Multiplying Polynomials by Monomials

This video tutorial covers the process of multiplying monomials and polynomials by distributing the monomial across each term in the polynomial. It explains the product rule for exponents and provides several example problems to illustrate the concepts. The tutorial also includes sections on calculating the area of a trapezoid and finding the area of a shaded region by subtracting the area of a smaller rectangle from a larger one.

What is the product rule for exponents?

• Divide the exponents

• Subtract the exponents

• Add the exponents

• Multiply the exponents

What is the result of multiplying a monomial by itself?

• A binomial

• A trinomial

• Another monomial

• A polynomial

When multiplying a monomial by a polynomial, what is the first step?

• Combine like terms

• Multiply the coefficients only

• Distribute the monomial to each term in the polynomial

• Apply the quotient rule

How do you handle variables when multiplying monomials?

• Multiply their coefficients

• Add their exponents

• Subtract their exponents

• Ignore the variables

What should you check after multiplying polynomials?

• If the exponents are negative

• If the answer is in standard form

• If the coefficients are prime numbers

• If the variables are in ascending order

In polynomial multiplication, what does distributing involve?

• Adding exponents of like terms

• Multiplying the monomial with each term of the polynomial

• Dividing the polynomial by the monomial

• Subtracting the polynomial from the monomial

How do you simplify the expression after distributing a monomial across a polynomial?

• By combining like terms

• By subtracting coefficients

• By dividing like terms

• By rearranging the terms randomly

After multiplying polynomials, what is the final step to ensure the answer is correct?

• Verify the polynomial is fully factored

• Confirm the polynomial is in ascending order

• Check for descending exponents

• Ensure all coefficients are positive

What is the formula for the area of a trapezoid?

• 1/2 * (base1 + base2) * height

• Base * height

• (Base1 + base2) / height

• 2 * (base1 + base2) * height

How do you find the area of a shaded region involving polynomials?

• Multiply the areas of both shapes

• Add the areas of both shapes

• Subtract the smaller area from the larger area

• Divide the larger area by the smaller area