This document provides examples of a student's work factorizing polynomials with 2, 3, and 4 terms. It outlines the steps to factor polynomials for each case. For a 2 term polynomial, the student looks for the difference of two perfect squares and writes the factored form as two binomials. For a 3 term polynomial, the student uses the "diamond method" to find two numbers whose product and sum match the coefficients. For a 4 term polynomial, the student groups like terms and finds the greatest common factor of each group.

1. CC GPS
Geometry
 Learning Objective
#34:
 Identify the steps to
the factoring process
for two terms, three
terms, and four terms

2. Practice Problems set 1:
(x2 – 25)
(x2 + 7x + 10)
(x3 + 7x + 2x + 14)
(x2 – 1)
(x2 – 6x + 9)
(5x4 – 15x3 + 10x2)

3. SOLUTIONS
(example of students response):
 (x2 – 25)
2 terms
Look for difference of 2
perfect squares
Solution is 2 binomials,
one +, one –
Square Root of the first
term in position 1,
Square Root of the
second term in position
2 for both binomials
(x + 5)(x – 5)
 (x2 – 1)
2 terms
Look for difference of 2
perfect squares
Solution is 2
binomials, one +, one –
Square Root of the first
term in position
1, Square Root of the
second term in position
2 for both binomials
(x + 1)(x – 1)

4. SOLUTIONS con’t
(example of students response):
 (x2 + 7x + 10)
3 terms
Identify a,b, & c from
ax2 + bx + c
Create diamond with
a •c in the North
position and b in the
South position
Find two numbers, East &
West positions, that
multiply to the North and
combine (add/subtract) to
the South
 (x + 2)(x + 5)
 (x2 – 6x + 9)
3 terms
Identify a,b, & c from
ax2 + bx + c
Create diamond with
a •c in the North
position and b in the
South position
Find two numbers, East &
West positions, that
multiply to the North and
combine (add/subtract) to
the South
 (x – 3)(x – 3)

5. SOLUTIONS con’t
(example of students response):
 (x3 + 7x + 2x + 14)
4 terms
Group like binomials
Find GCF for both sets
Identify matching “left
overs” for one binomial
and GCF’s for second
binomial
(x2 + 2)(x + 7)
 (5x4 – 15x3 + 10x2)
4 terms – in this case, it’s
necessary to separate
the middle term into two
terms
Group like binomials
Find GCF for both sets
Identify matching “left
overs” for one binomial
and GCF’s for second
binomial
(5x3 – 5x2)(x – 2)