Question

factor #2

Answer 1

z^2 +10z+25

Answer 2

turingtest wanna help me on my hw :D

Answer 3

sure :D
think of two numbers that add to 10 and multiply to 25

Answer 4

5 and 5

Answer 5

those will be the numbers that get added in the factoring you're doing
i.e. in\[(x+a)(x+b)\]those will be your a and b
in this case they're both 5

Answer 6

so the factoring is\[(x+5)(x+5)\]can we simplify that a little?

Answer 7

no any more 5 is a prime number

Answer 8

but we can write \[(x+5)(x+5)=(x+5)^2\]right ?
that's the neatest way to do it ;)

Answer 9

ya :D

Answer 10

on two our next question

Answer 11

in general, when you factor like that and get a=b, then you will have a perfect square like above

Answer 12

ok

Answer 13

x^2 -16x+48

Answer 14

ask your magificent questions

Answer 15

same thing only a little trickier...
we need two numbers that add to -16 and multiply to 48
make sure the signs match!

notice that the last number is positive, so both numbers must be negative to give a negative middle term and positive last term

find the numbers

Answer 16

ummmm

Answer 17

(x-?) (x-?)

Answer 18

I mean above that 48 is positive, and since that is the two numbers that we are looking for (call them a and b) both a and b must be negative

because a negative times a negative is a positive

Yes, good start writing it like that

Answer 19

now think of factors of 48 and try adding them together:
1+48=49 not 16
2+24=26 not 16
...
find the factors that add to 16

Answer 20

4*4

Answer 21

those multiply to 16, not 48
we need each pair of factors to multiply to 48 and /add/ to 16
just start going down the pairs of factors starting with 1 and check if they add to 16
1*48->1+48=49
2*24->2+24=26
continue
4*?...

Answer 22

12*4

Answer 23

there ya go :D

Answer 24

so what are a and b ?

Answer 25

so the answer is (x-12) (x-4)

Answer 26

yep :)

Answer 27

on to the next one

Answer 28

c^2-2c-15

Answer 29

again, same idea, but notice that this time both the second and third are negative, so what do we know about the signs of a and b
-2-3=-5 and we want -2
-2*-3=6 and we want -15
so no to that bit...

Answer 30

-2 and -13

Answer 31

do they add to -2 and multiply to -15 ?

Answer 32

?

Answer 33

no

Answer 34

well that's what we need
two numbers that add the the middle number and multiply to the last one

Answer 35

first of all think about the signs of a and b
the last number is -15 (notice it's negative)
what does that mean about the signs of a and b ?

Answer 36

both negatives

Answer 37

but the last number is a*b
if they were both negative the last number would be /positive/ because a negative times a negative is positive

Answer 38

remember our last example both a and b were negative, because the last term was positive and the middle term negative

Answer 39

it works like so:
if the last term is positive, and the second term is positive, a and b are positive

if the last term is positive, and the second term is negative, a and b are negative

if the last term is negative the a and be have /opposite signs/
(because that is the only way to get a negative last number)
Think about the reasoning for the rest of it too

Answer 40

well negative and positive

Answer 41

right

Answer 42

5 or -3

Answer 43

there is one more thing we can infer here too:

the middle number, which is a+b, is negative
that means that we will subtract the larger of the two numbers in our calculation

having said that reconsider your answer a little

Answer 44

(c+5) (c-3)

Answer 45

close, read what I wrote
what is a+b in your case ?

Answer 46

(c+5) (c+3)

Answer 47

...what is a+b ?

Answer 48

5 and 3

Answer 49

a+b is supposed to be the middle number you had originally
what is a+b for you? what should it be ?
(you were closer when we established that a and b should have opposite signs)

Answer 50

5 and -3

Answer 51

...add them, what do you get?

Answer 52

2

Answer 53

and what's it supposed to be?

Answer 54

what do you mean both middle numbers hsould be - and + ?

Answer 55

We are factoring\[x^2+Px+Q=(x+a)(x+b)\]if you foil out the parentheses you get\[(x+a)(x+b)=x^2+(a+b)x+ab=x^2+Px+Q\]looking at each side we can see that \[(a+b)=P\]and\[ab=Q\]in this case Q (the constant) is negative, so a and be must have different signs

You found the right numbers, but they still do not add to make P, which in your case is -2.

How can you fix that?

Answer 56

should*

Answer 57

a and b must have different signs*

Answer 58

5-3=2
and we want -2...

Answer 59

(c-5) (c+2)

Answer 60

-5+2=-3
and we want -2...
(-5)*2=-10
and we want -15...

Answer 61

the numbers must be 5 and 3, those are the only factors of 15

Answer 62

(c-5) (c+3)

Answer 63

that was an error

Answer 64

there we go :D

Answer 65

this stuff is a little tricky the first time you learn it, but it get's easy with practice

Answer 66

finallly btw turning test meet my friend calc

Answer 67

hi calc

Answer 68

I know him from real life ;D

Answer 69

There's a real life o-0

Answer 70

?

Answer 71

lol ?

Answer 72

I meant
'there's a real life ?'

Answer 73

For c^2 -2c -15, you have to find factors that add up to -2 and multiply to -15. Two factors that work are -5 and 3. Now, simply break up the c^2 since there is no coefficient and form (c - 5)(c + 3)

Answer 74

i know

Answer 75

nice job andrew well explain

Answer 76

wanna help with more

Answer 77

Sure

Answer 78

my next question is factoring binomial

Answer 79

the question is 144=-c^2 my answer is (c-12) (c-12)

Answer 80

Uh, unfortunately no.

Answer 81

This is a simple equation and not a polynomial

Answer 82

i got it (-c+12) (c+12)

Answer 83

So, since c^2 = 144, you need to use the opposite of PEMDAS.

Answer 84

Basically, you should get 2 numbers, not 2 binomials.