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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?

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.

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)

Jai Ganesh

Administrator

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.

Bob

Administrator

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

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)

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,436

Website

Re: Factoring Polynomials

6. a^4 + 1

This can't be factored, because sum of squares cannot be factored using real numbers.