factor polynomials by grouping

Front

What is the process of factoring polynomials by grouping?

Back

Factoring polynomials by grouping involves rearranging the terms of the polynomial into groups, factoring out the common factors from each group, and then factoring out the common binomial factor.

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What is a common factor in the context of polynomials?

Back

A common factor is a number or expression that divides two or more terms without leaving a remainder.

Front

How do you identify groups when factoring by grouping?

Back

To identify groups, look for pairs of terms in the polynomial that share a common factor, and group them accordingly.

Front

What is the first step in factoring a polynomial by grouping?

Back

The first step is to rearrange the polynomial into two groups that can be factored separately.

Front

What is the significance of the distributive property in factoring?

Back

The distributive property allows us to factor out common terms from groups of terms, which is essential in the factoring process.

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What does it mean to factor a polynomial completely?

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Factoring a polynomial completely means breaking it down into irreducible factors, which cannot be factored further over the set of real numbers.

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What is a binomial?

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A binomial is a polynomial that consists of exactly two terms.

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Can you provide an example of a polynomial that can be factored by grouping?

Back

Yes, an example is x^3 - 4x^2 - 4x + 16, which can be factored as (x-4)(x^2-4).

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What is the role of coefficients in polynomials?

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Coefficients are the numerical factors that multiply the variables in a polynomial, determining the polynomial's value.