Is (x - c) a Factor?

sologuitar · 2023-10-03 16:37:48

Use synthetic division to determine if x - c is a Factor of the given polynomial.

3x^4 + x^3 - 3x + 1; x + (1/3)

Bob · 2023-10-03 21:16:01

You might find it easier to change the divisor from x + 1/3 to (3x + 1)/3 It is enough to test if 3x + 1 is a factor.

Bob

sologuitar · 2023-10-04 10:33:33

Bob wrote:

You might find it easier to change the divisor from x + 1/3 to (3x + 1)/3 It is enough to test if 3x + 1 is a factor.
Bob

1. I noticed that you are Happy Days fan. I like Henry Winkler. By the way, Henry was a lousy pupil according to him.

2. How did you get from x + (1/3) to (3x + 1)/3?

3. How do I test if (3x + 1) is a factor of the polynomial?

Bob · 2023-10-04 19:59:05

May I remind you about overloading the forum with many posts in one go. You are risking an important post being missed entirely in the muddle.

I'm not a great fan of Happy Days, but I read this quote by him and liked it.

I put both terms over a common denominator. x + 1/3 = 3x/3 + 1/3 = (3x+1)/3

Use the division trick.

Bob

sologuitar · 2023-10-05 05:45:19

Bob wrote:

May I remind you about overloading the forum with many posts in one go. You are risking an important post being missed entirely in the muddle.
I'm not a great fan of Happy Days, but I read this quote by him and liked it.
I put both terms over a common denominator. x + 1/3 = 3x/3 + 1/3 = (3x+1)/3
Use the division trick.
Bob

Thank you, Bob. I will not post more than 3 questions per week moving forward.

amnkb · 2023-10-05 07:35:32

harpazo1965 wrote:

I like Henry Winkler. By the way, Henry was a lousy pupil according to him.

he has dyslexia which i guess nobody knew about when he was a kid

harpazo1965 wrote:

3x^4 + x^3 - 3x + 1; x + (1/3)

synthetic division:

-1/3 | 3  1  0 -3  1
     |   -1  0  0  1
     +--------------
       3  0  0 -3  2

long division:

          3x^3                -3
        +----------------------------
x + 1/3 ) 3x^4 + 1x^3 + 0x^2 - 3x + 1
          3x^4 + 1x^3
         ----------------------------
                              -3x + 1
                              -3x - 1
                             --------
                                    2

sologuitar · 2023-10-06 05:18:49

amnkb wrote:

harpazo1965 wrote:
I like Henry Winkler. By the way, Henry was a lousy pupil according to him.
he has dyslexia which i guess nobody knew about when he was a kid
harpazo1965 wrote:
3x^4 + x^3 - 3x + 1; x + (1/3)
synthetic division:

-1/3 | 3  1  0 -3  1
     |   -1  0  0  1
     +--------------
       3  0  0 -3  2
long division:

          3x^3                -3
        +----------------------------
x + 1/3 ) 3x^4 + 1x^3 + 0x^2 - 3x + 1
          3x^4 + 1x^3
         ----------------------------
                              -3x + 1
                              -3x - 1
                             --------
                                    2

Nicely-done on the long division. Can this be done using synthetic division?

sologuitar · 2023-10-06 06:15:06

amnkb wrote:

harpazo1965 wrote:
I like Henry Winkler. By the way, Henry was a lousy pupil according to him.
he has dyslexia which i guess nobody knew about when he was a kid
harpazo1965 wrote:
3x^4 + x^3 - 3x + 1; x + (1/3)
synthetic division:

-1/3 | 3  1  0 -3  1
     |   -1  0  0  1
     +--------------
       3  0  0 -3  2
long division:

          3x^3                -3
        +----------------------------
x + 1/3 ) 3x^4 + 1x^3 + 0x^2 - 3x + 1
          3x^4 + 1x^3
         ----------------------------
                              -3x + 1
                              -3x - 1
                             --------
                                    2

Synthetic Division

Drop down 3.

Change 1/3 to -1/3.

(-1/3)(3) = -1

(-1/3)(0) = 0

(-1/3)(-3) = 1

1 + 1 = 2

R = remainder = 2

Since the remainder is not 0, x + (1/3) is not a factor of the given polynomial.

Last edited by sologuitar (2023-10-06 06:15:39)

amnkb · 2023-10-07 02:33:01

harpazo1965 wrote:

3x^4 + x^3 - 3x + 1; x + (1/3)

amnkb wrote:

synthetic division:

-1/3 | 3  1  0 -3  1
     |   -1  0  0  1
     +--------------
       3  0  0 -3  2

harpazo1965 wrote:

Nicely-done on the long division. Can this be done using synthetic division?

yes

synthetic division:

-1/3 | 3  1  0 -3  1
     |   -1  0  0  1
     +--------------
       3  0  0 -3  2

sologuitar · 2023-10-07 04:29:59

amnkb wrote:

harpazo1965 wrote:
3x^4 + x^3 - 3x + 1; x + (1/3)
amnkb wrote:
synthetic division:

-1/3 | 3  1  0 -3  1
     |   -1  0  0  1
     +--------------
       3  0  0 -3  2
harpazo1965 wrote:
Nicely-done on the long division. Can this be done using synthetic division?
yes
synthetic division:

-1/3 | 3  1  0 -3  1
     |   -1  0  0  1
     +--------------
       3  0  0 -3  2

Thanks. I did it via synthetic division. I will post one or two problems later.

Math Is Fun Forum

#1 2023-10-03 16:37:48

Is (x - c) a Factor?

#2 2023-10-03 21:16:01

Re: Is (x - c) a Factor?

#3 2023-10-04 10:33:33

Re: Is (x - c) a Factor?

#4 2023-10-04 19:59:05

Re: Is (x - c) a Factor?

#5 2023-10-05 05:45:19

Re: Is (x - c) a Factor?

#6 2023-10-05 07:35:32

Re: Is (x - c) a Factor?

#7 2023-10-06 05:18:49

Re: Is (x - c) a Factor?

#8 2023-10-06 06:15:06

Re: Is (x - c) a Factor?

#9 2023-10-07 02:33:01

Re: Is (x - c) a Factor?

#10 2023-10-07 04:29:59

Re: Is (x - c) a Factor?

Board footer