Question

i need help with 3 others like this including this one:
6. Use the polynomial to answer the question.

6b3 + 9b2 - 12b

Which represents the polynomial in factored form?
(Points : 3)
3b3(2b2 + 3b - 4)

3b(2b2 + 9b2 - 12b)

3b2(3b2 + 6b - 9)

3b(2b2 + 3b - 4)

Answer 1

for factoring you are just pulling out the most that you can get from each term, start with the variables, they are easiest.\[b(6b^2+9b+12)\] there is no more like variables in all 3 terms. now move to the numbers, what will 6, 9, and 12 all divide by?

Answer 2

3

Answer 3

should be a -12 up there \[b(6b+9b-12)\]

Answer 4

6,912 are divisible by 3

Answer 5

*6,9,12

Answer 6

so pull the 3 out and divide each number by 3 and you have your answer

Answer 7

is it that easy? they make it so hard in the actual lesson

6/3 = 2
9/3 = 3
-12/3 = -4

Answer 8

so the answer is a?

Answer 9

how many b's did i pull out?

Answer 10

3

Answer 11

lol ok to what power did i pull b out

Answer 12

^3

Answer 13

or is that just the degree?

Answer 14

b^3 = b*b*b

Answer 15

the last term only had 1 b so how could i pull out b*b*b?

Answer 16

no because the degree is the highest
variable

Answer 17

are you saying you have b^2 * b?

Answer 18

because u pulled them out of the ()

Answer 19

factoring is just rearranging terms to find out other ways to write them just like 20 = 1*20=10*2=4*5 and B^3=B^2*b=b*b*b

Answer 20

i see

Answer 21

so one way to check your answer is to multiply each term by what's outside the parentheses and see if if gives you back the original function.

Answer 22

i see so:

the answer is d

because:

3b x 2b^2 = 6b^3

3b x 3b = 9b^2

and

3b x -4 = -12b

Answer 23

yes and just like you multiplied to check your answer when your trying to factor without a multiple choice you just want to find the biggest thing that all 3 are divisible by

Answer 24

7. Use the polynomial to answer the question.

16x2 - 25

Which represents the polynomial in factored form?
(Points : 3)
(4x + 5)(4x - 5)

(4x 5)(4x- 5)

(8x 5)(8x -5)

(8x + 5)(8x - 5)

Answer 25

but it's easiest to do it in steps, look for likenesses in all 3 terms, the lowest order is usually the easiest because if it has only 1 variable then that's all you can factor out. if it has none then you can only look for the greatest common factor

Answer 26

i went with a (used the foil method)

4x * 4x = 6x^2

4x x -5 = -25x

5 x 4x = 25x

5 x - 5 = -25

so i would have :

6x^2 -25x +25x -25

6x^2 - 25

Answer 27

ok once you learn some a few tricks this form is the easiest and you will see why, this one is missing the middle term and it's last term is negative. take the square of each term, then write that twice one with a (ax+b) and one with a (ax-b) that way when they multiply back out the abx and the -abx cancel out and disapear

Answer 28

like -25 +25?

Answer 29

no when you are multiplying polynomials you have to multiply all out so it would be like this

Answer 30

i'm going to do the first answer (4x+5)(4x-5) which happens to be the answer lol
so first (4x*4x) then (4x*-5) then (5*4x) then (5*-5)
so we have (16x²)+(-20x)+(20x)+(-25) add those all up

Answer 31

you go to love the foil method lol

Answer 32

so then i would be able to do the last one to right?
it is:
Use the polynomial to answer the question.
x2 - 8x + 15
Which represents the polynomial in factored form?
(Points : 3)
(x + 3)(x 5)

(x + 3)(x + 5)

(x - 3)(x + 5)

(x - 3)(x - 5)

Answer 33

1 would go into all

Answer 34

2x 4 = 8
and 3 x 5 = 15


thats why i thought it was suposed to look like this (x^2 -(8x) +15) or (x^2 -8x) and (8x +15)

Answer 35

these last 2 are diffrent from the first one, with these you are liiking for something in the form (ax+b)(cx+d) or (ax+b)²

Answer 36

so that means that foil would not work this time how would i go about solving the problem itself?

Answer 37

foil will take one of the answer set to the question

Answer 38

because (-) is first and (=) is second in the original problem:

(x - 3)(x + 5)

(x * x) = x^2
( x * 5) = 5x
(-3 * x) = - 3x
(-3 * 5 = -15

x^2 + 5x - 3x - 15?

x^2 + 2 - 15

Answer 39

here is how i factor polynomials, we are looking for our answer in a form like this (x±a)(x±b)

Answer 40

because that was not the answer i would say "b" would be it if not "a":

Answer 41

you con't subtract the x but the rest is right it would be x²+2x-15

Answer 42

but that is not the original problem

because of that i would say the one with both minus would be it

Answer 43

ok we want a positive 15 but we want the two x terms to add to -8 what would we have to multiple to get something that would add to -8x?

Answer 44

because 2 negative when multiplied make a positive:

(x - 3)(x-5)

x^2 - 5x- 3x+15

x^2 - 8 + 15

Answer 45

ok so let's get some intuition
looking at the last term (15)
it's positive and it's only effected by the b part in (x+b)
so for it to be positive it has to have 2 negatives or 2 positives multiplied together

Answer 46

i think you have it now

Answer 47

and i cant be 2 positives because then the 8 would not fit

Answer 48

correct

Answer 49

thank you :)

Answer 50

np