Select one of the factors of 3x2 + 10x + 3

Question

anonymous · Answer

thats not one of my options though. (3x + 1)

(3x + 3)

(3x – 1)

None of the above

myininaya · Answer

$$3x^2+9x+x+3$$
I just found two factors of 3(3) that added up to be 10
Factor this by grouping

myininaya · Answer

What factors does 3x^2 and 9x have in common?

anonymous · Answer

the factors they have in common is 3

myininaya · Answer

and x right?

myininaya · Answer

$$3x(x+3)+1(x+3)$$
Now we have two terms.
What do these two terms have in common?

anonymous · Answer

so the answer is none of the above because its not one of my options

myininaya · Answer

we aren't done

myininaya · Answer

I was just asking you what 3x^2 and 9x had in common so that we can factor this beast

anonymous · Answer

both have 3x in common?

myininaya · Answer

right so from the first two terms i factored out 3x
giving me
$$3x(x+3)+x+3$$

myininaya · Answer

But we can write this as
$$3x(x+3)+1(x+3)$$
since 1(x+3) is still x+3

myininaya · Answer

now what factors does 3x(x+3) and 1(x+3) have in common besides the factor 1?

anonymous · Answer

3x again?

myininaya · Answer

no they both have the factor (x+3) in common

myininaya · Answer

$$(x+3)(3x+1)$$

anonymous · Answer

so the answer is (3x + 1)

myininaya · Answer

x+3 and 3x+1 are both factors of the polynomial given

anonymous · Answer

x+3 & 3x+1 are the factors