How to pull out the greatest common factor of polynomials

The key is that all the terms of the polynomial need to share the factor being taken out. Any factor that’s shared by all the terms is called a common factor, and the factor that consists of everything which is shared by all of them is known as the greatest common factor. Factoring is “un-distributing,” which means that we do the opposite of distributing and take out (or “factor out”) the same factor from each term of the polynomial (and divide each term by that factor to get “what’s left” once it’s taken out).

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Factoring quadratic equations with coefficients

In this lesson we’ll look at methods for factoring quadratic equations with coefficients in front of the x^2 term (that are not 1 or 0). Factoring means you’re taking the parts of an expression and rewriting it as parts that are being multiplied together (the factors). Factoring a quadratic equation means we will write equations of the form ax^2+bx+c into the form (px+r)(qx+s), where a, b, c, p, q, and s are all real numbers and a≠1,0.

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Completing the square for quadratic polynomials

The zeroes of a single-variable polynomial are the values of that variable at which the polynomial is equal to 0. Completing the square is a method we can use to find the zeroes of a quadratic polynomial. Another way to say this is that completing the square is a method we can use to solve the corresponding quadratic equation (the equation that has the quadratic polynomial on one side and 0 on the other side).

Factoring polynomials using grouping

In this lesson we’ll look at factoring a polynomial using a method called grouping. When you have a polynomial, sometimes you can use factoring by grouping to help you get the factored parts. It means you need to look for terms in the polynomial that have values and terms in common and then group those parts together.

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Factoring quadratic polynomials

Factoring of quadratic polynomials (second-degree polynomials) is done by “un-FOILing,” which means we start with the result of a FOIL problem and work backwards to find the two binomial factors.

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Factoring out the greatest common factor from trinomials

The key to factoring is that every term in the trinomial needs to share the factor being taken out. Any factor that’s shared by all the terms is called a common factor, and the factor that consists of everything which is shared by all of them is known as the greatest common factor.

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Zero theorem for the roots of a polynomial function

The zero theorem allows you to solve for the roots of a polynomial function. Just factor the polynomial, set it equal to 0, and solve for the variable to find the roots.

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