Polynomials greatest common factor

Front

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, 3x^2 + 2x + 1 is a polynomial.

Front

What is the greatest common factor (GCF)?

Back

The greatest common factor (GCF) of two or more numbers is the largest number that divides all of them without leaving a remainder.

Front

How do you find the GCF of monomials?

Back

To find the GCF of monomials, identify the common factors in the coefficients and the lowest power of each variable present in all monomials.

Front

Factor the polynomial: 24c^5 - 12c^3

Back

12c^3(2c^2 - 1)

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Factor the polynomial: 56a^3 - 8a

Back

8a(7a^2 - 1)

Front

Factor the polynomial: 2n^3 + 16n + 12

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2(n^3 + 8n + 6)

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Factor the polynomial: 5k^3 + 7k^2 + k

Back

k(5k^2 + 7k + 1)

Front

Factor the polynomial: 4x + 6

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2(2x + 3)

Front

What is the first step in factoring a polynomial?

Back

The first step in factoring a polynomial is to find the GCF of all the terms.

Front

What does it mean to factor a polynomial completely?

Back

Factoring a polynomial completely means breaking it down into irreducible factors, which cannot be factored further.