Factoring Polynomials

Factoring Polynomials

Factor the following polynomials completely.

Techniques in Factoring Polynomials

• First, factor out the greatest common factor (GCF) from all of the terms.

• The other factoring techniques depend on how many terms there are.

• If there are two terms, use the Difference of Two Squares pattern or Sum or Difference of Cubes.

• If there are three terms in which the first and third terms are squares of numbers or expressions, it may be a perfect square trinomial.

• If there are three terms but it's not a perfect square trinomial, use factoring general trinomial

• If there are four terms, factor by grouping (The Grouping Method).

• Warning: To factor a polynomial completely, we frequently have to apply more than one technique. After factoring by any method, always take a close look at each of your factors to see if any of them can factored.

Multiple Choice

 $35a^5b^5-105a^6b^4-7a^4b^3$  

•  $7a^3b^4\left(5a^2b\ -\ 15a^2b-1\right)$  

• PRIME

•  $7a^4b^3\left(\left(5ab-15a^2b-1\right)\right)$  

Multiple Choice

 $4m^2n^2+25h^2n^2+4m^2+25h^2$  

•  $\left(4m^2+25h^2\right)\left(n^2+1\right)$  

• Prime Polynomial

•  $\left(2m+5h\right)\left(2m-5h\right)\left(n+1\right)\left(n-1\right)$  

Multiple Choice

• PRIME POLYNOMIAL

Multiple Choice

 $24k^2-54m^3$  

•  $6\left(4k^2-9m^3\right)$  

• PRIME POLYNOMIAL

•  $6m\left(2k+3m\right)\left(2k-3m\right)$  

Multiple Choice

 $3x^{2a}-75y^{2b}$  

• PRIME POLYNOMIAL

•  $3\left(x^a-5y^b\right)\left(x^a+5y^b\right)$  

•  $3\left(x^{2a}-25y^{2b}\right)$  

Multiple Choice

 $12k+60k^2+75k^3$  

• PRIME POLYNOMIAL

•  $3k\left(4+20k^{ }+25k^2\right)$  

•  $3k\left(2+5k\right)^2$  

Multiple Choice

 $11x^2-85xy-24y^2$  

•  $\left(11x+3y\right)\left(x-8y\right)$  

• PRIME POLYNOMIAL

•  $\left(11x-8y\right)\left(x+3y\right)$  

Multiple Choice

 $8w^3-x^{12}$  

• PRIME POLYNOMIAL

•  $\left(2w-x^4\right)\left(4w^2+2wx^4+x^8\right)$  

•  $\left(2w\ -\ x^6\right)\left(4w^2+2wx^6+x^8\right)$  

Multiple Choice

 $x^3-8y^3-6y^2+3xy$  

•  $\left(x+2y\right)\left(x^2-2xy+y^2+3y\right)$  

• PRIME POLYNOMIAL

•  $\left(x-2y\right)\left(x^2+2xy+4y^2+3y\right)$  

Multiple Choice

 $\ 2x^5-486$  

•  $2\left(x-y\right)\left(x^4+81x^3+27x^2+9x+3\right)$  

• Prime Polynomial

•  $2\left(x-3\right)\left(x^4-3x^3+9x^2+27x+81\right)$