SOLUTION: Need help with trinomials! Any guidance on this set would be GREATLY appreciated!! 3. a) Factor completely. v^3-5v^2-36v b)Solve and simplify: r^2+3r-18=0 c)Solve

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Need help with trinomials! Any guidance on this set would be GREATLY appreciated!! 3. a) Factor completely. v^3-5v^2-36v b)Solve and simplify: r^2+3r-18=0 c)Solve      Log On


   

Question 303320: Need help with trinomials! Any guidance on this set would be GREATLY appreciated!!
3. a) Factor completely.
v^3-5v^2-36v
b)Solve and simplify:
r^2+3r-18=0

c)Solve for the solution set.
(x+9)(x-13)(x+6)>0
d)Factor completely:
c^2+4c+4
e)Factor completely in factored form:
3x^7-15x^6+24x^5
f)Multiply
(-3n)^2 * (4n^9)^2
Thank you so much for your help!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first two to get you started. Please only post one problem at a time.


a)

v%5E3-5v%5E2-36v Start with the given expression.


v%28v%5E2-5v-36%29 Factor out the GCF v.


Now let's try to factor the inner expression v%5E2-5v-36


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Looking at the expression v%5E2-5v-36, we can see that the first coefficient is 1, the second coefficient is -5, and the last term is -36.


Now multiply the first coefficient 1 by the last term -36 to get %281%29%28-36%29=-36.


Now the question is: what two whole numbers multiply to -36 (the previous product) and add to the second coefficient -5?


To find these two numbers, we need to list all of the factors of -36 (the previous product).


Factors of -36:
1,2,3,4,6,9,12,18,36
-1,-2,-3,-4,-6,-9,-12,-18,-36


Note: list the negative of each factor. This will allow us to find all possible combinations.


These factors pair up and multiply to -36.
1*(-36) = -36
2*(-18) = -36
3*(-12) = -36
4*(-9) = -36
6*(-6) = -36
(-1)*(36) = -36
(-2)*(18) = -36
(-3)*(12) = -36
(-4)*(9) = -36
(-6)*(6) = -36

Now let's add up each pair of factors to see if one pair adds to the middle coefficient -5:


First NumberSecond NumberSum
1-361+(-36)=-35
2-182+(-18)=-16
3-123+(-12)=-9
4-94+(-9)=-5
6-66+(-6)=0
-136-1+36=35
-218-2+18=16
-312-3+12=9
-49-4+9=5
-66-6+6=0



From the table, we can see that the two numbers 4 and -9 add to -5 (the middle coefficient).


So the two numbers 4 and -9 both multiply to -36 and add to -5


Now replace the middle term -5v with 4v-9v. Remember, 4 and -9 add to -5. So this shows us that 4v-9v=-5v.


v%5E2%2Bhighlight%284v-9v%29-36 Replace the second term -5v with 4v-9v.


%28v%5E2%2B4v%29%2B%28-9v-36%29 Group the terms into two pairs.


v%28v%2B4%29%2B%28-9v-36%29 Factor out the GCF v from the first group.


v%28v%2B4%29-9%28v%2B4%29 Factor out 9 from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.


%28v-9%29%28v%2B4%29 Combine like terms. Or factor out the common term v%2B4


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So v%28v%5E2-5v-36%29 then factors further to v%28v-9%29%28v%2B4%29


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Answer:


So v%5E3-5v%5E2-36v completely factors to v%28v-9%29%28v%2B4%29.


In other words, v%5E3-5v%5E2-36v=v%28v-9%29%28v%2B4%29.


Note: you can check the answer by expanding v%28v-9%29%28v%2B4%29 to get v%5E3-5v%5E2-36v or by graphing the original expression and the answer (the two graphs should be identical).


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b)

r%5E2%2B3r-18=0 Start with the given equation

%28r%2B6%29%28r-3%29=0 Factor the left side



Now set each factor equal to zero:
r%2B6=0 or r-3=0

r=-6 or r=3 Now solve for r in each case


So the solutions are r=-6 or r=3