Dividing 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 synthetic division?

Back

Synthetic division is a simplified form of polynomial division that is used when dividing by a linear factor of the form (x - c).

Front

What is the degree of a polynomial?

Back

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

Front

How do you find the quotient in polynomial division?

Back

To find the quotient, divide the leading term of the dividend by the leading term of the divisor, then multiply the entire divisor by this result and subtract from the dividend.

Front

What is the remainder theorem?

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

What is the factor theorem?

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The factor theorem states that (x - c) is a factor of the polynomial f(x) if and only if f(c) = 0.

Front

What is the leading coefficient of a polynomial?

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The leading coefficient is the coefficient of the term with the highest degree in a polynomial.

Front

How do you set up synthetic division?

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To set up synthetic division, write the coefficients of the polynomial in descending order and place the value of c (from x - c) in a box on the left.

Front

What is the purpose of adding zeros in synthetic division?

Back

Adding zeros in synthetic division is necessary to account for missing degrees in the polynomial, ensuring that all coefficients are represented.

Front

What is the result of dividing (4x^2 - 24x + 35) by (2x - 5)?

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The result is 2x - 7.