Question

Factor the trinomial completely. a^4-2a^2-35

Answer 1

Do you know how to factor in general?

Answer 2

i know you have to look for a number that when you add you get 2 and when you multiply you get 35

Answer 3

but when i tried it out i got it wrong

Answer 4

Any idea what those two numbers are?

Answer 5

1 and 5?

Answer 6

Hmm does the product of 1 and 5 get you close to 35 or even add up to two?

Answer 7

If not, what are some multiples of 35 that we can assess?

Answer 8

5 and 7 is 35 and the only number i can think that gets 2 is 1. or does it have to be the same number to get 35 and 2?

Answer 9

No it doesn't have to be the same number. Bingo, you hit it :)

Answer 10

5 and 7 is your answer

Answer 11

Now put it in the equation to factor

Answer 12

Remember it's negative two :)

Answer 13

oh! so it would be (x+5) (x+7)?

Answer 14

Nope

Answer 15

Your first line should look like this

a^4 +5a^2 - 7a^2 -35

Answer 16

ahh i don't get it :/

Answer 17

sorry

Answer 18

Ah dw :) I'll help you understand it

Answer 19

Ready?

Answer 20

yes and thank you :)

Answer 21

Alright so you have that whole idea of factoring. How to factor?
Simply find two numbers that add up to the middle and multiply to the last. Right?
Alright, so the situation of factoring is not always the same. It's different. The answer may not look right to you, but it's right when you multiply it back up again.

Answer 22

In our case, we have an equation with a degree of 4.

Answer 23

How do we find it? Nothing changed. Same steps, different numbers.

Answer 24

Just like opening a potato bag, Different shapes, still the same method of cooking it.

Answer 25

Ready to move into the question?

Answer 26

perfect. yes

Answer 27

Alrighty :) So moving into the equation: a^4 - 2a^2 -35
We found two numbers, yeah? 7 and 5.
5 - 7 = -2
5*7 = 35

Perfect. All we gotta do now is put it into the equation.

Answer 28

Btw for the subtraction, 7 is a negative.
Hence, 5+(-7) = x
5 - 7 = x
-2 = x

Answer 29

You always add the numbers. The numbers however are not always positive.

Answer 30

Get it?

Answer 31

oh ok yes got it

Answer 32

now it's starting to make sense

Answer 33

Alright that's what I wanted to do. :)

Answer 34

Now that you have your two numbers, we insert them into the equation and factor :)

Answer 35

Wanna try that? Show me step by step so you don't confuse yourself. Remember same steps, different numbers. Just follow the equation. Don't force an answer that appears orthodox.

Answer 36

idk if i'm right.. um is it (a^2+5)(a^2-7)?

Answer 37

I would kiss you congrats, but I can't. AWESOME MAN. You learned well :)

Answer 38

You're right :)

Answer 39

Remember what I taught you, keep up the good work.

Answer 40

hahahaha! yay :) awesome thank you so much

Answer 41

Ahaha anytime Ma'am. See you around :)

Answer 42

see ya :)