Question

HELP ME PLEASE, PICTURE ATTACHED WILL GIVE MEDAL AND FAN

Answer 1

@e.mccormick @mathstudent55 @precious32 @zepdrix @Zioh @zzr0ck3r @Luigi0210 @MonaLove

Answer 2

@Whitemonsterbunny17 @asatt32 @Eytan99 @Wolfboy @RosieF

Answer 3

Let's look at where the trinomial comes from.
Instead of starting with a trinomial that needs to be factored, and then you don't know for sure if the trinomial can be factored until we try, we will start with a product of two binomials.

What is (2x + 3)(3x - 4) = ?
Can you use FOIL and find the trinomial?

Answer 4

yes

Answer 5

What do you get?

Answer 6

wait i'm going to do it now

Answer 7

ok

Answer 8

\[6x^2+x-12\] uhm im not quit sure if its that

Answer 9

Yes, you're correct.

Answer 10

Ok. Now we have a trinomial of the form ax^2 + bx + c that definitely can be factored because we got it by multiplying two binomials together.

Answer 11

The way I factor these trinomials is using the ac method.
This method is used to factor a trinomial of the form \(ax^2 + bx + c\)

The ac method:
1. Multiply ac together.
2. Find two factors of ac that add up to b. Call them p and q.
3. Break up bx into two parts, px and qx.
4. Factor the by grouping.

Answer 12

Now let's look at our trinomial.

\(6x^2 + x - 12\)

1. Multiply ac: \(6 \times (-12) = -72\)
2. Find two factors of ac that add up to b. ac = -72; b = 1
\(9 \times (-8) = -72\)
\(9 + (-8) = 1\)
3. Break up the term bx using the two factors we found above.

\(6x^2 + 9x - 8x - 72 \)

Answer 13

I just noticed that with our trinomial, a and b are positive, and c is negative.
Your problem states that a is positive and b and c are negative.
Let's modify our trinomial a little.

Let's start with this product.
(2x - 3)(3x + 4)

We use FOIL to get:
\(6x^2 -x - 12\)

Now we have a = 6, positive, and
b = -1, negative, and
c = -12, also negative just like the problem states.

Answer 14

Now let's do the ac method again for factoring.

1. Multiply ac: 6×(−12)=−72
2. Find two factors of ac that add up to b. ac = -72; b = 1
\(-9 \times = −72\)
\(-9 + 8 =-1\)
3. Break up the term bx using the two factors we found above.
\(6x^2 -9x+8x−72 \)

Answer 15

Ok. Now let's look at your question.

Answer 16

\(\large6x^2 - x - 12 = 6x^2 - 9x + 8x - 72\)

a is positive, and c is negative, so ac is negative.
The two factors we find, that the problem calls m and n, must be one positive and one negative, so that their product can be negative.

Answer 17

We can call m = -9 and n = 8, or
m = 8 and n = -9, so we don't know which one is larger than the other.
All we know is that one is positive and one is negative.

Answer 18

is it B

Answer 19

i think it is

Answer 20

B has both numbers negative. I think one number needs to be positive and the other one negative. I don't understand the part about |m| > |n| and |n| > |m|.