Mastering Long Division of Polynomials

This video tutorial focuses on dividing polynomials using long division. It begins with an example of dividing x squared plus 5x plus 6 by x plus 2, demonstrating the steps of dividing, multiplying, and subtracting. The second example involves dividing 2x cubed plus 8x squared minus 6x plus 10 by x minus 2, showing how to handle remainders. The final example covers dividing six x to the fourth minus nine x squared plus eighteen by x minus three, emphasizing the importance of maintaining standard order and handling zero coefficients. The video concludes with a summary of the polynomial division process.

What is the first step in dividing polynomials using long division?

• Add the polynomials

• Divide the leading terms

• Subtract the polynomials

• Multiply the polynomials

Tags

CCSS.HSA.APR.D.6

When dividing x^2 + 5x + 6 by x + 2, what do you get after the first division step?

• x^2

• x

• 5x

• 6

Tags

CCSS.HSA.APR.D.6

In the first example, what is the result of subtracting x^2 from x^2?

• x^2

• 2x^2

• 0

• x

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CCSS.7.EE.A.1

What is the final quotient when dividing x^2 + 5x + 6 by x + 2?

• x + 2

• x + 4

• x + 3

• x + 1

Tags

CCSS.HSA.APR.D.6

In the second example, what is the first term of the quotient when dividing 2x^3 + 8x^2 - 6x + 10 by x - 2?

• 2x^2

• 2x^3

• x^2

• x^3

Tags

CCSS.HSA.APR.D.6

What is the remainder when dividing 2x^3 + 8x^2 - 6x + 10 by x - 2?

• 46

• 0

• 10

• 36

Tags

CCSS.HSA.APR.B.2

In the third example, why is it important to include zero coefficients?

• To make subtraction easier

• To avoid errors in multiplication

• To maintain the standard order

• To simplify the division

Tags

CCSS.HSA.APR.D.6

What is the first term of the quotient when dividing 6x^4 - 9x^2 + 18 by x - 3?

• 6x^4

• 6x^3

• x^4

• x^3

Tags

CCSS.HSA.APR.D.6

What is the remainder when dividing 6x^4 - 9x^2 + 18 by x - 3?

• 453

• 145

• 18

• 0

Tags

CCSS.HSA.APR.B.2

What is the final quotient when dividing 6x^4 - 9x^2 + 18 by x - 3?

• 6x^3 + 18x^2 + 45x + 145

• 6x^3 + 18x^2 + 45x + 453

• 6x^4 + 18x^2 + 45x + 145

• 6x^4 + 18x^2 + 45x + 453

Tags

CCSS.HSA.APR.D.6