Question

Can someone explain to me how to do this? I don't need you to give me the answer but work with me until I can get the answer? Choose two trinomials from the list below to factor. Using complete sentences, explain how to factor each one. Be sure that the final factorization (or "answer") is a part of your explanation.


2x2 + 13x + 15
2x2 + 27x + 13
5x2 − 2x − 7
10x2 − 7x − 3
8x2 − 11x + 3

Answer 1

first pick two you want to factor

Answer 2

2x^+13x+15 and 5x^2-2x-7

Answer 3

ok great

Answer 4

let's start with 2x^+13x+15

Answer 5

2x^2+13x+15 *

Answer 6

okay.

Answer 7

to factor 2x^2+13x+15, we first multiply 2 and 15 (first and last coefficients) to get: 2*15 = 30

then we must find two numbers that

a) multiply to 30

AND

b) add to 13 (middle coefficient)

Answer 8

what are those two numbers?

Answer 9

ok hold on I suck at math so it might take a few minutes to figure it out

Answer 10

take all the time you need and you do NOT suck at math (having this negative attitude gets you nowhere, so stay positive)

Answer 11

3 and 10?

Answer 12

good, proof you don't suck at math

Answer 13

so this means that 13x turns into 3x + 10x and we use this to factor by grouping

Answer 14

So we break up 13x into 3x + 10x, group the terms into pairs, factor each pair separately, then factor out the overall GCF


2x^2 + 13x + 15

2x^2 + 3x + 10x + 15

(2x^2 + 3x) + (10x + 15)

x(2x + 3) + (10x + 15)

x(2x + 3) + 5(2x + 3)

(x + 5)(2x + 3)


So this means that 2x^2 + 13x + 15 factors to (x + 5)(2x + 3)

Answer 15

making sense?

Answer 16

kinda i'm kind of like answering it and understanding it lol that's why it is taking so long to write back. I'm sorry. But you helping me is honestly the best! I really appreciate it

Answer 17

that's ok, like I said, take all the time you need

Answer 18

x(2x + 3) + (10x + 15)
x(2x + 3) + 5(2x + 3)
(x + 5)(2x + 3
I don't understand this part? I got how you did it like up till here

Answer 19

I grouped the terms into pairs to get (2x^2 + 3x) + (10x + 15)

Answer 20

then focusing on the first parenthesis group only, I factored out the GCF of that group which is x to get

x(2x + 3) + (10x + 15)

Answer 21

with me so far?

Answer 22

Yes.

Answer 23

then I focused on the next group (10x+15) and factored out 5 to get 5(2x+3)

so this means

x(2x + 3) + (10x + 15)

turns into

x(2x + 3) + 5(2x + 3)

Answer 24

tell me when you're ready for the next step

Answer 25

okay im ready

Answer 26

then notice how we have a common term of (2x+3)

Answer 27

we then factor that out of the entire expression to go from

x(2x + 3) + 5(2x + 3)

to

(x + 5)(2x + 3)

Answer 28

Ok And that's the answer right?

Answer 29

correct

Answer 30

Okay. Can you work with me on the second one?

Answer 31

sure

Answer 32

first identify the first and last coefficients of 5x^2-2x-7

Answer 33

You're honestly amazing!

Answer 34

I'll let you do more of the steps, but I'll be here to help out

what are the first and last coefficients of 5x^2-2x-7

Answer 35

I multiply 5 and 7 right?

Answer 36

5 and -7 actually

Answer 37

Oops. I forgot to pay attention to the signs.

Answer 38

that's ok

Answer 39

what do you get when you multiply them

Answer 40

Is it -2?

Answer 41

5 times -7 = ???

Answer 42

-35?

Answer 43

now you need to find two numbers that

a) multiply to -35

AND

b) add to -2 (the middle coefficient)

Answer 44

Could you help me with this? I'm not very good with negatives

Answer 45

It might help to list all the ways to multiply to 35

Don't worry about negatives right now

Answer 46

So go ahead and list all those ways out

Answer 47

7 times 5 = 35

Answer 48

ok, now because 35 is actually negative, this means that one factor of 35 must be negative (but not both)

Answer 49

so which factor must be negative so that the two factors add to -2

Answer 50

-7?

Answer 51

good, so -7 + 5 = -2

Answer 52

which means -7x + 5x = -2x

Answer 53

so

5x^2-2x-7

breaks down into

5x^2 - 7x + 5x - 7

Answer 54

now factor by grouping

I'll let you take over

Answer 55

So (5x^2-7x)+(5x-7)

Answer 56

good start, keep going

Answer 57

start with the first group and find the gcf right?

Answer 58

yes, then factor that out

Answer 59

would it be x^2?

Answer 60

not quite

Answer 61

Hmm :/

Answer 62

5x^2 - 7x

the common factor between 5x^2 and -7x is not x^2, but it's pretty close

Answer 63

Oh! X?

Answer 64

yep

Answer 65

so factor out x to go from 5x^2 - 7x to ______

Answer 66

x(5x^2-7x)

Answer 67

no

Answer 68

x(5x-7x)

Answer 69

notice if you distributed the x on x(5x^2-7x), you would get x*5x^2 - x*7x = 5x^3 - 7x^2

Answer 70

what do you get when you distribute x(5x-7x)

Answer 71

5x^2-7x^2

Answer 72

so it would be 5x-7

Answer 73

so that's incorrect as well since we want 5x^2 - 7x

Answer 74

yes

5x^2 - 7x

factors to

x(5x - 7)

Answer 75

ok now they are both the same

Answer 76

yes, you can factor the second group (5x-7) into 1(5x-7)

Answer 77

so we go from

(5x^2-7x)+(5x-7)

to

x(5x-7)+1(5x-7)

Answer 78

what's next?

Answer 79

find a gcf from them both?

Answer 80

yep

Answer 81

it would be 1

Answer 82

no

Answer 83

the GCF is more than 1

Answer 84

uhm 3?

Answer 85

think of x(5x-7)+1(5x-7) as two terms

x(5x-7) and 1(5x-7)

Answer 86

Ugh i don't know :(

Answer 87

what thing does x(5x-7) and 1(5x-7) have in common

Answer 88

what's in common between those terms

Answer 89

(5x-7)

Answer 90

good

Answer 91

so factor that GCF out

Answer 92

how do I do that again?

Answer 93

one way you can do it is this

Answer 94

x(5x-7)+1(5x-7)

x___+1___ ... erase the "5x-7" terms

x+1 ... fully erased now

(x+1)(5x-7) .... now tack on the GCF 5x-7 as its own factor

Answer 95

woah huh?

Answer 96

hmm i guess that's hard to do in text form

Answer 97

we have this x(5x-7)+1(5x-7)

Answer 98

yes