Question

Using complete sentences, explain how to factor
2x2 + 13x + 15. Be sure that the final factorization (or "answer") is a part of your explanation.

Answer 1

what's the first term?

Answer 2

2x^2

Answer 3

what's the coefficient of that term

Answer 4

2 ?

Answer 5

what's the last term

Answer 6

15

Answer 7

you multiply the first coefficient (2) with the last term (15) to get 2*15 = 30

Answer 8

now you must find two numbers that

a) multiply to 30

AND

b) add to 13

Answer 9

10 * 3 = 30 and 10 + 3 = 13

Answer 10

good

Answer 11

that means you have to break 13x into 10x+3x

Answer 12

2x^2 + 13x + 15


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


now you factor by grouping

Answer 13

do you know how to do that?

Answer 14

No thats what I do not get

Answer 15

ok

Answer 16

you just pair the terms up like this


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


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

Answer 17

then you factor out the GCF from each group to get


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


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

Answer 18

what's next?

Answer 19

you have to multiply?

Answer 20

(2x^2 + 10x) + (3x + 15)
2x(x + 5) + 3(x + 5)
2x + 10 + 3x + 15 ?

Answer 21

no don't distribute back

Answer 22

factor further

Answer 23

what would I factor?

Answer 24

the two terms are 2x(x + 5) and 3(x + 5)

Answer 25

what's common between them

Answer 26

the 5

Answer 27

and x

Answer 28

so the x+5

Answer 29

you would factor that out to get

(2x+3)(x+5)

Answer 30

thats the answer?

Answer 31

yes

2x^2 + 13x + 15

factors to

(2x+3)(x+5)

Answer 32

expand out (2x+3)(x+5) for yourself and you'll see it simplifies to 2x^2 + 13x + 15

Answer 33

Can you check an answer for me?

Answer 34

sure

Answer 35

5x2 − 2x − 7

First multiply 5 and -7.
5 * -7 = -35

Then get a factor of -35 where the sum will be -2.
-7 * 5 = -35 and -7 + 5 = 2

Then you will put -7x + 5x where -2x is.

5x^2 − -7x + 5x − 7

Then group the first two terms and you have to pull out x and group the last two terms and factor out 1.

5x2 − -7x + 5x − 7
x( 5x - 7) + 1( 5x - 7)

Then you will pull out 5x- 7 because that is the common factor and your answer is

(5x - 7) ( x + 1)

Answer 36

you have two minus signs next to each other in 5x^2 − -7x + 5x − 7

Answer 37

oh okay thanks other than that?

Answer 38

other than that, it looks great

Answer 39

nice work

Answer 40

thanks you so much!

Answer 41

you're welcome