Question

how to factor a equation?

Answer 1

what is your equation?

Answer 2

x^2-6x-16

Answer 3

(x+a)*(x+b)

Answer 4

Hint:
x^2-8x +2x - 16

Answer 5

find an a and b so that when you expand

(x+a)*(x+b)

you get x^2-6x-16

Answer 6

how do you know which is a or b?

Answer 7

pick numbers

Answer 8

You have to split the middle term

Answer 9

a and b mulstiply to -16 and add up to -6

Answer 10

-6 = -8 + 2
-16 = -8*2

So:
x^2-6x-16
x^2-8x +2x - 16
x(x-8)+2(x-8)
(x-8)(x+2)

Answer 11

Those are the proper steps to factor

Answer 12

Unfortunately, a lot of students are taught to skip steps

Answer 13

mmmm...... i get it now thankyou very much!:D

Answer 14

ok here when you split -6x what do you have to split it to?

ax+bx what are the conditions for picking a and b?

Answer 15

*hero sorry

Answer 16

@timo86m, I'm sure you already know what they are.

Answer 17

im just really confused right now xD

Answer 18

the way i learned it was from a equation ax+by=c

Answer 19

no the way i was taught is

(x+a)*(x+b) =x^2+x*b+a*x+a*b

which to me says find a and b that multiply up to the constant and add up to the coefficient of the x term

Answer 20

they way you put it @hero is that students skip a step what step did i skip? Splitting the coeffeicent of x? in order to do that i must have had forehand knowneldge that it would be 2 and -8

Answer 21

You skipped the computational steps which directly show exactly the process of factoring from the trinomial to the product of two binomials.

Answer 22

lol idk i think i did show that

Answer 23

I just showed that you actually skipped steps. But it's okay, that's just how you were taught.

Answer 24

@timo86m

You start with \(ax^2 + bx + c\), so from that, explain how you end up with (\(x+a)(x+b)\).

Answer 25

she had no coefficient in x^2 term so it safe to assume (x+a)(x+b)

Answer 26

yeah i got it now:)

Answer 27

Even so, you can assume a = 1, you still haven't explained anything a^2 + bx + c is the general polynomial for factoring trinomials

Answer 28

Suppose the polynomial she gave was \(2x^2 + 11x + 9\). How would you explain it more generally since \(ax^2 + bx + c\) is the general polynomial term. I'm just curious what you will get when you factor in general.

Answer 29

@timo86m