Here are my attempts. Let me know if they are correct please> :) Thanks
Question (Find quotient): 9a^2-25b^2/3a-5b
My answer: 3a+5b
Find Quotient: y^4+3y-5/y^2+7
My answer:
y^4+3y-15/y^2+7
y^2+3y+8
Find Quotient:
This one i am confused on the ^the power signs..
6x^3-9x^2+5x+2/2x+3
The first one is correct since it factored nicely
I have no idea how you got the second answer.
It does not factor so you will have to do a long algebraic division.
I got
(y^4+3y-5)/(y^2+7)
= y^2 - 7 + (3y+45)/(y^2+7)
same thing for the last one, you need to do a long division ...
I got
3x^2 - 9x + 16 - 46/(2x+3)
Thank you very much. The first one is nice how it factors together. I get so lost with ones I cant factor nicely. :) Thanks you!
Your attempts are close, but there are a few mistakes. Let's go through each question step by step to correct them:
1. Find the quotient: (9a^2-25b^2)/(3a-5b)
To simplify this expression, we can factor the numerator and denominator:
9a^2 - 25b^2 = (3a + 5b)(3a - 5b)
Now we can cancel out the common factor of (3a - 5b) in the numerator and denominator:
(3a + 5b)/(3a - 5b)
Therefore, the correct answer is (3a + 5b)/(3a - 5b).
2. Find the quotient: (y^4 + 3y - 5)/(y^2 + 7)
To simplify this expression, we divide each term of the numerator by the denominator using long division:
___________________________
y^2 + 7 | y^4 + 0y^3 + 0y^2 + 3y - 5
- (y^4 + 7y^2)
------------------------------
-7y^2 + 3y - 5
- (-7y^2 - 49)
------------------------------
3y + 44
So the quotient is (y^2 - 7) with a remainder of (3y + 44).
Therefore, the correct answer is (y^2 - 7) + (3y + 44)/(y^2 + 7).
3. Find the quotient: (6x^3 - 9x^2 + 5x + 2)/(2x + 3)
Again, we can use long division to simplify this expression:
__________________
2x + 3 | 6x^3 - 9x^2 + 5x + 2
- (6x^3 + 9x^2)
--------------------------
-18x^2 + 5x + 2
- (-18x^2 - 27x)
------------------------
32x + 2
So the quotient is (3x - 6) with a remainder of (32x + 2).
Therefore, the correct answer is (3x - 6) + (32x + 2)/(2x + 3).
Let's go through each question and see if your attempts are correct:
Question: Find quotient of (9a^2 - 25b^2) / (3a - 5b)
Your answer: 3a + 5b
Your answer is incorrect. To find the quotient, we need to factor the numerator and denominator to see if any terms can be canceled out. Let's factor:
9a^2 - 25b^2 = (3a - 5b)(3a + 5b)
3a - 5b does not have any common factors with 3a + 5b, so the cancelation cannot occur. Therefore, the quotient remains as (9a^2 - 25b^2) / (3a - 5b).
So, your first attempt was incorrect.
Question: Find quotient of (y^4 + 3y - 5) / (y^2 + 7)
Your attempt: (y^4 + 3y - 15) / (y^2 + 7)
(y^2 + 3y + 8)
Your attempt is incorrect. To find the quotient, we can perform polynomial long division or synthetic division. Let's use polynomial long division:
____________________
y^2 + 7 | y^4 + 3y - 5
- (y^4 + 7y^2)
------------------
-7y^2 + 3y
- (-7y^2 - 49)
--------------
10y - 54
The remainder is 10y - 54. Therefore, the quotient is (y^4 + 3y - 5) / (y^2 + 7) = (y^2 - 7y - 10) + (10y - 54) / (y^2 + 7).
So, your second attempt was also incorrect.
Question: Find quotient of (6x^3 - 9x^2 + 5x + 2) / (2x + 3)
Your attempt: Unknown
As you mentioned being confused about the power signs (^), I'll guide you through the solution for this one.
We can again use polynomial long division:
_________
2x + 3 | 6x^3 - 9x^2 + 5x + 2
- (6x^3 + 9x^2)
------------------
-18x^2 + 5x
- (-18x^2 - 27x)
--------------
32x + 2
The remainder is 32x + 2. Therefore, the quotient is (6x^3 - 9x^2 + 5x + 2) / (2x + 3) = (3x^2 - 6x - 9) + (32x + 2) / (2x + 3).
Remember to include both the quotient and the remainder in the final answer.
I hope this helps clarify the process for finding quotients of polynomials using polynomial long division. Let me know if you have any further questions!