a polynomial is factored using algebra tiles. what are the factors of the polynomial? (x - 1) and (x + 3) (x…

a polynomial is factored using algebra tiles. what are the factors of the polynomial? (x - 1) and (x + 3) (x + 1) and (x - 3) (x - 2) and (x + 3) (x + 2) and (x - 3)

a polynomial is factored using algebra tiles. what are the factors of the polynomial? (x - 1) and (x + 3) (x + 1) and (x - 3) (x - 2) and (x + 3) (x + 2) and (x - 3)

Answer

Explanation:

Step1: Combine like - terms

The polynomial from the tiles is $x^{2}+x - 3x-3=x^{2}-2x - 3$.

Step2: Factor the quadratic polynomial

For a quadratic polynomial $ax^{2}+bx + c$ (here $a = 1$, $b=-2$, $c = - 3$), we need to find two numbers that multiply to $ac=-3$ and add up to $b=-2$. The numbers are $-3$ and $1$. So, $x^{2}-2x - 3=x^{2}-3x+x - 3=x(x - 3)+1(x - 3)=(x - 3)(x + 1)$.

Answer:

$(x + 1)$ and $(x - 3)$