Question

Please Help ill give medal



Rewrite x^2 6x+9 as a square of a linear expression.

Answer 1

http://www.mcdonalds.com/us/en/careers.html

Answer 2

douc bag

Answer 3

This is a blog where people help if u don't want to help and make fun of me then stay out of my way.

Answer 4

I just need a more clear cut information o how to solve this that's all.

Answer 5

You're not doing yourself any favors by consistently posting questions without showing any effort. This site exists to help you learn, not to do your homework for you. Without asking specific questions, or at the minimum showing your attempt, you do not provide any information to potential helpers regarding what you are struggling with. In fact, it is a sign of general laziness, and thus, you have a fantastic career at McDonald's awaiting you. Put effort into your work and it will pay off.

Answer 6

Well as you should know math isn't my strongest subject but I have As and Bs in pretty much everything else plus I can work FOR my dad.

Answer 7

Just because math isn't your strong subject doesn't mean you can be lazy with it. Math is involved with everything and it will improve your ability to analyze problems and develop a clearer perspective of seemingly unrelated situations. So, I ask again, what's your attempt, and what are you struggling to understand?

Answer 8

I just don't understand how to rewrite this problem.

Answer 9

Have you covered factoring in class?

Answer 10

Hint: you need to find two numbers that multiply to get 9, and add to get 6. Both numbers will be positive, since you have all positive signs in your expression.

Answer 11

I.e., all terms in your expression are positive.

Answer 12

A linear expression is an expression of degree 1.

Answer 13

like 2nd degree

Answer 14

Your expression is a 2nd degree polynomial, yes. The problem states to turn it into the square of a linear expression, i.e., the product of two linear expressions (degree 1) that are the same.

You are trying to get this expression into the form \[(a+b)^2\]

Answer 15

Which is the same as: \[(a+b)(a+b)\]

Answer 16

yes I figured that the (a+b)^2

Answer 17

Alright, so what is your a, and what is your b?

What two numbers multiply to get 9 and add to get 6?

Answer 18

my a is 6 and b is 9

Answer 19

\[(a + b)(a+b) = (a^2 + ab + ba + b^2)\]

No, \[(a+b)^2\] is the FORM of your final expression. Again, what two numbers multiply to get 9 and add to get 6? This is not a difficult question. Answer it.

Answer 20

For example, 4 and 4 multiply to get 16, and add to get 8.

Answer 21

oh 3*3 and 3+3

Answer 22

Yes, correct. So, your two numbers are 3 and 3 (they happen to be the same for this problem). They are your "b" terms in the form \[(a+b)(a+b)\]

Now what is your "a" term?

Answer 23

im not really sure actually.

Answer 24

It's x.

Try this:

\[(x+3)(x+3) = x(x+3) + 3(x+3)\] right?

Answer 25

oh... I guess that makes sense

Answer 26

If you distribute the x across the first (x+3) and the 3 across the 2nd (x+3) and combine like terms, you end up with your original equation, i.e., the "un-factored" equation. So you know you did it correctly.

Answer 27

ok what is i.e.

Answer 28

i.e. is short-hand for "that is"
e.g. is short-hand for "for example"

You can remember the difference by thinking "egg-zample"

Answer 29

Remember that \[(a+b)(a+b)\]is just the FORM of the factored expression. You are trying to get this expression into that FORM. The "b's" in that form are the two numbers that MULTIPLY to get your LAST term of the "un-factored" expression as well as ADD to get the MIDDLE term of the "un-factored" equation.

Answer 30

So its (x+3)(x+3)?

Answer 31

The form can and will change depending on your original expression. If you had a negative sign in the middle and a positive at the end then it would be in the form (a-b)(a-b) because two negative multiply to get a positive, and add to get a negative. Yes, (x+3)(x+3) is your answer.

Answer 32

Oh well then I should have told u it was a -6 I honestly didn't even see it

Answer 33

In the future, please initially show an attempt at your work or at least ask specific questions (or explain what you struggle with).

Answer 34

Well, if it is a -6 then you know what to do now, right?

Answer 35

its (x-3)^2 correct?

Answer 36

Good job. :)

Answer 37

ok well before u leave im going to need to make sure the next part is correct.

Answer 38

The part is Do the expression in Parts A and B have a common factor? Justify your answer.

The answer I got for A is (x-3) and (x-5)
What is the question asking?

Answer 39

Is this a different problem?

Answer 40

So would they be the same because of the x

Answer 41

no

Answer 42

It just has like different parts like Part A and b and c

Answer 43

we did B

Answer 44

Well, imagine this. Imagine that you have two expressions and you place one over the other in a fraction.

\[\frac{(a+b)(c+d)}{(a+b)}\]

You now that "anything over itself is 1," right? That is, if I had 45, and divided it by 45, the answer would be 1. Because of that, you know that you can "cancel" the common factors in the numerator and denominator of the fraction, right?

Answer 45

yes

Answer 46

So, the question is basically asking, what are the common factors among the factored expression from part A, and the factored expression from part B?

Answer 47

But u see Part A asked for two answers (x-3) and (x-5)

Answer 48

Well I imagine that you factored an expression to find those factors, right? Was the original expression in Part A: \[x^2 -8x + 15\]
?

Answer 49

Part A: Write the expression x^2-18x+45 as a product of two linear expressions. Show you work and justify each step.

Answer 50

Alright, well you did Part A slightly wrong. What two numbers multiply to get 45 and add to get -18?

Answer 51

Hint: both numbers will be negative, since they add to get a negative number, and multiply to get a positive number.

Answer 52

the (x+3) was wrong wasn't it?

Answer 53

5*9 and -8+-10

Answer 54

Yes, but they have to be the same two numbers for both multiplication and addition.

Answer 55

So no, those are not the right numbers.

Answer 56

5 * 9 comes to thought first because we memorized our multiplication tables. This multiplication is not normally memorized in elementary school. 3 * 15 = 45. 3 + 15 = 18. Right? But you need negative numbers, so what are they?

Answer 57

22.5*2 -9+-9

Answer 58

Yes, but they have to be the same two numbers for both multiplication and addition. Key: SAME NUMBERS.

Answer 59

For both addition and multiplication....

3 * 4 = 12 and 3 + 4 = 7. Those are two numbers that multiply to get 12 and add to get 7.

Answer 60

Notice that they are the same numbers used for both addition and multiplication....

Answer 61

oh so -9+-9 and 9*5

Answer 62

-3 * -15 = 45

-3 + -15 = -18

Same numbers used for both mult. and addition.

Answer 63

oh

Answer 64

Anyway, so your factored expression for Part A is (x-3)(x-15), right? So what is the common factor among the factored expressions from Part A and Part B?

Answer 65

Think back to the example I gave involving "canceling" terms in a fraction.

Answer 66

(x-3)

Answer 67

right?

Answer 68

I don't see your answer.

Answer 69

(x-3) is the same factor

Answer 70

Yes, that's right. Now that your done, I would like you to, in your own words, explain to me how to factor this equation:

\[x^2 + 5x + 6\]

Answer 71

can u change your 5x

Answer 72

Nope, that's the expression as it stands. What is your first step? How will you approach this problem?

Answer 73

"What two numbers..."

Answer 74

that 5 is kind of confusing me

Answer 75

I'll state it one more time. Commit this to memory. You need to find two numbers that when multiplied together get 6, and when added together get 5.

Answer 76

3+2 3*2

Answer 77

Right. Good. So, you understand that when looking at x2+5x+6 you need to find two numbers that multiply to get 6 and add to get 5, right?

Answer 78

correct

Answer 79

That's your first step. Now, you need to look at the signs. All the terms are positive. What does this suggest about your factored form?

Answer 80

that its posotive

Answer 81

Right, that all factors have positive terms.

Answer 82

So, what is the factored form of \[x^2+5x+6\]

?

Answer 83

(x-2)

Answer 84

No minus signs. You just said that all terms in the factored form are positive, right?

Answer 85

You are getting the form (a+b)(a+c) here, where a and c are your two numbers.

Answer 86

oh whoops (x+2) (x+3)

Answer 87

Yes, good job. So thanks for sticking around and showing some effort. I hope you have a better understanding of how to approach these problem. Now, for the analysis, note that this is for simple quadratic expression in the form x^2 + bx + c, e.g., x^2 + 5x + 6. If you start seeing more complicated expressions like 27x^2 + 5x + 99 (notice you have a coefficient, 27, on your leading term), the process is a little more complicated. But finding "two numbers that multiply to get... the last term, and add to get the coefficient of the middle term" is a good start. And looking at the signs.

Answer 88

Well if that does happen ill come looking for you to get some help on that but for now I have to got to bed but I have one more question for math that I will need help on from you tomorrow. Will that be fine?