Which polynomial has 3x + 4 as a factor?
12x^2 – 2x – 20
9x^2 – 3x – 8
12x^2 + 7x – 8
9x^2 + 3x – 12

- anonymous

Which polynomial has 3x + 4 as a factor?
12x^2 – 2x – 20
9x^2 – 3x – 8
12x^2 + 7x – 8
9x^2 + 3x – 12

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- anonymous

@ParthKohli @pooja195

- anonymous

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

- anonymous

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

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## More answers

- anonymous

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.

- anonymous

20?

- anonymous

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.

- anonymous

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

- anonymous

2 times 6 makes 12

- anonymous

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

- anonymous

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

- anonymous

12

- anonymous

does 12 = x^2?

- anonymous

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

- anonymous

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

- anonymous

im not sure

- anonymous

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

- anonymous

6

- anonymous

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

- anonymous

6

- anonymous

There is no 6 in the equation

- anonymous

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

- anonymous

a

- anonymous

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

- anonymous

x

- anonymous

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

- anonymous

are you there?

- anonymous

yeah

- anonymous

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

- anonymous

Behind the 2 and 6

- anonymous

yes, show me.

- anonymous

(2x) (6x)

- anonymous

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?

- anonymous

10 and -2

- anonymous

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?

- anonymous

no

- anonymous

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

- anonymous

1 and 12

- anonymous

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?

- anonymous

3 and 4

- anonymous

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

- anonymous

im not really sure

- anonymous

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

- anonymous

(3x) (4x)

- anonymous

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?

- anonymous

10

- anonymous

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?

- anonymous

-5

- anonymous

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

- anonymous

i think so

- anonymous

show me how you FOILed it out

- anonymous

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

- anonymous

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

- anonymous

2x

- anonymous

(3x+4)(4x-5)|dw:1443463356798:dw|

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