Solving Polynomials by Factoring

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What is factoring in polynomials?

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Factoring is the process of breaking down a polynomial into simpler components (factors) that, when multiplied together, give the original polynomial.

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What is the purpose of finding zeroes of a polynomial?

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The zeroes of a polynomial are the values of x that make the polynomial equal to zero. They are important for understanding the behavior of the polynomial graph and solving equations.

Tags

CCSS.HSF-IF.C.7C

Front

How do you factor by grouping?

Back

To factor by grouping, you group terms in pairs, factor out the common factor from each pair, and then factor out the common binomial factor.

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Tags

CCSS.HSF-IF.C.7C

Front

What is the first step in factoring a polynomial?

Back

The first step is to look for a common factor in all the terms of the polynomial.

Front

How do you check if your factorization is correct?

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You can check by multiplying the factors back together to see if you obtain the original polynomial.

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What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient determines the end behavior of the polynomial graph and influences the shape of the graph.

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What does it mean for a polynomial to be irreducible?

Back

A polynomial is irreducible if it cannot be factored into polynomials of lower degree with rational coefficients.

Tags

CCSS.HSA.APR.B.2