You have the following polynomial of Degree 3:
[tex]x^3+3x^2-4x-12[/tex]And the other polynomial (of Degree 2) is:
[tex]x^2+5x+6[/tex]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:
[tex]=\frac{x^3+3x^2-4x-12}{x^2+5x+6}[/tex]2. Now you can factor the numerator and the denominator:
a. For the numerator:
- Make two groups of two terms using parentheses:
[tex]=(x^3+3x^2)-(4x+12)[/tex]- Factor the Greatest Common Factor out (of each group):
[tex]=x^2(x+3)-4(x+3)[/tex]- Combine the factors together:
[tex]=(x^2-4)(x+3)[/tex]- Since, by definition:
[tex]a^2-b^2=(a+b)(a-b)[/tex]You can simplify it as following:
[tex]=(x-2)(x+2)(x+3)[/tex]b. For the denominator, find two numbers whose sum is 5 and whose product is 6. These would by 3 and 2. Then:
[tex]undefined[/tex]
