please explain why my answer is wrong!!!!!?

Question

ok so the problem is x^2-4x-5 (factor the trinomial)
this is my work:
i multiplied -5 by 1 and got -5 and then:
(x^2+1x)-(5x-5)
x(x+1)-5(x-1)
(x-5) + ?
my book says the answer is (x-5)(x+1). my question is why did they choose the x+1 over the x-1???

THANKS 2 all those who actually answered...my next question is why do i have to distribute the minus sign?

yaaay i get it now! THANKS GUYS!!! now i gtg finish my hw!

Answer 1

Factoring

x² - 4x - 5 = 0

The middle term is - 4x

Find the sum of the middle term

the first term x² = 1

multiply the first term 1 times the last term 5 equals 5 and factor

Factors of 5

1 x 5 . . .←. .use these factors

+ 1 and - 5 satisfy the sum of the middle term

insert + 1x and - 5x into the equation

x² - 4x - 5 = 0

x² + 1x - 5x - 5 = 0

Group factor

(x² + 1x) - (5x - 5) = 0

When there is a negative ( - ) symbol preceded a parenthesis the signs changes from a negative ( - ) to a positive (+)

x(x + 1) - 5(x + 1) = 0

(x - 5)(x + 1) = 0

- - - - - - - -s-

Answer 2

x^2-4x-5
I don't know how to explain this like this...but I'll try...First you have to find two numbers that, multiplied, are equal to 1 (because 1 is the number with x^2) which are 1 and 1. So we put it like this:
x^2-4x-5 (keep reading...then you'll see why)
1x
1x

Then we find two numbers that, multiplied, are equal to 5 (the number which has no variable on its side) which are 5 and 1. So we have:
x^2-4x-5
1x 5
1x 1
Now we cross multiply them:
1x X 1 = 1x
1x X 5 = 5x
Now we think: Is there a possible way that these two numbers are equal to -4??
Well yes..... 1x - 5x = -4x ..... So.....We turn
x^2-4x-5
1x 5
1x 1 To

x^2-4x-5
(1x - 5)
(1x + 1) We can get rid of the 1 that is with the x, so:

(x-5)(x+1) is the answer.....if you need any more help you can send me an email an we could work better through messenger.



And answering your second question:
...my next question is why do i have to distribute the minus sign?

Well.....1 - 5= -4 is not the same as 5 - 1 = 4 (which is the same as -1 + 5 = 4

Answer 3

If you look at the problem: x^2 - 4x - 5

When you factor problems such as these, you normally have 2 parenthesis, such as the answer suggests.

First you need to come up with x^2 and you do that by putting an x in both parenthesis. (x ) * (x )

The next step is finding multiples of 5 and in this problem there is only one solution. 1 times 5. So the 1 has to go in one of the parenthesis and the 5 in the other.

(x 1) * (x 5)

Because the last of the original equation is negative, one parenthesis has to have a minus and one has to have a plus. To determine which one is which, you look at the middle number, which is - 4. Therefore, the minus has to go with the 5 and the positive with the 1. -5+1= -4

(X+1) * (X-5)

Answer 4

You're thinking about it the wrong way. If you have an equation x^2 + nx + c, you need to find two factors of c that add up to the n. So you have -5 for c. You can use -1 * 5 or -5 * 1. Now add these numbers. 5 -1 = 4, -5 + 1 = -4. Since your n = -4, you need to use -5 and +1.
(x - 5)(x +1)

Answer 5

okay to factor you need to pay attention to the last number which is a negative five.

So from that, you know that one of the numbers are negative and the other is positive.

In other words, your answer should take this form:
(x- __ ) (x+___)
you have to think of the factors of that last number (5)
and there is only one possible combination and that is 5 and 1.

Now look at the middle number. (and disregard the x for now)
it's -4 right?

okay, from FOILing you know that the answer is either:
(x+5)(x-1)
OR
(x-5)(x+1)

Now which one is it?
From the number in the middle.
NEGATIVE 4 right?
So the bigger numerical factor (5 and 1, the 5 is the biggest) is going to follow the sign of the middle number.
In other words, since -4 is negative, so is 5.

The answer has to be (x-5)(x+4)
If you FOIL it:
F (first) = x*x --> x^2
O (outside) = x*-5 --> -5x
I (inside) = x* 1 --> +1x
L (last) = -5*1 --> -5

line them all up : x^2 -5x+x-5
= x^2 -4x -5

Do you sort of see what I mean? the number in the middle has to be the sum or difference between factors of the last number.

factors of -5 are: -1 and 5, or 1 and -5.
Now which one of those add up to -4?
1 and -5.

So the answer is (x-5)(x+1)

Sorry I'm so crap at explaining this. but if you need any further clarification, just email me at [e-mail] or something ;D

Answer 6

when there is no common term you automatically put an x in each parenthesi

(x )(x )
next look at the second sign. the second sign is a -. a - sign means you will have different signs in each of your factors to the trinomial. a + means you will have the same signs. since the first sign in the trinomial is a -, the first sign will be a _
(x- )(x+ )
now you look at the last number and sign. the last number is a 5 and the last sign is a -. therefore, you need to find two factors of 5 that subtract to the middle term, which is a 4. with five there is only one choice, 5 and 1. put the bigger number in the first parentheses.
(x-5)(x+1)
good luck

Answer 7

let's start again

x^2 - 4x - 5

( ) ( )

put an x in each bracket - this will give x^2 when you multiply

now you need to chose what 2 nos multiplied together make -5

1 and -5 or -1 and 5

since the adding of x's will give you -4x

you need -5 and +1

(x - 5)(x + 1)...............explanation below

= x^2 -5x +1x -5

It works!

If you do it this way you don't have to distribute anything.

Go back to the 2 brackets. Draw a curved line from x to x above the brackets. Now draw a curved line from 5 to 1 . This represents a pair of eyebrows.

Now draw a nose by joining the inside 5 to inside x underneath the brackets and a mouth by joining outside x to outside 1.

You have to do these 4 multiplication sums and add them together to work out the 2 brackets multiplied together.

Collect like terms that is squareds, x's and numbers and that is the answer to the multiplication of the 2 brackets.

The sum you are trying to do is the reverse of it. there is trial and error choosing the numbers and the signs.

Some won't work and you will be taught a formula for these

Answer 8

You are very close.

x^2 + x - 5x - 5 is correct. instead of doing this:

(x^2 + x) - (5x -5) Which is not correct because if you multiply the negative sign through you get:

-5x + 5 which is very different then what you have of -5x -5.

instead do the following:

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

Now when you factor you will get:
x(x + 1) + (-5)(x + 1)

Giving a final answer of:

(x - 5)(x + 1)

Answer 9

your book's right. think about your signs. they determine your middle term, the -4x

how are you going to get to -4x with a -1 and +5?

-1+5=4 but -5+1=-4

(x-5)(x+1) use foil to get

x^2 +x-5x -5 = x^2 -4x -5

there you are then.
the way i do this is just first set up the foil parentheses and try to fit it all in

(x- )(x+ )
has to be two x's because of x^2 and a positive and a negative because you have -5.

I knew the only factors of 5 are 1 and 5... I just have to do a kind of logical... guessing to figure out which one is negative and which is positive.

Answer 10

They chose (x-5)(x+1)= x^2 -4x -5 It is x+1

Your Work is pretty confusing, ill put it easier ok watch:

1. x^2 -4x -5........-Okay, x^2 means theres x on both sides and the -5 means that it has to be a - and + number cause both + equals + and both - still equals + so
(x+_)(x-_)

2. -5 means theres only 1 choice since its a prime number 5 and 1, whats left is deciding whether 5 is positive or 1, lets take a look

(x+5)(x-1)=x^2+4x...you can stop there cause you know +4x=/=-4x so it must be +1,-5, lets check (x+1)(x-5)

***(x+1)(x-5)=x^2+1x-5x-5....simplified to x^2-4x-5. It checks out. Good luck!