Question

13x^2-38x-3

Answer 1

do you want to factor it?

Answer 2

yah

Answer 3

\[13x^2 -38x-3\]\[=x^2 -38x -39\]\[=(x-39)(x+1)\]\[=\left(x-\frac{39}{13}\right)\left(x+\frac{1}{13}\right)\]\[=(x-3)(13x+1)\] Steps:
1. multiply the leading coefficient over to the constant to transform your quadratic into a function that is easy to factor.
2. find two factors that multiply to give -39 and ad to give -38
3. Since you have mulltiplied the coefficient, you now have to divide by it to keep the exact form of the original equation.
4. divide both factors by the coefficient and simplify whatever you can
5. Whatever does not divide, multiply it over to the variable.

Answer 4

wow - I've never seen that method before. Looks a bit complicated !!

Answer 5

is there a name for it?

Answer 6

is there a easy way?

Answer 7

Really? Pretty easy once you practice it. I don't like factoring with coefficients in front. They make my life harder than it needs to be.

Answer 8

That is probably the easiest way, other than using the quadratic formula.

Answer 9

but the quadricic formula wont come out the same answer right?

Answer 10

i think he means use the quadratic formula if you need to solve the equation f(x) = 0

Answer 11

- it sould come out with the same answer

Answer 12

she*

Answer 13

the way i would do this one is to play around with the factor of 13 and -3

Answer 14

sorry she

Answer 15

yeah see, my method avoids the guess and check approach. All you have to do is constantly remember how you are transforming the function and what you need to do to get the original equation back.

Answer 16

Another method would be to complete the square, (my favorite)

Answer 17

in this case the factoring is easy it must be 13 * 1 and either -3*+1 or 3*-1

Answer 18

so factoring a polymnial completly is easy?

Answer 19

some are - some are not

Answer 20

\[13x^2-38x-3\]\[=13\left(x^2-\frac{38}{13}x\right)-3\]\[=13\left(x^2 -\frac{38}{13}x+\frac{361}{169}\right)-3-\frac{361}{13}\]\[=13\left(x-\frac{19}{13}\right)^2 -\frac{400}{13}=0\]

Answer 21

Just showing you various methods of approach.

Answer 22

The one above is the completing the square method.

Answer 23

thank i really just cant get factoring in my head i dont get it

Answer 24

But yes, give the first method I showed you a try, you too @cwrw238 and then check back with my answer.

Answer 25

yea i looks like a good method but needs to be practiced. I supposed I'm used to my own method - i've used it since the early days and find it quite easy.

Answer 26

whats your method?

Answer 27

well - take this question
13x^2 - 38x - 3
now the only factors of 13 are 13 and 1 so the factors must be
(13x )(x ) where the blanks need to be filled in

Answer 28

now we need to get -38 from 13 * 1 and the factors of -3 which is -3*1
so its -3*13 + 1
so we have
(13x + 1)(x - 3)