Math  /  Algebra

Question13. Modélise ces polynômes. a) x2+x1x^{2}+x-1 b) 3x+23 x+2 c) 2x-2 x
4. Représente ces polynômes par un modèle. a) x2+3-x^{2}+3 b) 2x23x2 x^{2}-3 x c) 8

Studdy Solution

STEP 1

What is this asking? We need to represent the given polynomials using algebra tiles! Watch out! Pay close attention to the signs of the terms; they tell us whether to use positive or negative tiles.

STEP 2

1. Model polynomials from question 13.
2. Model polynomials from question 4.

STEP 3

Let's **start** with 13.a), x2+x1x^{2} + x - 1.
This polynomial has three terms: a positive x2x^{2} term, a positive xx term, and a negative constant term.

STEP 4

To represent x2x^2, we'll use a **big square tile**.
Since it's positive, it'll be, let's say, **blue**!

STEP 5

For the xx term, we'll use a **rectangular tile**.
It's also positive, so it's **blue** too!

STEP 6

Lastly, the 1-1 is represented by a **small square tile**, but this time it's **red** because it's negative!

STEP 7

Now, 13.b), 3x+23x + 2.
We have three positive xx terms and two positive constant terms.

STEP 8

That means we need **three blue rectangular tiles** (for the 3x3x) and **two small blue square tiles** (for the 22).

STEP 9

Finally, 13.c), 2x-2x.
This one is simple!
We just need **two red rectangular tiles** to represent the 2x-2x.

STEP 10

Moving on to 4.a), x2+3-x^2 + 3.
We have a negative x2x^2 term and a positive constant term.

STEP 11

So, we'll use one **red big square tile** for the x2-x^2 and **three small blue square tiles** for the 33.

STEP 12

Next, 4.b), 2x23x2x^2 - 3x.
We have two positive x2x^2 terms and three negative xx terms.

STEP 13

That's **two big blue square tiles** for the 2x22x^2 and **three red rectangular tiles** for the 3x-3x.

STEP 14

And last but not least, 4.c), 88.
This is just a constant term.

STEP 15

So we'll represent it with **eight small blue square tiles**!

STEP 16

We've successfully modeled all the polynomials using algebra tiles!
Remember, **blue represents positive** and **red represents negative**.

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