Question

1. Matt is asked to simplify x + x2 + x3 + 3x. Here is what he does:
x + x^2 + x^3 + 3x = 4x + x^2 + x^3
= 4x3 + x^3
= 5x^3
Did Matt do this problem correctly or incorrectly? If he did it correctly, then what math laws did he follow? If he did it incorrectly, then what math laws did he break?

2. Matt is asked to factor the following: x^2 + 3x + 2, but he is stuck after starting the “area” model. His starting point is below. Finish the factoring for him using our area model and describe in words what you are thinking.

Answer 1

How would you simplify \(\Large x+x^2+x^3+3x\)?

Answer 2

@kc_kennylau first you would combine like terms right?

Answer 3

Yep :)

Answer 4

So that would make it 4x+ x^2+x^3??

Answer 5

Yep :)

Answer 6

But can you combine 4x + x^2 to form 4x^3?

Answer 7

Okay...I don't know how to figure out the rest. (im not very good at math)

Answer 8

The rest means the second question or what?

Answer 9

No, it means I don't know the rest of the first question. If he did it correctly, which math laws did he follow and if he did it incorrectly, which math laws did he break?

Answer 10

First Did he do it correctly?

Answer 11

I think so...?

Answer 12

if he did it correctly then
x + x^2 + x^3 + 3x = 4x + x^2 + x^3
= 4x3 + x^3
= 5x^3
in the first line he added the powers of 4x+x^2=4x^1+x^2=4x^(1+2)=4x^3
appearly that was the logic he follows

Answer 13

yeah correct