Question

can someone please give me tips on solving quadratic equations by factoring :) thanks!

Answer 1

i found this website, but its the best i can give you, i have the same problem http://www.wolframalpha.com/input/?i=x^2%2By^2-18y%2B56%3D0%2C+x^2%2By^2%2B9x-15y%2B74%3D0

Answer 2

http://www.wolframalpha.com/ is the original website

Answer 3

Honestly, I don't know any tips, it just takes practice. Practice a lot and it'll be really easy and fun :)

Answer 4

how do you do them tho?

Answer 5

ok let me say somethimg here guys,

Answer 6

first of all it's not all quadratix experssions are factored directly,

Answer 7

becasue some are done only using the quadratic formula

Answer 8

second. in the direct factorization of quadratic experssions we follow trail and error method

Answer 9

and such method need some practising and showing some patcience at the begining.

Answer 10

it would'nt take time then to find your self an expert in that.

Answer 11

my strategy is to have explanation with example approach, so let's have some:

Answer 12

Ex#1) x^2+2x+4

Answer 13

have 2 brackets opened : ( ) ( )

Answer 14

take the x^2 term and distribut it as x * x , put each x in one of the bracket

Answer 15

(x ) (x )

Answer 16

for example how do i get positive at the 2nd term and negative at the third term... something like that

Answer 17

then we come to the very sinsitive step, that factorizing the last term

Answer 18

I'll show that now

Answer 19

we look at the third terim , that 4 and try to check 4 comes from multiplying 2 numers , what are the possibilites here

Answer 20

as we know 4=2*2 or 4=4*1

Answer 21

so what will be our choice here?

Answer 22

here, I have to change my example because it's not valid in the 2nd term to explain the idea, I'll do little change

Answer 23

Ex. 1) x^2 +4x+4

Answer 24

\[(x^2+2x-15)\]
(x ) (x )
Ask yourself: What times what equal 15? Answer: 5 and 3
(x 5)(x 3)
Ask yourself: What signs corresponds with which number? Answer: 5 and -3 because 5*(-3)=15 and -3+5=2 <-The middle term.
Therefore, the answer is (x+5)(x-3)

Of course, this process, like Raheen said, is trial and error, but after enough practice, you should be able to quickly recognize how to "mix and match."

Answer 25

now we can see 4=2*2 we can reach to the middle term by summing of the factors of 4 , that is 2+2

Answer 26

so x^2+4x+4= (x+2)(x+2)

Answer 27

regarding the signs we usualy look at the sing of the last term, if it is + , then we know that our two signs in the brackets would be identical, that is either +,+ or -,- , depending on the sign of the middle term

Answer 28

but if the sign of the third term was negative, then our 2 brackets signs would be +,- or -,+

Answer 29

Ex2) X^2 +5x+6 ,X^2 -5x+6 , X^2-5x-6 , what is the differnce between factoring these three quadratic experession ?

Answer 30

let's try the first one X^2 +5x+6 = ( x ) (x )

Answer 31

we distribute x^2 into x*x

Answer 32

then it's -,-

Answer 33

or +,+

Answer 34

well, it's +,+ or -,- , depending on the sign of the middle term

Answer 35

how do I solve it if the last term is a prime number?

Answer 36

the prin is 1* itself

Answer 37

X^2 -5x+6 , X^2-5x-6 , can you do the first one here

Answer 38

they are to let you know the differnce

Answer 39

(x-6)(x-1)
x^2-x-6x+6
x^2-5x+6
???

Answer 40

your posting looks to me interfering

Answer 41

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

Answer 42

why 3and 2? and why -,- ?

Answer 43

because 3*2 is 6

Answer 44

right

Answer 45

and - * - is +

Answer 46

exactly

Answer 47

I tel a point that you can test your facors in a fast way

Answer 48

anyway how did my post look interfering?

Answer 49

just in this (x-6)(x-1) x^2-x-6x+6 x^2-5x+6 ???

Answer 50

not all posts

Answer 51

ok try this x^2-5x-6

Answer 52

(x+1)(x-6)
x^2-6x+x-6

Answer 53

then I'd get x^2-5x-6

Answer 54

great

Answer 55

ok let's have this x^2-4x-5

Answer 56

(x-5)(x+1)
x^2+x-5x-5

Answer 57

then I'd get x^2-4x-5

Answer 58

great too

Answer 59

yepee :)

Answer 60

ok let me draw a fast method to check any time you carry this type

Answer 61

ok :)