Question

Factor each trinomial below. Please show your work and check your answer. (1 point each)

x2 – 8x + 15
a2 – a – 20
a2 – 5a – 20
a2 + 12ab + 27b2
2a2 + 30a + 100

Answer 1

Please help

Answer 2

For the first one: x^2 - 8 x + 15
x^2 - 5x - 3x + 15
x(x-5) -3(x-5)
(x-5)(x-3)
The check:
x(x-3)-5(x-3)
x^2-3x-5x+15
x^2-8x+15

Answer 3

Yeah thats what I got I wasn't sure I actually got (x-3)(x-5) but its the same thing right?

Answer 4

yep same thing

Answer 5

Ok thanks

Answer 6

what did you get for the others and I'll tell you if they are correct

Answer 7

or you haven't done them yet?

Answer 8

for the second one I got (a+8)(a-5)

Answer 9

no that's incorrect

Answer 10

the second one should be (a-5)(a+4)

Answer 11

Im working on them as we speak Im slow in math thats why its taking me a while to reply :/ math is my weakest subject

Answer 12

Can you show me how I got that because Idk how I screwed up

Answer 13

don't worry... speed isn't the key. as long as you do them properly and understand your steps

Answer 14

the way to think about it is:
first make sure there's a 1in front of your first exponent, for instance in the 2nd question: a2 – a – 20, the first exponent is a^2 which is also 1*a^2.
There is a 1 in front of it

Answer 15

And the 3rd one it came out to -4(a-5)

Answer 16

ok I can understand that because the "a" is really just 1^2 right?

Answer 17

the second step is multiply the first with the 3rd, i.e. a^2 and 20 = 20a^2
now, you're looking for two numbers which add to give you the second (-a), and multiply to give you 20a^2

Answer 18

no, a is a. when there's no number in front of it, it's the same as 1 x a^2

Answer 19

oh ok

Answer 20

yeah you want to begin by removing the number in front of your a^2.
So if you had a 5a^2, you would divide all of the numbers by 5 so that you're left with a^2

Answer 21

In this case, there's no number in front of a^2 so you're good

Answer 22

anyhow, the two numbers that multiply to give you -20x, and add to give you -a are -5x and +4x

Answer 23

so it would be (a-5)(a+4) because 5*4 = 20 and the 20 a's = a^2 so 20a^2?

Answer 24

wouldn't it be (a+5)(a+4) because its a positive 20?

Answer 25

because (-5x)*(+4x) = -20x (because - * + = -, and 5*4 = 20)

Answer 26

oh ok that makes a lot more sense thanks!

Answer 27

the question has a -20. sorry i said x instead of a :)

Answer 28

yeah. so that's how you get (a-5)(a+4)

Answer 29

so the work would come out to
a^2-a-20
a^2*20 = 20a^2
(a-5)(a+4)
?

Answer 30

no

Answer 31

you'd write it as
a^2 -a -20
a^2 -5a+4a-20
a(a-5)+4(a-5)
(a-5)(a+4)

Answer 32

essentially, you break the center into the two values that you found

Answer 33

ok thanks Im skipping the 3rd one and working on the 4th one right now because I just completely got lost in the 3rd one

Answer 34

the 4th question is the same idea: a2 + 12ab + 27b2
you want to find the two values that will add to give you 12ab and multiply to give you 27a^2b^2

Answer 35

27 being an odd number how would do this because 27 won't equal out to any 2 numbers

Answer 36

sorry i had to log out for a second

Answer 37

two values that add to give +12ab and multiply to give +27a^2b^2 is +9ab and +3ab

Answer 38

a2 + 12ab + 27b2
a2 + 9ab + 3ab + 27b2
a(a+9b) + 3b(a+9b)
(a+9b)(a+3b)

Answer 39

are you still there?

Answer 40

And the fifth one is: 2a2 + 30a + 100
2(a^2 + 15a + 50)
the values that add to give 15a, and multiply to 50a^2 are 10a and 5a
2(a^2 + 5a + 10a + 50)
2[a(a+5) +10(a+5)]
2(a+5)(a+10)

Answer 41

Thank you very much i was working trying to work on the second part of the paper right now thats why I didn't answer but thanks so much you have made my life a lot easier.

the second part is a lot harder from the first thats why I skipped ahead and went onto it

It’s your turn to be a game show host! As you know, in the game of Math Time, the contestants are given an answer and they must come up with the question that corresponds to the given answer.

Your task for this portion of the assignment is to create two different “answers” (and the questions that accompany them) that the host could use for the final round of Math Time. The questions and answers you create must be unique. Check out the example and hint below, if needed. - second part

the example it gives me is
i.e. Question for Host: x2 + 6x + 5 is the product of these two binomials.
Expected Question from Contestant: What is (x + 5)(x + 1)?

Answer 42

okay

Answer 43

looks fun enough... it's exactly the same thing as the first set. they give you a binomial and you have to factor it to get the question

Answer 44

So would x^2 + 11x + 10
what is (x+10)(x+1)

be a correct answer?

Answer 45

yes

Answer 46

Thank you!