CC GPS Geometry

Learning Objective #34:

Identify the steps to the factoring process for two terms, three terms, and four terms

Practice Problems set 1:

(x2 – 25)

(x2 + 7x + 10)

(x3 + 7x + 2x + 14)

(x2 – 1)

(x2 – 6x + 9)

(5x4 – 15x3 + 10x2)

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)

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)

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)