Factoring

Question 1

List all factorizations of 6

Answer 1

16, 23

Question 2

list all factors of 28

Answer 2

128
214
4*7

factors= 1,2,4,7,14,28

Question 3

What is a prime number?

Answer 3

can only be divided by itself, p.e 7, 19… except 1 and 2

Question 4

Find the prime factorization of 24!

Answer 4

Draw a tree. Only one which can´t stand on top is 124.
we take 212. 2 is a prime number, so mark it, but we can further break down 12 in 26, so mark 2 and break down 6 in 23, mark both.

Note! you can also do 3*4 or start with an other factorization, result is the same.

Prime factoritaion of 24: 222*3 can also be written as: 2**3 * 3

Question 5

Find the greatest common factor of 12x3y2
and
18x2y4

Answer 5

write out:
322xxxyy
332xxyyyy
find what they have in common: 32xxyy = 6x2y2

Question 6

Factor out the greatest common factor:

4x2+12y3

18p3-9p5

Answer 6

gcf=4

4(x2+3y3) # find out whats in parentheses by dividing term with gcf

9p3(2-p2) # 2-p**2 because you divide under fraction so exponents 5-3

Question 7

Find gcf of 6x2 y2+9x3 y4-3x2 y5

Answer 7

3x2 y2 # y**2 because it is smallest exponent

Question 8

Put into binominal: 7x(2x+1)+3(2x+1)=

Answer 8

(2x+1)(7x+3)

Question 9

Factor by grouping. Only if you have 4 term polynominals!!!

15x3+10x2-12x-8

Answer 9

(3x+2)(5x**2-4)

Question 10

Factoring trinominals with coefficient 1: Reverse FOIL Method.
x**2+3x-10

Answer 10

(x+5)(x-2)
why?
split x**2 up. then find the factorials of -10(because 1*-10). The sum of one of the options needs to fit to the midterm(3x). Take this option and you´re done! ;)

Question 11

Factoring trinominals if coefficient is not 1.
5x**2+12x+7

1. Make a 4 term polynominal out of it.
2. you´ll see what you have to do now.

Answer 11

AC-Method because it is ax**2+bx+c
multiply 5*7=35. Find the factorial which also adds up to the mid term. It is 5*7. So write:
5x**2+7x+5x+7, then:
X(5X+7)+1(5X+7)
(5X+7)(X+1)

Question 12

4x**2-81 transform to binominal ()()

Answer 12

(2x+9)(2x-9)

Question 13

How to prove if you have a prime polynomial?

Answer 13

Search for factorials of C, or A*C if you have a coefficient which is not 1. If they don´t let them add up to b xou have a prime polynomial.

Question 14

Proof why these are primes:
2x**2-17

3x**2+2x+9

Answer 14

To factor a binominal, it has to be a difference of squares.

27 has no factorial which adds up to 2

Question 15

Make it into a Binominal (with a number upfront)

5x**2-45

Answer 15

find gcf, divide it with the numbers, put it upront befor the pair of parentheses

5(x**2-9)
5(x+3)(X-3)