Question

Match each expression on the left with its quotient on the right.

(x – 5x − 6) = (x – 6)
(x³ + x² − x − 1)
(x³ + 2x² − 2) ÷ (x² + x − 1)
x² + 2x + 1)
x+1
x+1R-1
x-1

Answer 1

To match expressions with their quotients, we can use long division. The quotient for (x³ + x² − x − 1) ÷ (x² + x − 1) is x + 2 - (1/(x² + x − 1)).

Step-by-step explanation:

To match each expression on the left with its quotient on the right, we can divide the expressions using long division. Let's start with the first expression:

(x³ + x² − x − 1) ÷ (x² + x − 1)

We divide x³ by x² and get x, then multiply (x² + x − 1) by x, giving us x³ + x² − x. Subtracting this from the original expression, we get 2x² ÷ (x² + x − 1). Continuing the process, we divide 2x² by x², giving us 2, and multiply (x² + x − 1) by 2, giving us 2x² + 2x − 2. Subtracting this from the previous step, we get 4x - 1.

The final quotient is x + 2 - (1/(x² + x − 1)).

Learn more about Dividing Polynomials