HW Multiplication and Monomial Division of Polynomials

Front

What is the product of \( (2r)(r^2 + 3r - 7) \)?

Back

The product is \( 2r^3 + 6r^2 - 14r \).

Front

Simplify \( \frac{x^8}{x^3} \).

Back

The simplified form is \( x^5 \).

Front

Simplify \( \frac{m^2n + m^6n^3}{mn} \).

Back

The simplified form is \( m + m^5n^2 \).

Front

Simplify \( \frac{-18x^5 - 12x^3 - 6x^2}{-3x} \).

Back

The simplified form is \( 6x^4 + 4x^2 + 2x \).

Front

What is \( 6b^3 + 12b^4c^2 \) divided by \( 3b^2 \)?

Back

The result is \( 2b + 4b^2c^2 \).

Front

What is a monomial?

Back

A monomial is a polynomial with only one term, such as \( 3x^2 \) or \( -5y \).

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the expression.

Front

What is the product of two polynomials?

Back

The product of two polynomials is obtained by multiplying each term of the first polynomial by each term of the second.

Front

What is the quotient of two polynomials?

Back

The quotient of two polynomials is the result of dividing one polynomial by another.

Front

What is the zero exponent rule?

Back

Any non-zero number raised to the power of zero equals one, i.e., \( a^0 = 1 \) for \( a \neq 0 \).