Question

Factor completely 2xsquared +7x+4

Answer 1

Is this a test question?

Answer 2

no its for some hw

Answer 3

In any Quadratic with three terms in the form of ax^2 + bx + c, take a * c.

Once you have foud this product, see what numbers would be factors of a*c, and yet add up to b. These could be negative too.

In your example, we will take 2 * 4 which is what?

Answer 4

8

Answer 5

oh i messed up its -4

Answer 6

Good, now what are some factors of 8 that when added together make 7?

Answer 7

in the equation

Answer 8

i have no idea

Answer 9

ah! ok, so -8, so what are some factors of -8 that could add up to +7?

Answer 10

OK, name some factors of -8.

Answer 11

4,2 and 8

Answer 12

OK, so -2 and 4 multiplied = -8, when we add them together we get +2, so this is not the one we are looking for. Any other factors?

Answer 13

1 and other than that i have no idea

Answer 14

ok, 1 * -8 = -8 and 1 + -8 = -7...close! Could we somehow change the sign to make these work?

Answer 15

im guessing we can but im not sure how

Answer 16

well if we tried -8 and +1, could we flip the signs?

Answer 17

okay

Answer 18

So if we tried -1 and +8, then -1 * 8 = -8 and -1 + 8 = +7... it works!

Answer 19

okay yay ahh then what do i do

Answer 20

You need to be able to try all the factors and all combinations of positive and negatives.

Answer 21

After that, you rewrite your original equation while using these two new numbers

Answer 22

2x^2 -1x + 8x - 4

Answer 23

Notice that we have not changed anything since -1x + 8x = 7x

Answer 24

okay yeah

Answer 25

from here, we will factor by grouping, so we will put parantheses around the first two terms, and then parantheses around the second two terms... (2x^2 - 1x) + (8x - 4)

Answer 26

Now look at the first group, do these terms have anything that can be pulled out?

Answer 27

factor but not the x

Answer 28

Well since they both share an x, we can pull an x out!

Answer 29

oh i was looking at the second one okay

Answer 30

So 2x^2 - 1x = x (2x - 1)

Answer 31

okay

Answer 32

OK, now for the second group. Do they share anything?

Answer 33

a common factor

Answer 34

yes, what common factor?

Answer 35

2 or 4

Answer 36

and

Answer 37

perfect!

Answer 38

4 is the largest common factor!

Answer 39

okay

Answer 40

so 8x - 4 = 4(2x - 1)

Answer 41

So now our equation 2x^2 + 7x - 4 = x(2x - 1) + 4(2x - 1)

Answer 42

so now both terms have what in common?

Answer 43

the 2x -1

Answer 44

Excellent! So we factor that out and we get (2x - 1) (x + 4)

Answer 45

Done!

Answer 46

thank you so much

Answer 47

No problem!