Module 7 Assignments 1-4

Question 1

Factoring means write as a product
Find the GCF of the numerator coefficient
Find the GCF of the Variable factor
The product of the factors found in steps 1&2 is the GCF of the monomial
Check by multiplying

Answer 1

Examples:10x^3,20y^2z^5,45xz^3

GCF: 5x2^5 =5*2^5
6x^5-8x^4+2x^3

2x(z+7)+(2+7)

Question 2

Find two numbers whose product is c and whose number is b. The factored formed of x^2+bx +c is (x+ one number)(x+ other number)

Answer 2

Example:(x+6)(x+3)
x^2+3x+6x+18
x^2+9x+18

Question 3

Find two numbers whos product is -2 and whose sum is -24.

Answer 3

(x-6)(x+4)
x^2+4x-6x-24

3x^2-18x+24
3(x^2-6x+8)
3(x-4)(x-2)

Question 4

Find two numbers whos product is -2 and whose sum is -24.

Answer 4

(x-6)(x+4)
x^2+4x-6x-24

3x^2-18x+24
3(x^2-6x+8)
3(x-4)(-2)

Question 5

Factoring a Trinomial of the Form ax^2+bx+ c
write all pairs of factors of ax^2
write all pairs of factors of c
If no combinationsexists, the polynomial is prime

Answer 5

example:
18x^4+21x^+6x^3
3x^2(6x^2+2)

Question 6

Multiplying and factoring are reverse processes.
Perfect Square Trinomials: a^2+2ab+b^2=(a+b)^2
a^2-2ab+b^2=(a-b)^2

Answer 6

Example:

4x^2-12x+9

Question 7

Difference of Two Squares

a^2-b^2(a+b)(a-b)

Answer 7

9x^2-49
(3x)^2-(7)^2
(3x+7)(3x-7)
(X^2+16+64)-x4
(X+8)(X+8)-x^4