Question

post test: polynomials
use the algebra tiles to determine the polynomial equivalent to this expression.
(expression in a box: maybe a fraction or division, and then an image of algebra tiles with columns labeled x, -1, -1 on the left and a grid of tiles on the right. then multiple choice options:
a. ( x^2 + 6x )
b. ( x + 6 )
c. ( 2x - 12 )
d. ( x - 12 ))

Explanation:

The expression given is $\frac{x^2 + 4x - 12}{x - 2}$ (assuming a typo and the numerator is $x^2 + 4x - 12$). We can perform polynomial long division or factor the numerator.

Step 1: Factor the numerator

We factor $x^2 + 4x - 12$. We need two numbers that multiply to $-12$ and add to $4$. Those numbers are $6$ and $-2$. So, $x^2 + 4x - 12 = (x + 6)(x - 2)$.

Step 2: Simplify the fraction

Now we have $\frac{(x + 6)(x - 2)}{x - 2}$. Since $x
eq 2$ (to avoid division by zero), we can cancel out the $(x - 2)$ terms.

$\frac{(x + 6)(x - 2)}{x - 2} = x + 6$

Looking at the algebra tiles, the area model (with length $x - 2$ and we're finding the width) should also result in $x + 6$. The tiles represent the division, and the result of dividing the polynomial (represented by the tiles) by $x - 2$ is $x + 6$.

Answer:

B. $x + 6$