Factoring: Using the X-Box method
Part 1: Understanding how to multiply quickly without FOIL. – Note*** coefficient of x’s are 1.
Complete the following X’s to multiply.
(x + 5)(x + 4) = ________________________
(x +2)(x – 8) = __________________________
(x – 2)(x + 9) = _________________________
(x – 11)(x – 4) = ________________________
Factoring: Using the X-Box method
Part 2: Working backwards with the X’s to factor. Note*** - coefficient of x2 is 1.
Complete the following X’s to factor.
x2 + 10x + 25 = ________________________
x2 – 3x – 54 = ____________________
x2 – 13x + 22 = _________________________
x2 + 5x – 50 = _____________________
Factoring: Using the X-Box method
Part 3: X-Box factoring – Note***x2 does not always have a coefficient of 1.
To factor any polynomial in the form ax2 + bx + c, where a can be any value.
1) Multiply a by c.
2) Complete an X, using the numbers you found in step 1.
3) Complete a box (area model)
4) Write the factors.
Factor the following.
3p2 – 2p – 5 = _______________________
2n2 + 3n – 9 = __________________________
3n2 – 8n + 4 = _______________________________
5n2 + 19n + 12 = ________________________________
2v2 + 11v + 5 = ______________________________
Factoring: Using the X-Box method
Practice On Your Own – Group A
For the following: Factor the odd problems and multiply the evens. The other group’s problems will match with your
group’s answers.
1)
15n2 – 27n – 6
2)
2(n + 9)(n – 6)
3)
2n2 + 5n + 2
4)
(7a + 4)(a + 7)
5)
9k2 + 66k + 21
6)
(5x – 3)(x – 3)
7)
4n2 – 15n – 25
8)
Not factorable
9)
k2 – 13k + 40
10)
(a + 2)(a + 9)
11)
n2 – n – 56
12)
(n -2)(n – 3)
13)
b2 – 6b + 8
14)
(n + 2)(n + 4)
15)
5n2 + 10n + 20
16)
2(k + 5)(k + 6)
17)
a2 – a – 90
18)
(p + 10)(p + 1)
Factoring: Using the X-Box method
Practice On Your Own – Group B
For the following: Multiply the odds and factor the evens. The other group’s problems will match with your group’s
answers.
1)
3(5n + 1)(n – 2)
2)
2n2 + 6b – 108
3)
(2n + 1)(n + 2)
4)
7a2 + 53a + 28
5)
3(3k + 1)(k + 7)
6)
5x2 – 18x + 9
7)
(n – 5)(4n + 5)
8)
x2 – 4x + 24
9)
(k – 5)(k- 8)
10)
a2 + 11a + 18
11)
(n + 7)(n – 8)
12)
n2 – 5n + 6
13)
(b – 4)(b – 2)
14)
n2 + 6n + 8
15)
5(n2 + 2n + 4)
16)
2k2 + 22k + 60
17)
(a – 10)(a + 9)
18)
p2 + 11p + 10
Name: __________________________
Date: _________________
Homework 7.0 day 2 Factoring
Factor the following. Use either guess and check or the X-Box method.
1)
4x2 – 35x + 49
2)
4n2 – 17n + 4
3)
6x2 + 7x – 49
4)
6x2 + 37x + 6
5)
-6a2 – 25a – 25
6)
6n2 + 5n – 6
7)
16b2 + 60b – 100
8)
b2 + 8b + 7
9)
n2 – 11n + 10
10)
m2 + m – 90
11)
n2 + 4n – 12
12)
n2 – 10n + 9
13)
b2 + 16b + 64
14)
m2 + 2m – 24
15)
5v2 – 30v + 40
16)
2p2 + 2p – 4
17)
4v2 – 4v – 8
18)
x2 – 15x + 50
19)
v2 – 7v + 10
20)
p2 + 3p – 18
21)
6v2 + 66v + 60