Rewrite middle term as sum of two terms and factor complet

[exw9141]

12w^2+9w+4 I am suppose to use the ac method

a=1 b=9 c=4

ac=12(4)=48

mn=48 and m+n=9

i got the factors of 48 1*48 2*24 3*16 4*12 6*8

I cannot see a combination that will sum up to 9...What am I doing wrong?

 

[exw9141]

the question was wrong should be middle term 19

so with that corrected is the answer 12w^2+16w+3w+4

is that factored completely

 

[stapel]

s the answer 12w^2+16w+3w+4[?] s that factored completely[?]

Is isn't factored at all, actually....

"Factored" means "taken apart into its factors" or "rewritten as a product of factors". To "factor" the number 6, one would write "3×2", rather than any sort of sum such as "1 + 2 + 3". Adding and multiplying are not the same, so summands and factors are not the same.

This question is asking you to find the two binomials that were multiplied to obtain the resulting quadratic. In other words, instead of giving you, say, (x + 2)(x + 3) and asking for the product x² + 5x + 6, they're giving you x² + 5x + 6 and asking you to do something along the lines of the following:

. . . . .x² + 5x + 6

. . . . .x² + 2x + 3x + 6

. . . . .(x² + 2x) + (3x + 6)

. . . . .x(x + 2) + 3(x + 2)

. . . . .(x + 2)(x + 3)

Hope that helps a bit. If not, please reply with specifics, showing your steps. Thank you.

Eliz.

 

[Mrspi]

the question was wrong should be middle term 19

so with that corrected is the answer 12w^2+16w+3w+4

is that factored completely

As Eliz pointed out, it isn't factored (written as a product) AT ALL. But, you are ready to factor at this point....and you will use "factoring by grouping."

Group the first two terms together, and the last two terms together:
12w^2 + 16w + 3w + 4

Remove a common factor of 4w from the first two terms, and a common factor of + 1 from the last two terms:

4w(3w + 4) + 1(3w + 4)

Now, (3w + 4) is a common factor. Remove it, and you have
(3w + 4)(4w + 1)

THERE! It is written as a product. To check to see that this factorization is correct, you can multiply the two binomials together; you should get the expression you started with.

 

[exw9141]

thanks for the help