Question

I WILL MEDAL AND FAN JUST HELP ALREADY!!!!!

I just need help with this:

Part A: Write the expression x2 + 7x + 12 as a product of two linear expressions. Show your work and justify each step.

Part B: Rewrite x2 + 4x + 4 as a square of a linear expression.

Part C: Do the expressions in parts A and B have a common factor? Justify your answer.

Answer 1

@triciaal @mathmale @mathstudent55 @zepdrix @pooja195 @ParthKohli @jim_thompson5910 @Opcode

Answer 2

I think you should solve the quadratic equations for boths a and b

Answer 3

a) gives you \[(x+3)(x+4)\]

b) gives you \[(x+2)(x+2)=(x+2)^2\]

Answer 4

@khally92 How did you get your answer for b?

Answer 5

@triciaal Help

Answer 6

@Zela101

Answer 7

@ayeshaafzal221 @magepker728 @zepdrix

Answer 8

@Thebossofme191 @OceanChild @Opcode @PizzaLover123 @Agl202 @Anaise

Answer 9

:o

Answer 10

(I have already written down the answer for part A, I need help with Part B and C)

Answer 11

How did @khally92 get (x + 2)^2 as her answer?

Answer 12

\[\large\rm x^2+4x+4\]You can do factor by grouping if you've gotten good with that method.

Answer 13

Factors of 4: 2*2 is one way to do it, yes?

Answer 14

Do you mean x^2 + 3x + 4x + 4?

Answer 15

Wait, nvm. I thot we were using the same equation as part A nvm

Answer 16

:P

Answer 17

Yes 2 and 2 would be the best

Answer 18

x2 + 2x + 2x + 4

Answer 19

(x2 + 2x) + (2x + 3)

Answer 20

*(2x + 4)

Answer 21

GCF

Binomial 1: x

Binomial 2: 2

Divide GCF

x(x + 2) + 2(x + 2)

Answer 22

Join together:

(x + 2)(x + 2)

Answer 23

OHHHHHHH

Answer 24

grouping is a little bit longer of a way to do it,
but ya it always works so that's nice :)

Answer 25

A: (x+3)(x+4)
B: (x+2)(x+2)

Common factor?

Answer 26

Does it start with an x and end with an x?

Answer 27

Hint, this is a factor in orange here \(\large\rm \color{orangered}{(x+3)}(x+4)\)

Answer 28

Ima assume that the comon factor is x, correct?

Answer 29

Example: \(\large\rm x(x-2)(x+3)\)
In this example, x is a factor.

In your problems, both A and B, x is `not` a factor.
x is `part of` a factor, but it's not a factor by itself.

Answer 30

How is x + 3 a factor though?

Answer 31

21 = 7*3

Therefore 7 is a factor of 21.

x^2+4x+4 = (x+2)*(x+2)

Therefore (x+2) is a factor of x^2+4x+4

Answer 32

But how is x + 3 a common factor?

Answer 33

Things that multiply together are factors.

Answer 34

(x+3) is not a common factor,
it's a factor of the polynomial in A,
but not a factor of the polynomial in B.

Answer 35

So there are no common factors then, correct?

Answer 36

correct :)

Answer 37

Hooray! Thanks for all your help @zepdrix . I'd give you owlbucks but I don't have any. :(

Answer 38

owl what? 0_o
oh those still exist? hah

Answer 39

You can get letters of recommendation and stuff with them

Answer 40

Anyways, ima go finish the question.

ill be back in like 7 minutes. Or I won't be back at all. Either Way! :)