Algebra-2

This question evaluates the student's ability to perform long division of polynomials. The problem requires the student to divide a quadratic polynomial by a linear polynomial and find the quotient.

Key Concept Explanation
The key concept here is the long division of polynomials, where the leading term of the dividend is divided by the leading term of the divisor to get the first term of the quotient. This process is repeated until the degree of the remainder is less than the degree of the divisor.

Step-by-step Solution
Step 1. Set up the long division:
We want to divide (the dividend) by (the divisor).
Step 2: Divide the Leading Terms
Divide the leading term of the dividend ( ) by the leading term of the divisor ( ): . This gives the first term of the quotient: .
Step 3: Multiply and Subtract
Multiply the entire divisor ( ) by the first term of the quotient ( ):
Subtract this product from the original dividend:

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