Let me work it out real quick, then give you a step by step
okay sounds good
Is that a guy in the Picture
Im talkin to the rapper
It's basically factoring, thats why
And yeah, just some black dude ;P So, do you know basic factoring?
kind of.. but im real bad at math lol especially dealing with fractions and factors
Alright, let's take an square equation for example x^2 + 6x + 9 To factor it, the answer will be in the form of ( )( ), right? Since the x^2 is x times x, you can put one x in each of the parenthesis, to get: (x )(x ) Now, the second part, 6x, represents addition. The third part, 9, represents multiplication. So, can you think of two numbers that add to 6, and also multiplies to 9?
3+3= 6 3x3+ 9
i meant 3x3=9 lol
Right, so 3 and 3. We can add that to the parenthesis (x 3)(x 3) Now all were missing is the operation sign. For factoring, the operation sign is always either + or -. Let's put a + in both for the first try (x+3)(x+3), this is when you do the FOIL method. Idk if you've heard of that?
um ive heard of it when i moved to FL but it always confused me
Yeah, factoring is a tough one to teach lol So basically it means, First, Outside, Inside, Last You would multiply the first thing in the first parenthesis by the first thing in the second parenthesis. Both of those values are x, and x times x is x^2 Same with the outside. The outside of the first is an x and the outside of the second is a 3. 3 times x is 3x Inside is a 3 and a x, which is 3x And last is the last thing in each of the parenthesis, which is a 3 and 3. 3 and 3 = 9
okay that makes sense
Awesome! So we combine every answer we found, getting x^2 + 3x + 3x + 9 Then we would combine like terms. 3x and 3x both have just x on the end So our final answer is x^2 + 6x + 9. That's what we started with
So they decided to present you with a overly complication problem. Luckily if you look at the answer choices, they've already given one factor for each part of the fraction, so you just have to find the other to make sure if it's correct
i think its c
So lets' start with A 4z + 3 ------ z + 2 Using the FOIL Method for the top first: (4z + 3)(?????) First: 4z and ? would make 12z^2 (The 12z^2 is from your original question)
Mmm, it's not C
wouldnt it be 4z+3 again sorry im slow lol
Almost 4z and 4z would be a 16z^2, you see it? Because 4x4=16 and z*z = z^2
oh 4z and 3z would be 12z^2
Yes! Exactly (4z +3)(3z ?) Now, lets do the outside, which is well easier. 3 and ? multiply to get 12?
3 and 4
Yep, so let's add that (4z + 3)(3z 4) Now the hardest part: Seeing if that symbol between 3z and 4 is a + or - If it's a +, that would be (4z +3)(3z +4). We can test the outside first and see +3 times +4 = +12, but the original says -12, so it's not that. If we do minus (4z+3)(3z-4), it gives us -12, but doing the foil method, 4z x 4 is 16z and 3z times 3 is 9z. +16z added onto a +9z is a 25z, but the original said -25z Since + or - doesn't work for any of these. 4z+3 isn't right That all make sense? Seeing 4z+3 doesn't work, we can automatically remove two answer choices
So the answer must have 4z-3 on the top Now to figure out the bottom, we do the same thing. They gave us z-2 and z+2 as choices. Since A is out, let's start with B, z+2 (Z + 2)(????) Z times ? would equal 3z? (3z in the original) 2 times ? would equal 8?
-8, not 8
z times 3 would equal 3z
2 times -4
Right! So let's use those (z +2)(3z -4) 3z times z = 3z^2 2 times -4 = -8 The outsides are z and -4, which equals -4z The insides are 2 and 3z, with is 6z -4z + 6z = 2z When you put those 3 answers together you get 3z^2+2z-8! So B must be the answer
Since 3z^2+2z-8 is the same as the original denominator
Thank you so much for all the help :)
No problem! Hope it all made sense!
it did thanks again!