
(x + ___) (x+ ___)
6 =
1 * 6 [1 + 6 = 7]
-1 * -6 [-1 + -6 = -7]
2 * 3 [2 + 3 = 5 which is the coefficient of x so these are your factors]
-2 * -3 [-2 + -3 = -5]
(x + 2)(x + 3)

Quadratic formula:
(x - ___) (x - ___)
x = [-5 +/- sqrt(25 - 4(1)(6))] / 2
x = [-5 +/- sqrt(25 - 24)] / 2
x = [-5 +/- sqrt(1)] / 2
x = [-5 +/- 1] / 2
x = -3, -2
(x + 2)(x + 3)

Answer 10

(x+3)(x+2)