Multiplication and Division of Polynomials

Flashcards covering the multiplication and division of monomials, binomials, and multinomials using various techniques like distributive property and FOIL.

What is the product of the monomials $(3x^{2})$ and $(4x^{2})$ according to the transcript?

$$12x^{n}$$

What is the product of the monomials $(-6ab)$ and $(2ab)$?

$$-12a^{2}b^{2}$$

What is the product of the monomials $(-9d^{3}e)$ and $(-2de^{3})$?

$$18d^{4}e^{4}$$

What is the product of $(xyz^{3})$ and $(x^{2}y^{2}z)$?

$$x^{3}y^{3}z^{4}$$

What is the product of $(5m^{2}n)$ and $(-3m^{3}n)$?

$$-15m^{5}n^{2}$$

What is the quotient of $\frac{45x^{3}}{9x}$?

$$5x^{2}$$

What is the quotient of $\frac{-42a^{3}b^{4}}{6ab}$?

$$-7a^{2}b^{3}$$

What is the quotient of $\frac{56m^{4}n^{2}}{-7mn}$?

$$-8m^{3}n$$

When multiplying the binomials $(x+8)(x+3)$ using the distributive property, what is the final simplified expression?

$$x^{2} + 11x + 24$$

According to the notes, what are the three techniques or forms mentioned for multiplying binomials?

Distributive Property, FOIL Method, and Vertical Form.

What does the FOIL acronym stand for in binomial multiplication?

First, Outer, Inner, and Last terms.

What is the result of dividing $x^{2} - 13x + 42$ by $x - 7$ using the long division method shown in the notes?

$$x - 6$$