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The partial factorization of [tex]$x^2 - 3x - 10$[/tex] is modeled with algebra tiles.

Which unit tiles are needed to complete the factorization?

A. 2 negative unit tiles
B. 2 positive unit tiles
C. 5 negative unit tiles
D. 5 positive unit tiles

Sagot :

GinnyAnswer
To complete the factorization of the quadratic expression [tex]\(x^2 - 3x - 10\)[/tex], you need to determine which unit tiles accurately represent the constants in the factors.

Step-by-step:

1. Write down the given quadratic expression:
[tex]\[x^2 - 3x - 10\][/tex]

2. Factorize the quadratic expression:
We need to find two binomials whose product gives us the quadratic expression. After factorizing, we get:
[tex]\[(x - 5)(x + 2)\][/tex]

3. Identify the constant terms in the factors:
In the factored form [tex]\((x - 5)(x + 2)\)[/tex], we have two constants:
- One is [tex]\(-5\)[/tex], which corresponds to the factor [tex]\((x - 5)\)[/tex]
- The other is [tex]\(+2\)[/tex], which corresponds to the factor [tex]\((x + 2)\)[/tex]

4. Determine the unit tiles required:
- The term [tex]\(-5\)[/tex] indicates that we need 5 negative unit tiles.
- The term [tex]\(+2\)[/tex] indicates that we need 2 positive unit tiles.

Therefore, the correct unit tiles needed to complete the factorization are:
- 5 negative unit tiles
- 2 positive unit tiles
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