Question

(12v² + 2012 – 56v + 33) / (4v – 4) A) v² + 3 B) 3v² + 8v + 8 C) 3v² + 6v + 14 D) 3v² - 8v - 8

Answer 1

The solution to the expression (12v² + 2012 – 56v + 33) / (4v – 4) is 3v² + 8v + 8. Option B is answer.

Explanation:

To solve the expression (12v² + 2012 – 56v + 33) / (4v – 4), we can start by factoring the numerator:

12v² - 56v + 2045 = 4(3v² - 14v + 511)

Now we can rewrite the expression as:

(4(3v² - 14v + 511) + 33) / (4v - 4)

We can simplify the numerator by distributing the 4:

(12v² - 56v + 2044 + 33) / (4v - 4)

Simplifying further, we get:

(12v² - 56v + 2077) / (4v - 4)

Now we can factor out a 4 from the numerator:

4(3v² - 14v + 519) / (4v - 4)

We can simplify the expression by factoring out a 4 from the denominator:

4(3v² - 14v + 519) / 4(v - 1)

The 4s cancel out, leaving us with:

3v² - 14v + 519 / (v - 1)

Now we can use polynomial division to divide the numerator by the denominator:

3v + 17

___________

v - 1 | 3v² - 14v + 519 - (3v² - 3v) ------------- -11v + 519 -(-11v + 11) ------------ 8v + 519

Therefore, the expression (12v² + 2012 – 56v + 33) / (4v – 4) simplifies to 3v² + 8v + 8. Option B is answer.