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#1 2021-11-01 10:21:29
- jadewest
- Member
- Registered: 2021-02-20
- Posts: 44
Factoring Polynomials
Hi,
I need help solving this problem.
10. Suppose a football is kicked from the ground and its height, h, in feet above the ground is given by h = -3.9t2 + 15.6t.
The time, t, represents the number of seconds after the ball is kicked. At what time does the football hit the ground?
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#2 2021-11-01 13:12:51
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 48,403
Re: Factoring Polynomials
Hi jadewest,
Hitting the ground would mean the height above the ground is 0. Set h to zero. Then solve for t.
There's two solutions to h = 0, the first is trivial t= 0 and that's before you kick.
You have an equation that looks like:
Add
to both sides.Now divide t from both sides:
t = 4 seconds.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#3 2021-11-02 05:10:40
- jadewest
- Member
- Registered: 2021-02-20
- Posts: 44
Re: Factoring Polynomials
Hi,
Thank you for your help! I have solved the other exercises, I just need to see if they are correct.
A. Factor the following polynomials completely.
1. 125x3 + 64
(5x)3 + 43
125x3 + 64 = (5x + 4) ( (5x)2 - (5x) (4) + 42 )
(5x + 4) ( 25x2 - 20x + 16 )
2. x9 + 1
(x3)3 + 13
x9 + 1 = (x + 1) (x2 - (x) (1) + 12)
(x + 1) (x2 - x + 1)
3. 2m4 - 2mn3
2m3
2m3 (m) - 2m3 (n)
2m3 (m - n)
4. 3a4 + 81a
3a
3a (a3) + 3a (27)
3a (a3 + 27)
B. Can these be factored using the methods (GCF, squares, cubes) discussed in this lesson? Yes or No? Explain why or why not in a complete sentence.
5. 7x5 - 64y
This can't be factored, because 7 and 64 don't share a GCF.
6. a4 + 1
This can't be factored, because sum of squares cannot be factored using real numbers.
7. a4 – 64
This can be factored with the difference of squares which leads to the answer: (a2 + 8) (a2 - 8)
C. Factor completely using Grouping
8. xy – 5y – 2x + 10
y (x - 5) - 2 (x - 5)
(x - 5) (y - 2)
9. x3 + x2 - x – 1
x2 (x +1) - 1 (x + 1)
(x + 1) (x2 - 1)
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#4 2021-11-02 16:39:45
- Jai Ganesh
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- Registered: 2005-06-28
- Posts: 48,403
Re: Factoring Polynomials
Hi jadewest,
1.
.2.
3.
.4.
Remaining, you may do the rest.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#5 2021-11-02 22:20:40
- Bob
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- Registered: 2010-06-20
- Posts: 10,621
Re: Factoring Polynomials
hi jadewest,
It is sometimes unclear when you want a power. Most posters either use Latex (http://www.mathisfunforum.com/viewtopic.php?id=4397 ot put ^ to indicate a power.
So for number 4:
3a4 + 81a becomes 3a^4 + 91a or
using Latex.You are right to factorise the 3a
But can you go further?
27 is a perfect cube so (a+3) should be a factor.
So you're looking at
Q5 and Q6 I agree with your answers.
Q7. As you can write √ 8 as 2 √ 2 this can be factored further using difference of squares again on the second bracket.
Q8 good.
Q9. Again there's more as x^2 -1 will factorise.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob 
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#6 2021-11-03 09:41:02
- jadewest
- Member
- Registered: 2021-02-20
- Posts: 44
Re: Factoring Polynomials
Hi,
I apologize for the confusion! I put ^ to indicate power.
A. Factor the following polynomials completely.
1. 125x^3 + 64
(5x)^3 + 43
125x^3 + 64 = (5x + 4) ( (5x)^2 - (5x) (4) + 42 )
(5x + 4) ( 25x^2 - 20x + 16 )
2. x^9 + 1
(x^3)^3 + 1^3
x^9 + 1 = (x + 1) (x^2 - (x) (1) + 1^2)
(x + 1) (x^2 - x + 1)
3. 2m^4 - 2mn^3
2m^3
2m^3 (m) - 2m^3 (n)
2m^3 (m - n)
4. 3a^4 + 81a
3a
3a (a^3) + 3a (27)
3a (a^3 + 27)
B. Can these be factored using the methods (GCF, squares, cubes) discussed in this lesson? Yes or No? Explain why or why not in a complete sentence.
5. 7x^5 - 64y
This can't be factored, because 7 and 64 don't share a GCF.
6. a^4 + 1
This can't be factored, because sum of squares cannot be factored using real numbers.
7. a^4 – 64
This can be factored with the difference of squares which leads to the answer: (a^2 + 8) (a^2 - 8)
C. Factor completely using Grouping
8. xy – 5y – 2x + 10
y (x - 5) - 2 (x - 5)
(x - 5) (y - 2)
9. x^3 + x^2 - x – 1
x^2 (x +1) - 1 (x + 1)
(x + 1) (x^2 - 1)
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