Question

how do I factor 2x^2+3x-5

Answer 1

Again, find a product that when you multiply 2 * -5 gives you -10 and when added gives you +3

5 * -2 = -10
5 + -2 = 3

2x^2 + 5x - 2x - 5

x(2x + 5) -1(2x + 5)

(2x + 5)(x - 1)

Answer 2

okay i did all of that what do i do next

Answer 3

(2x + 5)(x - 1) is the fully factored form, so once you get there, you're done

Answer 4

okay thank you i have another one

Answer 5

ok go ahead

Answer 6

okay 6x^2+11x+3 factor

Answer 7

that is in the form ax^2 + bx + c

where

a = 6
b = 11
c = 3

see how I'm getting this?

Answer 8

yues and no the x ?? confuse me

Answer 9

well we don't know what x is in 6x^2+11x+3, so we just leave it as x for now

Answer 10

same for ax^2 + bx + c

Answer 11

okay so what do i do next

Answer 12

what is the value of a*c ?

Answer 13

a: 6 and c: 3 right

Answer 14

good, so a*c = ???

Answer 15

6^3 right ??

Answer 16

a*c means a times c

Answer 17

a is 6, c is 3, so a*c = 6*3 = ??

Answer 18

yeah that is what i put okay you can go on to the next step now

Answer 19

what is 6*3

Answer 20

18 right

Answer 21

good

Answer 22

so you need to find two numbers that

multiply to 18 AND add to 11 (11 is the middle coefficient)

Answer 23

random numbers

Answer 24

two whole numbers

Answer 25

what two whole numbers both multiply to 18 AND add to 11

Answer 26

i don't really know

Answer 27

what are some ways to multiply to 18?

Answer 28

using whole numbers

Answer 29

1,2,3,8 right

Answer 30

3*6 is one way to multiply to 18, what's another?

Answer 31

2*9 right

Answer 32

good, what happens when you add 2 and 9?

Answer 33

you get 11 ohhh i see now okay move on

Answer 34

so the numbers 2,9 both multiply to 18 and add to 11

Answer 35

that means we break up 11x into 2x + 9x

Answer 36

6x^2+11x+3

turns into

6x^2+2x+9x+3

Answer 37

okay what do we do from there

Answer 38

you factor by grouping

Answer 39

have you done that before?

Answer 40

no i don't think so

Answer 41

first you group the terms in pairs like this

6x^2+2x+9x+3

(6x^2+2x)+(9x+3)

Answer 42

What can you factor from (6x^2+2x)

Answer 43

6x^2

Answer 44

no

Answer 45

what is the GCF of 6x^2 and 2x

Answer 46

6

Answer 47

6 is not a factor of 2

Answer 48

2

Answer 49

is a factor of both 2 and 6, good

Answer 50

what else is a factor of 6x^2 and 2x

Answer 51

i don't know

Answer 52

what do they share together?

Answer 53

other than a factor of 2

Answer 54

6, and 12

Answer 55

x^2 is the same as x*x, agreed?

Answer 56

yes

Answer 57

so let's find the prime factorization of 6x^2 and 2x