Question

Simplify using synthetic division: (x^2 - 2x - 35) ÷ (x - 5).

A. x - 7
B. x + 7
C. x - 5
D. x + 5

Answer 1

To simplify the given expression using synthetic division, you can follow these steps:

Set up the synthetic division. Write the divisor (x - 5) and the dividend (x² - 2x - 35) in long division format.

Write the coefficients of the dividend inside the division symbol. For x² - 2x - 35, the coefficients are 1, -2, and -35.

Write the zero of the divisor outside the division symbol. The zero of x - 5 is 5.

Bring down the first coefficient (1). Multiply the zero of the divisor (5) by this number and write the result under the next coefficient (-2). Add these numbers together and write the result underneath.

Repeat this process for the remaining coefficients.

The numbers on the bottom line represent the coefficients of the quotient. The degree of the quotient is one less than the degree of the dividend.

Following these steps, you’ll find that the simplified form of the expression is x - 7. So, the correct answer is: A. x - 7

Answer 2

The polynomial (x^2 - 2x - 35) divided by (x - 5) is simplified using synthetic division to find the quotient, which is x - 7, corresponding to option A.

Step-by-step explanation:

To simplify the given polynomial (x^2 - 2x - 35) ÷ (x - 5) using synthetic division, we set up the synthetic division as follows:

1. Place the coefficient of x in the dividend in descending order of power. Since x^2 - 2x - 35 is already in that order, we use 1 (coefficient of x^2), -2 (coefficient of x), and -35 (constant term).
2. Write the zero of the divisor (x - 5), which is 5, to the left.
3. Perform the synthetic division process:

You should bring down the first coefficient (1) and then multiply it by the zero of the divisor (5), and write the result underneath the second coefficient (-2). Next, add -2 and the multiplication result (5) to get the new coefficient.

Continue this process until all coefficients have been processed. The result of the synthetic division will give us the coefficients of the quotient.

After performing the synthetic division, the quotient is x - 7. So, the answer is option A. x - 7.

To check if this is reasonable, we can multiply (x - 7) by (x - 5) and confirm that it gives us the original polynomial x^2 - 2x - 35.