Dividing Polynomials by monomials

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What is a monomial?

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A monomial is a polynomial with only one term, which can be a constant, a variable, or a product of constants and variables raised to non-negative integer powers.

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

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Dividing a polynomial by a monomial involves simplifying each term of the polynomial by the monomial, reducing the degree of the terms.

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What is the result of dividing 15x^9 by 3x?

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5x^8.

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What is the first step in dividing a polynomial by a monomial?

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Identify the leading term of the polynomial and divide it by the monomial.

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What is the general formula for dividing a polynomial by a monomial?

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For a polynomial P(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0 and a monomial m = bx^k, the result is P(x)/m = (a_n/b)x^{n-k} + (a_{n-1}/b)x^{n-1-k} + ... + (a_1/b)x^{1-k} + (a_0/b)x^{-k}.

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What happens to the degree of a term when dividing by a monomial?

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The degree of the term decreases by the degree of the monomial.