Factoring Polynomials

The process of factoring polynomials is essentially deconstructing a polynomial into its most basic elements, known as factors. These factors, when multiplied, will yield the original polynomial. This process bears considerable similarity to the prime factorization of numerical values. It is a vital tool in simplifying intricate expressions, providing solutions to polynomial equations, and assessing the properties of polynomial functions.

Finding the GCF of a Polynomial

Find the greatest common factor (GCF) of the polynomial 12x3+16x2+20x.

Factoring Out Greatest Common Factor (GCF)

Factor out the greatest common factor (GCF) from the polynomial 12x336x2+24x.

Identifying the Common Factors

Factor the polynomial 12x336x2+24x

Cancelling the Common Factors

Simplify the expression x33x2+2xx2x

Factoring Trinomials

Factor the trinomial x23x4.

Trinomial Squares

Factorize the following trinomial square: x26x+9

Factoring Using Any Method

Factorize the polynomial 2x35x223x+30.

Factoring a Difference of Squares

Factorize the following polynomial using the difference of squares method: x29

Factoring a Sum of Cubes

Factorize the sum of cubes x3+8

Factoring by Grouping

Factorize the polynomial 3x36x2+2x4 by grouping.

Factoring a Difference of Cubes

Factor the polynomial x38

Determine if an Expression is a Factor

Is x+2 a factor of the polynomial 2x2+4x+2?

Determining if Factor Using Synthetic Division

Determine if the polynomial 4x410x3+4x210x+4 can be factored by the binomial 2x1 using synthetic division.

Find the Factors Using the Factor Theorem

Find the complex zeros of the following polynomial function. Write f in factored form. f(x)=x38x2+25x26

Determining if the Polynomial is a Perfect Square

Determine if the polynomial x42x2y2+y4 is a perfect square. If so, factor it.

Expand using the Binomial Theorem

Expand the binomial (x+2)4 using the Binomial Theorem, and then factor the resulting polynomial.

Finding All Integers k Such That the Trinomial Can Be Factored

Find all integers k such that the trinomial x2kx+12 can be factored over the integers.