Question

a polynomial is factored using algebra tiles. which polynomial was factored? options: $x^2 - 2x - 8$, $x^2 + 2x - 8$, $x^2 - 2x - 4$, $x^2 + 2x - 4$

Explanation:

Step1: Analyze the algebra tiles for \(x^2\) term

There is 1 \(+x^2\) tile, so the coefficient of \(x^2\) is 1.

Step2: Analyze the algebra tiles for \(x\) terms

There are 2 \(+x\) tiles and 4 \(-x\) tiles. The total for \(x\) terms: \(2x - 4x=- 2x\).

Step3: Analyze the algebra tiles for constant terms

There are 8 \(-\) (constant -1) tiles, so the constant term is \(-8\).

Step4: Form the polynomial

Combining the terms, the polynomial is \(x^2-2x - 8\).

Answer:

\(x^2 - 2x - 8\) (the first option)