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 \( \frac{10x^8y^5}{4x^2y^5} \)?

Back

To simplify, divide the coefficients (10/4) and subtract the exponents of like bases: \( \frac{5x^{8-2}}{1} = \frac{5x^6}{2} \).

Front

What is the quotient of \( \frac{15x^9-40x^6}{5x^3} \)?

Back

The quotient is obtained by dividing each term: \( 3x^6 - 8x^3 \).

Front

How do you divide \( \frac{8x^2-4x+12}{2x} \)?

Back

Divide each term by \( 2x \): \( 4x - 2 + \frac{6}{x} \).

Front

What is the result of dividing \( \frac{15w^2-12w+9}{3} \)?

Back

The result is \( 5w^2 - 4w + 3 \).

Front

How do you handle negative coefficients in polynomial division?

Back

Negative coefficients are treated like positive coefficients; just ensure to apply the negative sign to the result appropriately.

Front

What is the importance of simplifying polynomials before division?

Back

Simplifying polynomials can make the division process easier and clearer, reducing the chance of errors.

Front

What is the role of exponents in polynomial division?

Back

Exponents determine how terms are divided; when dividing like bases, subtract the exponents.

Front

How do you divide polynomials with multiple variables?

Back

Divide each term separately, applying the same rules for each variable as you would for a single variable.