Question

what are the factors of x^2-5x+6 ?

Answer 1

What two numbers multiply to 6?

Answer 2

3 & 2

Answer 3

notice how they add to 3+2 = 5

we want this sum to be -5 and NOT +5

Answer 4

correct

Answer 5

however,

-3 + (-2) = -5

and

-3 * (-2) = 6

so the two numbers -3, -2 multiply to 6 and add to -5

Answer 6

meaning that

x^2-5x+6

factors to

(x-3)(x-2)

Answer 7

so how would i solve the problem

Answer 8

it's shown above

Answer 9

\(\large \begin{array}{cccllll}
x^2&-5x&+6\\
&\uparrow &\uparrow \\
&-3-2&-3\cdot -2
\end{array}\)

Answer 10

jim_thompson5910 how would i do it step by step solving

Answer 11

it's more like a trial and error kind of thing

you list out the possible ways to multiply to 6. Then you add up the factors to see which pair adds to -5

Answer 12

6 = 6*1
6+1 = 7... doesn't work

6 = 3*2
3+2 = 5 ... doesn't work

etc etc

Answer 13

would you do the solving i am stuck

Answer 14

it's already solved for you

Answer 15

where

Answer 16

You were asked to factor x^2-5x+6 and jim-thompson showed you it factors to:
(x-3)(x-2). Those are the two factors.

Answer 17

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

Answer 18

That the process ?

Answer 19

Yes. But look at jim_thompson's explanation on how to arrive at the -2 and -3 numbers.
In x^2-5x+6 you will have to ask yourself what two numbers multiply to +6 and add to -5? Here, -2 and -3 multiply to +6 and add to -5. Once we know the two numbers we can straightaway write the factors as (x-2)(x-3) or if you prefer you can proceed in steps as shown in my previous reply.

Answer 20

If you wish you can try factoring x^2 + 3x - 10

Answer 21

Correct but how can i first solve im really stuck

Answer 22

Are you asked to factor or are you given an equation to solve?

Answer 23

factor

Answer 24

Let us try factoring x^2 + 3x - 10.
The last term is -10 and the middle coefficient is +3
What two numbers multiply to -10 and add to 3?

Answer 25

5 and 2

Answer 26

Correct. But +5 and -2 because
5 * (-2) = -10 (last term)
5 + (-2) = 3 (middle coefficient)

So the factors are (x+5)(x-2)

Answer 27

Oh okay so to factor x^2- 5x =6 is what ?

Answer 28

3 and 2 correct

Answer 29

First bring the 6 to the left:
x^2 - 5x - 6 = 0

You might be tempted to say 3 and 2 but to multiply 3 and 2 and get a -6 they have to be of opposite signs. If you try various combinations: -3 and + 2 or 3 and -2 it does not add to -5.

So consider some other factors of 6 other than 3 and 2.
What two other numbers multiply to 6?

Answer 30

How about 1 and 6? They multiply to two and with proper sign they can be made to add to -5.
1 and -6 multiply to -6
1 + (-6) add to - 5

So the factors are: (x+1)(x-6)

Answer 31

Oh

Answer 32

Yes. Try various factors. If one set of factors does not work try another set.

Answer 33

How about x^2 - 5x - 36?

Answer 34

Factors of 36 are:
1 and 36
2 and 18
3 and 12
4 and 9
6 and 6

Which one of these pairs, with proper sign would multiply to -36 and add to -5?

Answer 35

12 and 3

Answer 36

?

Answer 37

please factor my problem

Answer 38

which one? All the problems you posted have been factored.

Answer 39

Im just asking for x^2-5x+6

Answer 40

But earlier you posted it as x^2- 5x =6 ( '=' instead of '+'). Typo?

Answer 41

sorry it was a typo

Answer 42

its a plus sign

Answer 43

x^2-5x+6
Same question: What two numbers multiply to +6 and add to -5?

Answer 44

3 and 2

Answer 45

Yes, 3 and 2 is correct.
Next, what should be the signs of 3 and 2.
Remember they have to multiply to +6 which means both have to be the same sign. Either +3 and +2 OR -3 and -2. In both cases they will multiply to +6.
But it should also add to -5. So what should be the signs? +3 and +2 OR -3 and -2?

Answer 46

3 is negative and 2 positive

Answer 47

They cannot be opposite signs because they will multiply to a negative number but we want positive 6. So they have to be the same sign. Both positive or both negative.