- jchick

solve and show all work for a2 – a – 20 and a2 – 5a – 20

- chestercat

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- myininaya

what are you solving?

- jchick

Factor each trinomial below. Please show your work and check your answer.

- myininaya

ok for the first one we have
a^2-a-20
a^2-1a-20
so first step is to ask yourself what two integers multiply to by -20 and add up to be -1?

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## More answers

- jchick

What do you mean?

- myininaya

\[ax^2+bx+c \\ \text{ when } a=1 \text{ and if the expression is "factorable" } \\ \text{ then you should be able to find } \\ \text{ two integers so that when you multiply them together you get } c \\ \text{ and when you add them together you get } b\]
for example:
\[x^2+5x+6 \\ \text{ the question here first to answer is: } \\ \text{ what two integers multiply to be 6 } \\ \text{ and add up to be 5}\]
well 2(3)=6 and 2+3=5
so the factored form of
\[x^2+5x+6 \text{ is } (x+2)(x+3)\]

- jchick

a2 – a – 20
(a )(a )
-4*5 10*-2
(a+4)(a-5)
a2 -5a+4a-2
-a
a2 – 5a – 20
(a )(a )
10*-2 -5*4
(a-5)(a+4)
a2 + 12ab + 27b2
(a )(a )
9*3
(a+3b)(a+9b)
a2 +9ab+3ab+27b
a2 +12ab+27b

- jchick

Right?

- myininaya

yes to the first one:
a^2-a-20=(a-5)(a+4)
since -5*4=-20 and -5+4=-1
no to the second one:
a^2-5a-20
this does not equal (a-5)(a+4)
-5(4)=-20 but -5+4 isn't -5

- myininaya

and the third one looks good

- jchick

a2 – a – 20 (a )(a ) -4*5 10*-2 (a+4)(a-5)

- myininaya

so you got 2/3 correct

- myininaya

you just need to fix the second one

- jchick

Ok

- jchick

I will try

- myininaya

a^2-5a-20
are there two integers that multiply to be -20 and add up to be -5?

- myininaya

possible pairings that multiply to be -20:
1(-20)
-1(20)
2(-10)
-2(10)
4(-5)
-4(5)

- myininaya

do any of those pairs also add up to -5?

- myininaya

which equation is true if any:
1+(-20)=-5
-1+20=-5
2+(-10)=-5
-2+10=-5
4+(-5)=-5
-4+5=-5

- jchick

None

- myininaya

you are right

- jchick

They are all false

- myininaya

so that means that this is a prime trinomial

- myininaya

means it is not "factorable"

- myininaya

I put factorable in quotation marks because it only really means it isn't factorable over the integers

- jchick

Ok

- jchick

So I am not sure on the second one

- myininaya

it isn't factorable

- myininaya

it is prime

- jchick

Ok thanks

- myininaya

a^2-5a-20 does not factor

- myininaya

unless you can factor over the reals?

- myininaya

which I don't think that is the instructions

- jchick

No but how would I write this just say it is prime?

- myininaya

you can either say not factorable or prime

- myininaya

which ever vocabulary your teacher prefers really
but either saying is fine in general

- jchick

Part 1:
Factor each trinomial below. Please show your work and check your answer.
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
Question 2:
a2 – 5a – 20
Prime and cannot be factored.
Question: 3
a^2 - a - 20
a^2 -5a+4a-20
a(a-5)+4(a-5)
(a-5)(a+4)
Question 4:
a^2 + 12ab + 27b^2
a^2 + 9ab + 3ab + 27b^2
a(a+9b) + 3b(a+9b)
(a+9b)(a+3b)
Question 5:
2a2 + 30a + 100
2(a^2 + 15a + 50)
the values that add to give 15a 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)
Question 6:
Part 2: (5 points)
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.
1 point for creating the two questions and answers.
2 points per question/answer for accuracy.
Example:
Question for Host: x2 + 6x + 5 is the product of these two binomials.
Expected Question from Contestant: What is (x + 5)(x + 1)?
HINT: Create the two binomials first and then use the distribution method to find their simplified product. The simplified product is the answer and the two binomial factors, the expected question.
Hosts question 1: The product of these two binomials is x2+x-20
Answer: What is (x+5)(x-4)
Hosts question 2: The product of these two binomials is x2+7xy+12y
Answer: What is (x+3y)(x+4y)

- jchick

how does this look?

- jchick

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