Question

What is the quotient of (xº+3x?-4x-12)-(4+5x+6)?A: X + 2B: X-2C: x + 6D: X-6

Answer 1

You have the following polynomial of Degree 3:

`x^3+3x^2-4x-12`

And the other polynomial (of Degree 2) is:

`x^2+5x+6`

The Quotient is defined as the result of a Division. Then, you can find it as following:

1. You can express the Division as following:

`=(x^3+3x^2-4x-12)/(x^2+5x+6)`

2. Now you can factor the numerator and the denominator:

a. For the numerator:

- Make two groups of two terms using parentheses:

`=(x^3+3x^2)-(4x+12)`

- Factor the Greatest Common Factor out (of each group):

`=x^2(x+3)-4(x+3)`

- Combine the factors together:

`=(x^2-4)(x+3)`

- Since, by definition:

`a^2-b^2=(a+b)(a-b)`

You can simplify it as following:

`=(x-2)(x+2)(x+3)`

b. For the denominator, find two numbers whose sum is 5 and whose product is 6. These would by 3 and 2. Then: