Algebraic Division with Long Division: Polynomials Divided by Linear Expressions

The video tutorial explains how to use long division to divide polynomials by linear expressions. It begins with a simple quadratic example, demonstrating the factorization and division process. The tutorial then progresses to more complex polynomials, illustrating the use of a cover-up system to simplify the division. The video also addresses handling remainders and provides a comprehensive guide to mastering polynomial division.

What is the first step in dividing a polynomial using long division?

• Multiply the divisor by the dividend

• Place the dividend inside the division symbol

• Subtract the divisor from the dividend

• Add the divisor to the dividend

When dividing X^2 + 6X + 8 by X + 2, what is the result after the first subtraction?

• X^2 + 4X

• 2X

• 4X

• 6X

What is the purpose of the cover-up method in polynomial division?

• To simplify the divisor

• To eliminate the remainder

• To multiply the dividend

• To focus on one term at a time

In the division of 3X^3 - 10X^2 + X + 6 by X - 3, what is the first term of the quotient?

• 3X^2

• X^2

• 3X

• X

What is the final quotient when dividing 3X^3 - 10X^2 + X + 6 by X - 3?

• 3X^2 + X - 2

• 3X^2 + X + 2

• 3X^2 - X - 2

• 3X^2 - X + 2

How do you handle a remainder when dividing polynomials?

• Multiply it by the divisor

• Subtract it from the dividend

• Add it to the quotient

• Ignore it

What is the remainder when dividing 3X^3 - 10X^2 + X + 8 by X - 3?

• 0

• 1

• 2

• 3