Divide polynomials

Front

What is polynomial division?

Back

Polynomial division is the process of dividing a polynomial by another polynomial, similar to long division with numbers.

Front

What is the result of dividing a polynomial by a monomial?

Back

When dividing a polynomial by a monomial, each term of the polynomial is divided by the monomial.

Front

How do you simplify the expression \( \frac{-12a^{4} + 6a^3}{6a^3} \)?

Back

To simplify, divide each term in the numerator by the denominator: \( -2a + 1 \).

Front

What is the quotient of \( \frac{18y^{6} + 9y^{4} - 12y^2}{3y^2} \)?

Back

The quotient is \( 6y^{4} + 3y^2 - 4 \).

Front

What is the first step in dividing polynomials?

Back

The first step is to arrange the polynomials in descending order of their degrees.

Front

What is the remainder theorem in polynomial division?

Back

The remainder theorem states that the remainder of the division of a polynomial \( f(x) \) by \( x - c \) is equal to \( f(c) \).

Front

How do you handle a polynomial with multiple terms when dividing by a monomial?

Back

Divide each term of the polynomial by the monomial separately.

Front

What is the result of dividing \( \frac{8x^2 - 4x + 12}{2x} \)?

Back

The result is \( 4x - 2 + \frac{6}{x} \).

Front

What does it mean to factor a polynomial before division?

Back

Factoring a polynomial means rewriting it as a product of its factors, which can simplify the division process.

Front

How do you divide \( \frac{8x^8 - 8x^2 - 28x}{4x} \)?

Back

Divide each term by \( 4x \) to get \( 2x^7 - 2x - 7 \).