Question

What is the quotient when 4x² − 36 is divided by x + 3?

A. 4(x − 3)
B. 2(x − 3)
C. 4(x + 6)
D. 2(2x − 3)

Answer 1

The correct answer is option A. 4(x - 3), obtained by factoring the difference of squares 4x² - 36 as (2x + 6)(2x - 6) and dividing by x + 3.

Step-by-step explanation:

To find the quotient when 4x² - 36 is divided by x + 3, we need to perform long division.

1. Start by dividing the first term of the dividend (4x²) by the divisor (x + 3).
2. Write the quotient (4x) above the line.
3. Multiply the divisor (x + 3) by the quotient (4x) and subtract the result from the dividend (4x² - 36).
4. Write the new dividend (-12x) below the line.
5. Divide (-12x) by the divisor (x + 3) to get the new quotient (-12).
6. Write the new quotient (-12) above the line.
7. Multiply the divisor (x + 3) by the new quotient (-12) and subtract the result from the new dividend (-12x) to get a remainder of 0.
8. Write the remainder (0) as a fraction and simplify to get the final quotient.

Therefore, the quotient when 4x² - 36 is divided by x + 3 is 2(x - 3).