Question

I need somebody to go step by step through factoring problems that have the leading coeeficiant infront of the first x

2x^2 + 11x + 12

Answer 1

There are multiple ways to do this. How have you been taught?

Answer 2

LA, i remember my teacher telling me i would have to multiply 2 and 12 so i get 24x but i do not remember further

Answer 3

Okay. Once you get 24x, you are looking for factors that give you 24 and add up to 11.

Answer 4

Your choices are:
1 * 24
2 * 12
3 * 8
4 * 6

Answer 5

2x^2+8x+3x+12
2x(x+4)+3(x+4)
(2x+3)(x+4)

Answer 6

okay so 8 and 3

Answer 7

and then u split the middle term or something right?

Answer 8

Settling on 3 * 8, you rewrite 2x^2 + 11x + 12 as 2x^2 + 8x + 3x + 12
Notice we did not change the value of the equation.
We did however go from 3 terms to 4 terms...

Answer 9

ok let me write it down real wuick hang on

Answer 10

Now you can factor by grouping.

Answer 11

just write your factors with your 8 and 3; just remember to divide out the 2 you used in the beginning

Answer 12

okay now do i group them into like two sets?

Answer 13

one way is to make 3 columns and use trial and error

2x^2 +12 +11x
-----------------------------
2x * x 4 * 3 3 * 2x + 4 * x = 10x - incorrect
4 * 2 x + 3 * x = 11x - correct

so factors are (2x + 3 )( x + 4 )

Answer 14

2x^2 + 8x + 3x + 12
2x (x + 4) + 3 (x+4)

Now again factor out what is common:
(x + 4) (2x + 3)

Answer 15

wait this is where i get confused

Answer 16

i dont see wheere you are getting that

Answer 17

See link below for full step by step solution

http://www.algebra.com/algebra/homework/quadratic/Quadratic_Equations.faq.question.473453.html

Answer 18

Okay.

I split the four terms into two binomials:

(2x^2 + 8x) + (3x + 12)

Answer 19

then you might wanna try this way;

you found 8 and 3 already so set it up:

(x+8) (x+3) ; but we gotta divide out that 2 from the front

(x+8/2) (x+3/2) ; thats better, now simplify

(x+4) (x+3/2) ; if we still got a fraction, stick the bottom in front

(x+4) (2x+3) and we are done

Answer 20

I then factor each binomial.

(2x^2 + 8x) + (3x + 12)
Looking first for a GCF, I find 2x in the first binomial and 3 in the second binomial.

Answer 21

okay i see it so far

Answer 22

So (2x^2 + 8x) becomes 2x(x + 4)
and (3x + 12) becomes 3(x+4)

Answer 23

ok right there. where did 12 come from

Answer 24

So that leaves me with:

2x(x + 4) + 3(x+4)

Answer 25

alright i see it but how does 8x turn into just 4

Answer 26

Recall we broke up (2x^2 + 8x) + (3x + 12) into 2 separate binomials.

Answer 27

Because when we distribute 2x(x + 4) we go back to 2x^2 + 8x

Answer 28

2x * x is 2x^2, 2x * 4 is 8x

Answer 29

alright so this is the full problem, what one would be the answer?


2x2 + 11x + 12
Which of the following is one of the factors?

(2x + 4)

(x + 4)

(x + 3)

prime

Answer 30

(x + 4)

Answer 31

Since 2x^2+11x+12 = (x+4)(2x+3) as shown above, this means that x+4 and 2x+3 are both factors. So the answer is choice B since that's the only factor shown in the list of choices.