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MA.912.A.4.3 Factoring Polynomials

What You Need To Know...

Factor polynomial expressions.

  1. The benchmark will be assessed using MC (Multiple Choice) items.
  2. Students will completely factor polynomial expressions, which may include a greatest common factor, difference of two squares, and trinomials.
  3. Items should be set in either real-world or mathematical contexts.
  4. Distractors may include expressions that are equivalent to the correct answer, but are not completely factored.

Example One

Members of the art club want to raise money for their next field trip.  They plan to decorate greeting cards with glitter and origami animals made of origami paper.  They wrote the expression below to help calculate their total expenses.
 

(np + ng) + nc

where:

c = cost of one greeting card
g = cost of glitter per card
p = cost of origami animals per card
n = number of cards

Which of the following expressions is equivalent to the expression above?

A. n(p + g + c)
B. n(p + g) + c
C. 3n(p + g) + c 
D. 3n(p + g + c) 
 

CLICK HERE FOR SOLUTION

Example Two

If   x3.jpg, which of the following shows the expression below in simplest form?

4-3B.jpg

A.  3(x + 9)
B.  3(x – 3) 
C.  3(x + 3) 
D.  3(x – 9) 

 

 

CLICK HERE FOR SOLUTION

Example Three

The area of a rectangle is 2x2 - 7x - 15.  Which of the following shows possible dimensions of the rectangle?

 A_4_3_Choices.png

CLICK HERE FOR SOLUTION

Additional Examples

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Greatest Common Factor

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Factor by Grouping

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Leading Coefficient of 1

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Other Leading Coefficient

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Difference of Squares

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Factor and Simplify

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Reference Sheet