Factoring Polynomials

Factoring Polynomials

Factoring out the GCMF

​Difference of Two Squares

​Sum and Difference of Two Cubes

​Perfect Square Trinomial

Multiple Choice

Factor the polynomial $$18m^2n^4-12m^2n^3+24m^2n^2$$ . 

• $$\left(6m^2n^4\right)\left(18-12n+24n^2\right)$$  

• $$\left(6m^2n^2\right)\left(3n^2-2n+4\right)$$  

• prime

GCMF of Two or More Monomials

Multiple Choice

Factor the polynomial  $$81c^4d^2-100b^6$$  .

• $$\left(9cd-10b\right)\left(9cd+10b\right)$$  

• $$\left(9c^2d-10b^3\right)\left(9c^2d+10b^3\right)$$  

• prime

Multiple Select

Which of the following is /are a sum or difference of two cubes?

• $$53x^3-2$$  

• $$375x-81x^3$$  

• $$216x^9y^3-125y^{12}$$  

• $$27x^{15}+1$$  

• $$x^6+1$$  

Multiple Choice

What is the factored form of  $$27x^{15}+1$$  ?

• $$\left(3x^5+1\right)\left(9x^{10}-3x^5+1\right)$$  

• $$\left(3x^5+1\right)\left(9x^{10}+3x^5+3x\right)$$  

• $$\left(3x^5+1\right)\left(3x^{10}-4x^5-1\right)$$  

Fill in the Blanks

$4x^2+$  

  $+25$  

Complete the trinomial so that it is a perfect square trinomial.

Multiple Choice

$$4x^2+20x+25$$  

Express the trinomial in factored form.

• $$\left(2x+5\right)^2$$  

• $$\left(2x+5\right)\left(2x-5\right)$$  

• $$\left(2x+25\right)^2$$  

Open Ended

What are the steps in factoring by grouping?

​Factoring by Grouping

​STEPS

​

​ 1. Factor the terms with common factors

​ 2. Factor out the GCMF in each group

​ 3. Factor out the common binomial factor

​ 4. Simplify if needed

Multiple Choice

Factor  $$5mn+25m+3n^3+15n^2$$  .

• $$\left(n+5\right)\left(5m+3n^2\right)$$  

• $$\left(5mn\right)\left(1+5n+3n^2+3n\right)$$  

• $$\left(5m^2+3n^2\right)\left(n+5\right)$$  

Multiple Choice

Factor  $$6b^3+16b^2-15b-40$$  .

• $$\left(2b+5\right)\left(2b-5\right)\left(3b+8\right)$$  

• $$\left(2b^2-5\right)\left(3b+8\right)$$  

• $$\left(3b+8\right)\left(2b^2+5\right)$$  

Multiple Choice

Factor $$7xy-28x^3-y+4x^2$$  .

• $$\left(7x-1\right)\left(y-4x^2\right)$$  

• $$7x\left(y-4x^2\right)-y+4x^2$$  

• $$\left(7x\right)\left(y-4x^2\right)$$