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.

Front

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.

Tags

CCSS.HSA.APR.D.6

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Back

Front

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

Back

5x^8.

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Back

Tags

CCSS.HSA.APR.D.6

Front

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

Back

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

Tags

CCSS.HSA.APR.D.6

Front

Back

Tags

CCSS.HSA.APR.D.6

Front

Back

Tags

CCSS.HSA.APR.D.6

Front

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}.

Tags

CCSS.HSA.APR.D.6

Front

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.