Question

Part A: Write the expression x2 - 18x + 45 as a product of two linear expressions. Show your work and justify each step.

Part B: Rewrite x2 - 6x + 9 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

oh where is said x2, I meant x^2

Answer 2

When it says that, it just means to factor them like in this one
\[x^2+2x+1=(x+1)(x+1)\]
can you do it now?

Answer 3

Um, I'm not really sure what that means.

Answer 4

ok, have you heard of completing the square yet?

Answer 5

I might have.

Answer 6

Like, if you explain it, I think I know what it is.

Answer 7

This should help explain better than I can https://www.khanacademy.org/math/algebra/quadratics/factoring_quadratics/v/Example%201:%20Solving%20a%20quadratic%20equation%20by%20factoring

Answer 8

I double checked, yours are just factoring

Answer 9

ok thank you!

Answer 10

Check back after you watch it, and we can go over the rest of the problem

Answer 11

ok

Answer 12

Okay, I finished

Answer 13

@FibonacciChick666

Answer 14

alright, so do you have any ideas on how to start part A?

Answer 15

@QuestionsWolf

Answer 16

we find a number that adds to -18 and multiplies to 45

Answer 17

good! so now, it's easiest to start with the factors of 45 can you tell me them?

Answer 18

45 and 1, 5 and 9, 15 and 3,

Answer 19

now, do any of those add to 18?

Answer 20

15 and 3

Answer 21

good, now the only issue is that we need a -18, any ideas on how we can get that?

Answer 22

Have a number that is negative

Answer 23

tell me the two numbers then? I don't quite understand your response

Answer 24

Um, -15 and -3

Answer 25

perfect! so then what does \(x^2-18x+45=?\)

Answer 26

x^2 - 15 - 3 + 45

Answer 27

uhm so go back and look at the factoring video or my original response. You want two things multiplying each other

Answer 28

to = that polynomial

Answer 29

Im not really sure what you are asking?

Answer 30

remember this:
When it says that, it just means to factor them like in this one
x2+2x+1=(x+1)(x+1)

can you do it now?
So you want that format

Answer 31

okay, let me see.

Answer 32

x^2 - 15x - 3x + 45
(x^2 - 15x) + (-3x + 45)
x(x - 15) + -3(x + -15)
(x - 15)(x - 15)

(x - 15)(x - 3)

Answer 33

yup yup can't say I've ever seen it broken down that way, but that works

Answer 34

Oh xD well thank you!

Answer 35

so you just follow the same algorithm for part b

Answer 36

really great idea for expanding it like that... I never would have thought of it

Answer 37

Thank you, and thank you for your help! :)

Answer 38

np if you have problems with the next part just message me