Dividing Polynomials

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What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, 2x^2 + 3x - 5 is a polynomial.

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What is a monomial?

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A monomial is a polynomial with only one term. For example, 5x^3 is a monomial.

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What does it mean to divide a polynomial by a monomial?

Back

Dividing a polynomial by a monomial involves dividing each term of the polynomial by the monomial.

Front

How do you divide the polynomial 2x^8 - 8x^2 - 28x by the monomial 2x?

Back

Divide each term: (2x^8)/(2x) - (8x^2)/(2x) - (28x)/(2x) = x^7 - 4x - 14.

Front

What is the result of dividing (24x + 4) by (6x + 1)?

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The result is 4.

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Factor both the numerator and denominator, then cancel common factors to simplify.

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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

What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a binomial of the form (x - c).