Question

Which polynomial has 3x + 4 as a factor?

12x^2 – 2x – 20


9x^2 – 3x – 8


12x^2 + 7x – 8


9x^2 + 3x – 12

Answer 1

@ParthKohli @pooja195

Answer 2

can you tell me what a factor is and how it works?

Answer 3

a number or quantity that when multiplied with another produces a given number or expression.

Answer 4

Then we need to look at each answer to see if these contain the desired factors. Start with A and see what you can factor out. Is it what we are looking for? If yes, then this is your answer, if no go to the net one and do it again.

Answer 5

20?

Answer 6

Perhaps this isn't factoring out something, but what are the factors of the problem. When you FOIL the factors you would get the problem you now see.

Answer 7

What time what makes twelve, what times what makes twenty, when added them together do they produce the middle term?

Answer 8

2 times 6 makes 12

Answer 9

Good Job,
so the first part of what you should be writing down is
(2 )(6 )

Answer 10

Since you have an x^2 next to the 12 what do we need to multiply that gives us x^2?

Answer 11

12

Answer 12

does 12 = x^2?

Answer 13

2*6=12
?*?=x^2

Answer 14

a*a=a^2
b*b=b^2
?*?=x^2

Answer 15

im not sure

Answer 16

look at the example I just gave. What did I multiply to get a^2?

Answer 17

6

Answer 18

a*a=a^2
what is being multiplied here?

Answer 19

6

Answer 20

There is no 6 in the equation

Answer 21

There are two letters being multiplied together. What are the letters?

Answer 22

a

Answer 23

yes, so if a * a = a^2
what letters do we need to get x^2?

Answer 24

x

Answer 25

Yes, so now show me where the x's go in what you are writing down

Answer 26

are you there?

Answer 27

yeah

Answer 28

where do the x's go
(2 )(6 )

Answer 29

Behind the 2 and 6

Answer 30

yes, show me.

Answer 31

(2x) (6x)

Answer 32

ok but leave some space because we need to put more of the problem inside
(2x )(6x )

12x^2 – 2x – 20

so we have the 12x^2 now what factors make up -20?

Answer 33

10 and -2

Answer 34

ok.
but let's take a look at what question we are being asked.
Do any of the factors have 3x + 4 as a factor?

Answer 35

no

Answer 36

so let's look at 12x^2 again. instead of 2*6 is there anything else when multiplied that equals 12?

Answer 37

1 and 12

Answer 38

yes, 1 and 12 do = 12
but are they the factors we are looking for?
are there any factors that we are looking for that =12?

Answer 39

3 and 4

Answer 40

Good job. so show me how you write that down with our x's

Answer 41

im not really sure

Answer 42

Well, we had (2x )(6x ) before, but we found out 2*6 are not part of our factors. Now, using our factors replace 2 and 6 with 3 and 4

Answer 43

(3x) (4x)

Answer 44

ok. Now we are still working on our -20. and 2 and -10 are not part of our factor that we are looking for. 3x + 4
which numbers contain one of our factors when multiplied give us -20?

Answer 45

10

Answer 46

Do you see that we have part of the correct answer
(3x )(4x )
3x + 4
Now we need to use the 4 to get -20.
What could we multiply 4 by to give us -20?

Answer 47

-5

Answer 48

ok. So lets put them in
(3x+4)(4x-5) now FOIL it out and tell me if it is = 12x^2 – 2x – 20

Answer 49

i think so

Answer 50

show me how you FOILed it out

Answer 51

I mutiplied 3 and 4 and got 12x. Then I multiplied 4 and -5 and got -20

Answer 52

What is FOIL? Isn't there more multiplication to be done?

Answer 53

2x

Answer 54

(3x+4)(4x-5)