Download Factoring Using GCF, DOTS, and trinomials

Algebra I
Module 3
Test #6 Review
Name
Period
Date
For the test Wednesday, you need to know the following topics:
 Multiplying & squaring binomials
 Factoring using GCF, DOTS, & basic trinomials
 Factoring trinomials with leading coefficients
 Factoring completely
Multiplying & Squaring Binomials
Express the following in standard form.
1.) (x – 5)(x + 2)
2.)
(x – 7)(x – 8)
3.)
(x + 5)2
4.)
(2x – 3)(x + 1)
5.)
(3x + 1)(2x – 5)
6.)
(x2 – 5x + 10)(2x – 3)
Factoring Using GCF, DOTS, and trinomials
 When factoring, what should you ALWAYS look for first?
 DOTS stands for the D
Of T
S
 When factoring trinomials, you need to find two numbers that will
to the LAST number but
or
to the middle number.
 Factoring completely is a MAJOR hint that you will need to factor
once.
than
Factor the following expressions.
1.) x2 – 36
2.)
2x3 – 18x2 + 6x
3.)
x2 – 2x – 35
4.)
x2 – 8x + 15
5.)
x2 + 17x + 16
6.)
9x2 – 64
7.)
3x5 + 6x3 – 21x2
8.)
x2 – 9x + 20
9.)
64x2 – 9y2
10.) If the area of a rectangle is expressed as x4 – 25y2, then the product of the length and
the width of the rectangle could be expressed as
(a)
(c)
(x2 – 5y)(x2 – 5y)
(x2 + 5y)(x2 – 5y)
11.) Factor
(b)
(d)
x3 + 4x2 + 3x + 12
(x – 5y)(x + 5y)
(x4 + y)(x – 25y)
1.)
4x2
– 25
FACTORING PRACTICE
2.) x2 – 11x + 18
3.)
x2 + 15x – 34
4.)
x2 – 9x + 20
5.)
12x7 – 20x5 + 16x4
6.)
2x3 + 8x2 – 4x
7.)
9x2 – 25y2
8.)
x2 – 11x + 18
9.)
15x7 – 30x2 + 40x
10.) x2 – 8x – 20
Factoring Trinomials with Leading Coefficients
1.)
3x2 + 10x – 8
2.)
4x2 – 5x – 6
3.)
2x2 + 3x – 20
4.)
4x2 + 11x + 6
Factor the following expressions completely.
1.) x3 – 13x2 – 30x
2.)
x4 + 5x2 – 6
3.)
4.)
x4 – 16
Factoring Completely
x4 – 10x2 + 25
5.)
x4 – 10x2 + 9
6.)
81x4 – 1
7.)
25x4 – 16
8.)
2x3 + 8x2 – 24x
1.)
2x2
3.)
x2 – 8x – 20
4.)
x4 – 7x2 + 6
5.)
x2 + 20x + 36
6.)
2x3 – 16x2 + 10x
–8
FACTORING PRACTICE
2.) 3x2 + 30x + 48
7.)
x2 + x – 20
8.)
9.)
x2 – 11x + 18
10.) x2 + 15x – 34
1.)
x8
3.)
x2 – 15x – 544
– 256
4x2 – 25
Challenge Questions
2.) 81x4 – 16
4.)
x2 – 67x + 990