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Mathematics 40 Online
EndersWorld:

Factoring... again... (1 of 11)

EndersWorld:

\[12x^2-5x-3\] a=12 b=-5 c=-3 ac=-36 (1)(36) (2)(18) (3)(12) (4)(9) (6)(6)

Hero:

Looks good so far :)

EndersWorld:

\[-9+4=-5/] \[-9*4=-36\]

Hero:

Good

EndersWorld:

\[12x^2-(9+4)x-3\]

EndersWorld:

\[12x^2-9x+4x-3\]

EndersWorld:

\[3x(4x-3)+1(4x-3)\]

Hero:

Looks really great so far!!

Hero:

Oh but wait ...

EndersWorld:

Yes?

Hero:

\(12x^2-(9+4)x-3\) Start with this step. This step is correct. Then continue from here but remember to DISTRIBUTE the negative.

EndersWorld:

\[12x^2-9x-4x-3\]

Hero:

Very good. Now you may continue.

EndersWorld:

\[(12x^2-9x)-(4x-3)\]

EndersWorld:

\[3x(4x-3)-1(4x-3)\]

Hero:

Ah, I see what you did now. Should have caught that one. You keep forgetting to properly replace the five with an equivalent expression. 5 = 9 - 4 not 9 + 4

Hero:

Because 9 + 4 = 13 which is clearly not 5 so you have to be careful when replacing

Hero:

\(12x^2-(9-4)x-3\) This is correct

EndersWorld:

What?

Hero:

9 - 4 = 9 + 4 = Answer that above then we can continue

EndersWorld:

5 13

Hero:

Okay, do you understand now which expression is the correct expression to replace with 5?

EndersWorld:

9-4

Hero:

Very good. So now, can you continue from here? \(12x^2-(9-4)x-3\)

EndersWorld:

\[12x^2-9x-4x-3\]

Hero:

Well, then you'd have the same expression as before. When you distribute the negative the signs within parenthesis flip flop.

Hero:

The positive number becomes negative. The negative number becomes positive.

EndersWorld:

\[12x^2-9x+4x-3\]

Hero:

There we go. Now you may finish finally.

EndersWorld:

Ugh... I feel dumb.. I’m still getting \[3x(4x-3)1(4x-3)\]

Hero:

There is a plus missing. Otherwise it is correct.

EndersWorld:

\(\color{#0cbb34}{\text{Originally Posted by}}\) @EndersWorld Ugh... I feel dumb.. I’m still getting \[3x(4x-3)+1(4x-3)\] \(\color{#0cbb34}{\text{End of Quote}}\)

Hero:

Yes, very good. Now factor out the binomial common to each factorization.

EndersWorld:

\[(3x+1)(4x-3)\]

EndersWorld:

I need to go.

Hero:

Okay, well keep practicing. You're making huge progress. Never give up!

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