Understanding Polynomial Division

The video tutorial explains how to divide polynomials and express the quotient in a specific form. It begins by introducing the concept of polynomial division and the structure of the quotient. An example problem is set up, where a polynomial is divided by x squared. The tutorial proceeds with a term-by-term division, ensuring the remainder's degree is less than the divisor's. Finally, the expression is finalized in the required form, demonstrating the correct approach to polynomial division.

What is the form of the quotient when dividing two polynomials?

• a of x minus b of x equals q of x plus r of x over b of x

• a of x plus b of x equals q of x times r of x over b of x

• a of x times b of x equals q of x minus r of x over b of x

• a of x over b of x equals q of x plus r of x over b of x

Tags

CCSS.HSA.APR.D.6

What is the degree of r of x compared to b of x in the quotient form?

• Greater than the degree of b of x

• Not related to the degree of b of x

• Less than the degree of b of x

• Equal to the degree of b of x

Tags

CCSS.HSA.APR.D.6

What is the first step in dividing 7x to the sixth plus x to the third plus 2x plus 1 by x squared?

• Subtract x squared from each term

• Divide each term by x squared

• Add x squared to each term

• Multiply each term by x squared

Tags

CCSS.HSA.APR.A.1

What is the result of dividing 7x to the sixth by x squared?

• 7x to the third

• 7x to the second

• 7x to the fourth

• 7x to the fifth

What is the result of dividing x to the third by x squared?

• x squared

• x

• x cubed

• 1

Tags

CCSS.HSA.APR.D.6

How do you express 2x divided by x squared in the desired form?

• 2x over x squared

• 2 over x

• 2x

• 2x squared

Why is it important to rewrite the polynomial in the desired form?

• To make it more complex

• To increase the degree of the polynomial

• To simplify calculations

• To match the required format

Tags

CCSS.HSA.APR.D.6

What happens to terms with a lower degree than x squared during division?

• They are multiplied by x squared

• They are left as they are

• They are divided by x squared

• They are added to x squared

Tags

CCSS.HSA.APR.D.6

What is the final form of the polynomial after division?

• 7x to the fourth plus x plus 2x plus 1 over x squared

• 7x to the fourth plus x plus 2x over x squared

• 7x to the fourth plus x plus 1 over x squared

• 7x to the fourth plus x plus 2x over x squared plus 1 over x squared

Tags

CCSS.HSA.APR.D.6

What is the purpose of checking the answer after rewriting the polynomial?

• To make the polynomial longer

• To ensure the polynomial is complex

• To verify the solution is correct

• To change the polynomial's degree

Tags

CCSS.HSA.APR.D.6