Help with factoring?

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Katez

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Okay, so I absolutely do not understand factoring at all. I can't even do simple equations that involve factoring just because I can't do the one step. Right now in my college Pre-Calculus class we're doing fuctions, and I have this problem:

Find the zeros of the function algebraically.
f(x)= 2x² - 7x - 30


I figured out how to find the zeros by solving for x but I can't factor for the life of me. Can someone please explain it in a way that someone really, really stupid could understand?
 
Katez said:
Okay, so I absolutely do not understand factoring at all. I can't even do simple equations that involve factoring just because I can't do the one step. Right now in my college Pre-Calculus class we're doing fuctions, and I have this problem:

Find the zeros of the function algebraically.
f(x)= 2x² - 7x - 30


I figured out how to find the zeros by solving for x but I can't factor for the life of me. Can someone please explain it in a way that someone really, really stupid could understand?
Click to expand...

What are the zero's of the function?

to brush-up, go to:

http://www.purplemath.com/modules/solvquad.htm
 

Ola , It's GRAPHICALLY . . .

Graph the parabola and look for the points where it cuts the x'0x axis .

Solve F(x) = 0

When you've got the x values & you want to factorise f(x) . . . Use : a(x - x' )(x - x")

You know what " a " represents ?


 
I can't factor for the life of me. Can someone please explain it in a way that someone really, really stupid could understand?

My answer to that question is "no". Factoring is a process of changing a quantity either expressed as a single term or as a sum or difference of terms into the same quantity expressed in terms of things multiplied together.

For instance if I have the quantity 12, I can express that as numbers multiplied together. Possibilities include 1*12, 2*6, and 3*4. That is assuming that we want to limit ourselves to using whole numbers. We could consider 1/2 * 24, 1/3 * 36, etc.

If you have an expression which is the sum and/or difference of terms, to factor it simply means to change it into some quantities that when multiplied together produce the original expression. There are many different procedures that will accomplish this, too many for us to explain. Most texts start with monomial factoring --- 2x+6 = 2(x+3) because 2(x+3) = 2x+6.
They then move on to factoring trinomials, such as the one you presented. FOIL is a common mnemonic device sometimes presented as a means of accomplishing the factorization. Maybe you could google FOIL to help you.
 


2x^2 - 7x - 30

This can be factored by trial-and-error, but only if you first have a good grasp of multiplying two binomials (FOIL, anyone?)

This can also be factored using a process called "Factoring by Grouping".

Grouping simply means associating. (Do you know the Associative Property of Real Numbers?)

Search for lessons and examples using Google with keywords: factor by grouping

Here's how I do the factorization by grouping.

Ax^2 + Bx + C

2x^2 - 7x - 30

A = 2
B = -7
C = -30

In the polynomial, I want to rewrite the middle term -7x as a sum of two terms. For example, like so:

2x^2 + Jx + Kx - 30

In other words, the sum of J + K must equal B. That is, Jx + Kx = -7.

Okay, so far?

I don't know what the actual numbers J and K are, yet, but here's what I do next.

Find the product A(B)

2(-30) = -60

Now I find two numbers (J and K) whose product is -60 and whose sum is -7

J * K = -60

J + K = -7

Since the multiplication table is instant, I can find these numbers mentally: -12 and 5.

-12(5) = -60

-12 + 5 = -7

(If you can't do this mentally, then ask me to show you how to find J and K by solving the system of two equations directly above.)

Now that I know J and K, I can rewrite the polynomial.

2x^2 - 12x + 5x - 30

Next comes the grouping part (the Associate Property); I group the first two terms together, and I group the last two terms together.

(2x^2 - 12x) + (5x - 30)

I continue by factoring each of these groups.

The two terms in the first group are 2x^2 and -12x. Their factored forms are (2)(x)(x) and (-12)(x).

By inspection, I see that 2 and x are common factors because x obviously appears in both and (since the multiplication table is instant) is know that -12 factors as (2)(-6).

In other words, 2 and x are the only factors that appear in both factorizations (2)(x)(x) and (2)(-6)(x).

So, I factor out 2x from the first group.

2x^2 - 12x = 2x(x - 6)

Do you "see" why there's an x and -6 inside the other factor? After removing factors (2)(x) from (2)(x)(x), all that's left is x. After removing factors (2)(x) from (2)(-6)(x), all that's left is -6. That's factoring, in a nutshell.

Using the same strategy, I factor the second group by inspection.

5x - 30 = 5(x - 6)

Next, I rewrite the polynomial grouping using the groups' factored forms.

2x(x - 6) + 5(x - 6)

Ah ha. I recognize that there is now a common factor of (x - 6) on each side of the + sign. Therefore, I can factor out (x - 6).

(x - 6)(2x + 5)

Done. 8-)

I wish you good fortune, in your studies.

 
Aladdin said:
Ola , It's GRAPHICALLY . . .
Click to expand...
No, it's ALGEBRAICALLY. It was in the directions.


Thank you mmm4444bot, you were the most helpful.
 
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