Factoring Polynomials Using GCF (with some solving)

 $2x^3+10x^2-x-4$  

 $10x^2+2x^3-x-4$  

 $2x^3-10x^2+x-4$  

 $2x^3+10x^2-4-x$  

2x²

11x²

22x

11x

The greatest common factor is not 5x. It is 15x

When factoring the polynomial, there should be three terms inside the parenthesis.

It is not in standard form

Corrected answer: $15x\left(x^2+2x+3\right)$

Corrected answer: $5x\left(3x^2+2x+1\right)$

Corrected answer: $2\left(16x^2+6x+3\right)$

Corrected answer: $2x\left(16x^2+6x+3\right)$

Corrected answer: $3\left(15x^2+4x+2\right)$

Error: the student forgot to bring down the GCF with the factored problem.

Error: the GCF should have been 2x not just 2.

 $4x\left(4x^3-8x+16\right)$  

 $2x^2\left(2x^2-4x+8\right)$  

 $x\left(4x^4-8x^2+16x\right)$  

 $4x\left(x^3-2x+4\right)$  

  $2x^2\left(7+5x^2-9x\right)$  

 $2x\left(5x^3-9x^2+7x\right)$  

 $2x^2\left(5x^2-9x+7\right)$  

 $2x\left(7x+5x^3-9x^2\right)$  

{x|x=9}

{x|x=-9}

{x|x=0, 9}

{x|x=-9, 0}

The student needed to distribute first

The student did not solve correctly. The solution should be {x | x = -5}

There should be two answers; {x | x = 0, 5}

The student's work is correct

 $12x^2+24x=0;\$  {x|x=0, 12}

 $12x^2=24x;\$  {x|x=0, 2}

 $12x^2=24x;\$  {x|x=12}

 $12x^2+24x=0;\$   {x|x=0, 2}