Question

Part 1: Explain, in complete sentences, whether or not the expression x2 + 24x + 144 fits one of the special patterns. If so, which one? (2 points)

Part 2: Explain how the polynomial is factored. (2 points)

Part 3: Provide the factors. (2 points)

Answer 1

were you able to get anywhere with this one?

Answer 2

nope-_-

Answer 3

ok let's try to factor x^2 + 24x + 144

Answer 4

can you find me two numbers that multiply to 144 (last term) AND add to 24 (middle coefficient)?

Answer 5

are you able to find two such numbers?

Answer 6

im horrible at this stufff..... helppp

Answer 7

ok how about 1 and 144

1*144 = 144 ...yes
1+144 = 145 ... no (we want them to add to 24)

Answer 8

2 and 72?

2*72 = 144 .... yes

2 + 72 = 74 ... no

Answer 9

3 and 48?

3*48 = 144 ... yes

3+48 = 51 ... no

Answer 10

you keep going until you have the two numbers add to 24

Answer 11

make sense?

Answer 12

yeahh.. im still lost.

Answer 13

ok it turns out 12 and 12 both multiply to 144 and add to 24

Answer 14

so x^2 + 24x + 144 factors to (x+12)(x+12)

Answer 15

which is basically a perfect square since (x+12)(x+12) is the same as (x+12)^2

Answer 16

alright

Answer 17

a useful formula is this

(ax+b)^2 = a^2*x^2 + 2*a*b*x + b^2

which is a formula used to expand out any perfect square

Answer 18

and it turns out that x^2 + 24x + 144 is in that form above

Answer 19

does that help? or are you still stuck?

Answer 20

Alright..

Answer 21

& yeah I kinda am.

Answer 22

ok where are you stuck

Answer 23

the wholee thingg.

Answer 24

you saw how I factored x^2 + 24x + 144 into (x+12)^2 right?

Answer 25

yes

Answer 26

so that shows us that x^2 + 24x + 144 is a perfect square trinomial

Answer 27

all perfect square trinomials are of the form

(ax+b)^2 = a^2*x^2 + 2*a*b*x + b^2

Answer 28

in this particular case, a = 1 and b = 12

Answer 29

ok

Answer 30

so we can see that if we plug in a = 1 and b = 12, we get

(ax+b)^2 = a^2*x^2 + 2*a*b*x + b^2

(1*x+12)^2 = (1)^2*x^2 + 2*1*12*x + (12)^2

(x+12)^2 = x^2 + 24x + 144

Answer 31

ok

Answer 32

so that's what they mean by special patterns

Answer 33

basically it fits the form a^2*x^2 + 2*a*b*x + b^2, which is a perfect square

Answer 34

starting to get clearer (a bit)?

Answer 35

yeah a little

Answer 36

ok just keep practicing and it'll become even more clearer (hopefully)

Answer 37

so let's answer this one by one (part by part)

Answer 38

Part 1: Explain, in complete sentences, whether or not the expression x2 + 24x + 144 fits one of the special patterns. If so, which one? (2 points)

Part 2: Explain how the polynomial is factored. (2 points)

Part 3: Provide the factors. (2 points)

Answer 39

Part 1: Explain, in complete sentences, whether or not the expression x2 + 24x + 144 fits one of the special patterns. If so, which one? (2 points)

it fits the form a^2*x^2 + 2*a*b*x + b^2 where a = 1 and b = 12

this basic form is a perfect square trinomial

Answer 40

alright

Answer 41

Part 2: Explain how the polynomial is factored. (2 points)

I'll let you answer this part. Use the formula I provided to get you started

Answer 42

able to get anywhere with it?

Answer 43

@jim_thompson5910 nice job :)