Polynomial Operations and Properties

The video tutorial by Alfauzia Nihar from Atom Tuition covers the basic operations on polynomials: addition, subtraction, multiplication, and division. It provides step-by-step instructions and examples for each operation, emphasizing the importance of like terms and standard form. The tutorial also briefly introduces division of polynomials, mentioning polynomial long division and synthetic division.

What is the first step in adding polynomials?

• Subtract the coefficients

• Multiply the coefficients

• Divide the coefficients

• Collect all the like terms

When adding polynomials, how should the final answer be written?

• In reverse order

• In alphabetical order

• In any random order

• In standard form

In the example of adding 2a + 3b and -4b + 5a, what is the result?

• 7a - b

• 7a + b

• 3a + 7b

• 3a - 7b

What is the first step in subtracting polynomials?

• Multiply the coefficients

• Change the sign of the terms to be subtracted

• Divide the coefficients

• Add the coefficients

In the subtraction example, what is the result of subtracting 9pq from 4pq?

• -13pq

• -5pq

• 5pq

• 13pq

What is the first step in multiplying polynomials?

• Subtract the coefficients

• Multiply the numerical and literal coefficients separately

• Add the coefficients

• Divide the coefficients

When multiplying polynomials, what should be done with the exponents of like bases?

• Divide the exponents

• Add the exponents

• Subtract the exponents

• Multiply the exponents

What is the result of multiplying the numerical coefficients 5 and 8?

• 40

• 58

• 13

• 80

In division of polynomials, how should a monomial be divided by another monomial?

• Divide the numerical and literal coefficients separately

• Add the coefficients

• Subtract the coefficients

• Multiply the coefficients

What is the key step in dividing a polynomial by a monomial?

• Multiply each term by the monomial

• Add each term to the monomial

• Divide each term by the monomial

• Subtract each term from the monomial