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Polynomial factorization: FAQ

What is factoring?

Factoring is the process of breaking down a polynomial into smaller pieces (or "factors") that, when multiplied together, will give you the original polynomial.

Why do we factor polynomials?

Factoring is a useful technique for solving polynomial equations. By breaking a polynomial down into smaller factors, we can often simplify the equation and find the solutions more easily.

What is a monomial?

A monomial is a polynomial with just one term. For example, 2, x, minus, 3, y, squared, and 5 are all monomials.

What is the greatest common factor?

The greatest common factor (GCF) of two or more terms is the largest factor that all the terms have in common. For example, the GCF of 6, x, squared and 9, x is 3, x.

How do we take common factors out of a polynomial?

To take common factors out of a polynomial, we divide each term by the GCF. For example, to factor 6, x, squared, plus, 9, x, we divide both terms by the GCF, 3, x, to get 3, x, left parenthesis, 2, x, plus, 3, right parenthesis.

What are polynomial identities?

Polynomial identities are equations that are true for all values of the variable. For example, the difference of squares identity, a, squared, minus, b, squared, equals, left parenthesis, a, plus, b, right parenthesis, left parenthesis, a, minus, b, right parenthesis, is true for any values of a and b.

Where are these topics used in the real world?

There are many applications for factoring polynomials. For example, engineers may use these techniques in signal processing or control theory, while scientists might use them in modeling physical phenomena.

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• How can you factorise n^4+6n^3+11n^2+6n+1?