Factoring Polynomials Using GCF (with some solving)

Write the polynomial in standard form. $10x^2+2x^3-4-x$  

•  $2x^3+10x^2-x-4$  

•  $10x^2+2x^3-x-4$  

•  $2x^3-10x^2+x-4$  

•  $2x^3+10x^2-4-x$  

Fill in the purple box that correctly factors the polynomial using GCF.

Fill in the purple box with the monomial that correctly factors the polynomial using GCF.

• 2x²

• 11x²

• 22x

• 11x

Find the error and correct it. You should mark two answers

• 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: $5x\left(3x^2+2x+1\right)$

Find the error and correct it. There should be two selected answers for this problem.

• 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.

Factor the polynomial using GCF. $4x^4-8x^2+16x$  

•  $4x\left(4x^3-8x+16\right)$  

•  $2x^2\left(2x^2-4x+8\right)$  

•  $x\left(4x^4-8x^2+16x\right)$  

•  $4x\left(x^3-2x+4\right)$  

Write the polynomial in standard form and then factor using GCF.

 $14x^2+10x^4-18x^3$  

•   $2x^2\left(7+5x^2-9x\right)$  

•  $2x\left(5x^3-9x^2+7x\right)$  

•  $2x^2\left(5x^2-9x+7\right)$  

•  $2x\left(7x+5x^3-9x^2\right)$  

Solve the factored polynomial

 $5x\left(x+9\right)=0$  

• {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

Write the polynomial in standard form and then solve. 

 $24x=-12x^2$  

•  $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}