casey is dividing $x^{3}-2x^{2}-10x + 21$ by $x^{2}+x - 7$ using a division table. his work is shown here…

Explanation:

Step1: Perform polynomial long - division

We divide (x^{3}-2x^{2}-10x + 21) by (x^{2}+x - 7). We first find the term to multiply (x^{2}+x - 7) to get the leading term of (x^{3}-2x^{2}-10x + 21). We multiply (x^{2}+x - 7) by (x) to get (x^{3}+x^{2}-7x). ((x^{3}-2x^{2}-10x + 21)-(x^{3}+x^{2}-7x)=x^{3}-2x^{2}-10x + 21 - x^{3}-x^{2}+7x=-3x^{2}-3x + 21). Then we multiply (x^{2}+x - 7) by (- 3) to get (-3x^{2}-3x + 21). So (x^{3}-2x^{2}-10x + 21=(x - 3)(x^{2}+x - 7)).

Step2: Identify the value of (A)

Since the quotient of (\frac{x^{3}-2x^{2}-10x + 21}{x^{2}+x - 7}) is (x-3), the value of (A) (assuming (A) is related to the quotient) is (-3).

Answer:

A. -3