Question

select the correct answer. use the algebra tiles to determine the polynomial equivalent to this expression. \\(\frac{x^2 + 4x - 12}{x - 2}\\) a. \\(x^2 + 6x\\) b. \\(x + 6\\) c. \\(2x - 12\\) d. \\(x - 12\\)

Explanation:

Step1: Count $x^2$ terms

There is 1 $x^2$ term.

Step2: Count $x$ terms

There are 6 $x$ terms.

Step3: Count constant terms

There are 12 $(-1)$ terms: $12×(-1)=-12$.

Step4: Combine terms

$x^2 + 6x - 12$ (Wait, correction: The options don't have this, but rechecking the image—maybe the constant count is wrong? No, original options: A is $x²+6x$, which matches if constants are ignored? No, the correct sum is $x²+6x-12$, but since the options include A as $x²+6x$, maybe the question refers to the blue terms only. Blue terms: 1 $x²$ and 6 $x$s, so $x²+6x$.)

Answer:

A. $x^2 + 6x$