Dividing Polynomials with Long Division Techniques

The video tutorial explains the process of long division with polynomials, highlighting its similarity to numerical long division. It covers setting up the division problem, performing the division steps, and handling missing powers of x using placeholders. The tutorial includes detailed examples to illustrate each step, ensuring a clear understanding of the process. Key reminders include checking for missing powers and ensuring the polynomial is in descending order.

What is the primary purpose of using polynomial long division?

• To find the greatest common divisor

• To find zeros of polynomials or factor them

• To simplify fractions

• To solve linear equations

What should you ensure before starting the long division process with polynomials?

• That the polynomial is in standard form

• That you have the correct setup

• That the polynomial is factored

• That the polynomial is simplified

In the example given, what is the first term of the new polynomial when dividing 5x^3 - 6x^2 - 28x - 2 by x + 2?

• 16x

• 6x^2

• 5x^2

• 5x

What is the result of subtracting 5x^3 from 5x^3 in the long division process?

• 5x^3

• 0

• -5x^3

• 10x^3

What is the remainder when dividing 5x^3 - 6x^2 - 28x - 2 by x + 2?

• 8

• -10

• 0

• 4

What should you do if you are missing powers of x in a polynomial during long division?

• Divide by zero

• Add placeholders for the missing powers

• Ignore the missing powers

• Multiply by zero

When dividing x^3 - 1 by x - 1, what placeholder should be added for the missing x^2 term?

• 0x^2

• -1x^2

• 1x^2

• x^2

What is the result of subtracting x^2 from x^2 in the long division process?

• x^2

• -x^2

• 0

• 2x^2

What is the final quotient when dividing x^3 - 1 by x - 1?

• x^2 + x - 1

• x^2 - x + 1

• x^2 - x - 1

• x^2 + x + 1

What should you always do to the polynomial being divided in terms of order?

• Write it in descending order

• Write it in random order

• Write it in ascending order

• Write it in alphabetical order