Question

I need help factoring this problem 9+16xsquared+24x

Answer 1

9+16x^2+24x can be arranged using the commutative property to be into ax^2+b^x+c form. (standard form.) therefore, you can make it: 16x^2+24x+9, which factors into (using my method (x-factor) but you can do it any other way) (16x+12)^2, which simplifies into (4x+3)(4x+3).

Answer 2

(3x+4)^2 is that right

Answer 3

No, if you have (3x+4)(3x+4), it will simplify into (9x^2+24x+16), which, while it has the same numbers, is not the same value as the original trinomial

Answer 4

so because 3x+3x=6*4 so it would (3x+4)(3x+4)

Answer 5

Well, 3x+3x=6x, Im not entirely sure where you got 6*4, but I'll try to explain step-by-step exactly how I got (4x+3)(4x+3) and how I checked it, if that's where youre getting confused.

16x^2+24x+9. There are a few ways you can do this. You can't factor out a GCF (greatest common factor) because there isn't one in this trinomial. You could use guess-and-check method, AC method, box method. Im sure your teacher has gone over at least one. I don't want to confuse you further, but since I don't really like those methods, I'm going to explain using the x-factor method. I'll also add a picture in a moment of how its normall set up.

16x^2+24x+9. A=16 B=24 C=9.

To start this method, you'll usually draw an "X" under neither the trinomial (in image). In the first little triangle, you'll do (A*C). So in this case, 16x9=144. In the bottom triangle, you'll have the value for "B", which is 24. In both of the side triangles you'll have "Ax+__". In this case, it will be "16x+__". To fill in the blank, you'll need to find a number that has a product of 144, and a sum of 24. In this case, it will be '12'. So in both side triangles, you'' have '16x+12'. This binomial, though, has a GCF. You'll divide out a 4(the gcf), and you'll have 4x+3 on either side. Your solution is (4x+3)(4x+3).

To check, you'll FOIL your solution out. (just like you would multiply to check a division problem). (4x+3)(4x+3). 4x*4x equals 16x^2. 4x*3 equals 12x, 3*4x equals 12x, and 3*3 equals 9. You currently have (16x^2+12x+12x+9). Combine like terms, and you'll have (16x^2+24x+9), a trinomial that matches your original one.

If you don't understand any of this, tell me. What i just explained is the exact process I went through to get the solution to your problem.