Question

I dont understand polynomials at all, can you help me with this? 3a²-14a+15

Answer 1

What about it?

Answer 2

(3a-5)(a-3)

Answer 3

@gaby6 , why do you say that? Do you know what Heather's question is?

Answer 4

I dont see how to get that?

Answer 5

I need to know how to solve this...

Answer 6

define 'solve'

Answer 7

^ good question.

Answer 8

using a polynomials strategy & explain the process

Answer 9

[If there is no equals sign, it is not an equation, and there is nothing to solve for.]

You can find roots of that polynomial, you can attempt to factor it. You can use it as a function and rewrite it in vertex form. There are all sorts of things you could do.

Answer 10

factor the polynomials using whatever strategy seems appropriate. State what methods you will use and then demonstrate the methods on your problems, explaining the process as you go. Discuss any particular challenges those particular polynomials posed for the factoring.

Answer 11

Ah, factoring. Wonderful. I recommend splitting the middle term.

Answer 12

huh? 14/2 is 7? not sure what to do after that

Answer 13

You won't necessarily split it half, but it needs to be split in such a way that the two numbers are factors of 45. (Because 3×15=45)

Answer 14

The way to start is to multiply the leading coefficient (the number on the x^2, in your case, 3) by the constant (the number at the end, in your case 15).
Then find other factor pairs of that number that you can add or subtract to make the middle term.
Get it?

Answer 15

There are other strategies too, such as a guess-and-check method that some people prefer, but I tend to not be very lucky at guessing, so I like this method because it works every time.

Answer 16

so, 3 * 15 =45 now i have to find a number that 14 factors into 45?

Answer 17

Sortof, you want to find factors of 45 that add up to 14.

Answer 18

so factors are 1, 3 , 5 , 9 ,15, and 45
and....9 & 5 = 14?

Answer 19

Exactly!
Now you know that it is factorable. (if you couldn't find any factor-pair that works, then the number is prime.

Ok, so now you can split that -14x into -9x and -5x.

Answer 20

Sorry, -14a into -9a and -5a.

Answer 21

so were do this numbers factor into the end

Answer 22

I forgot the variable was a, not x. :">

Answer 23

3a² - 14a + 15 becomes 3a² - 9a - 5a + 15.
Now you can factor-by-grouping: factor the first two terms and the last two terms separately.

Answer 24

how do i factor 3a² - 9a when they are both not a²

Answer 25

They both at least have 1 a each and another common factor too.

Answer 26

the common factor ios 3? so does it become a² -3a

Answer 27

Each term has 3a as a common factor. Taking that out makes 3a(a-3).

Answer 28

ok so the 2nd half has a common factor of 5?

Answer 29

Not just a 5, but a -5.

Answer 30

leaving -5(a+3)??

Answer 31

-5(a-3)
The (a-3) has to match the other one.

Answer 32

ok, so the finally is 3a(a-3) -5(x-3)??? is that hows it wrote?

Answer 33

That is how it is written, yes.

So now you have
\[\large 3a(a-3)-5(a-3)\]
The (a-3) is a common factor, so when you take that out, you'll have
\[\large (3a-5)(a-3)\]

Answer 34

thank you this was a HUGE help, a lot more then i thought