Q: How do you factor each polynomial by its GCF?

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In algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem.The factor theorem states that a polynomial has a factor if and only if

The GCF is 2.

The GCF of 12x and 20x to the fourth power is 4x

The GCF of 20 and 4 is 4. That factors to 4(5x - 1)

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Factor the polynomial x2 - 10x + 25. Enter each factor as a polynomial in descending order.

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The GCF is 5x2

An expression that completely divides a given polynomial without leaving a remainder is called a factor of the polynomial. This means that when the polynomial is divided by the factor, the result is another polynomial with no remainder. Factors of a polynomial can be found by using methods such as long division, synthetic division, or factoring techniques like grouping, GCF (greatest common factor), or special patterns.

You split the current values into a common factor, in this case the greatest common factor (hence "GCF"). e.g. 24x + 144x = 12x (2 + 12)

Its true

It is not possible to give a sensible answer to this question. The greatest common factor (GCF) refers to a factor that is COMMON to two or more numbers or polynomials. If you have only one number or polynomial there is nothing for it to have a factor in common with!

(x-2)(x-3)

(x-3)(x+8)