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Usimov [2.4K]
3 years ago
9

Use synthetic division and remainder theorem p(x) = 3x^3 - 5x^2 - x + 2. p(-1/3)=

Mathematics
1 answer:
Alik [6]3 years ago
7 0

Answer:

5/3

Step-by-step explanation:

-1/3 goes on the outside and since we have our polynomial in standard form with no in between terms missing, 3,-5,-1,2 go inside because they are the coefficients of our polynomial.

-1/3   |   3      -5          -1          2

       |

         -------------------------------------

First step bring the 3 down inside. (3+0=3)

-1/3   |   3      -5          -1          2

       |

         -------------------------------------

           3

Whatever goes below the bar, must be multiplied by outside number and put directly below next number inside.

-1/3   |   3      -5          -1          2

       |             -1

         -------------------------------------

           3

The numbers lined up vertically are added to get the numbers underneath the bar.

-1/3   |   3      -5          -1          2

       |             -1

         -------------------------------------

           3        -6

Again any number below the bar gets multiply to the number outside.

-1/3   |   3      -5          -1          2

       |             -1          2

         -------------------------------------

           3        -6

Again the numbers lined up vertically above the bar get added to get the number that goes underneath the bar there.

-1/3   |   3      -5          -1          2

       |             -1          2

         -------------------------------------

           3        -6          1

Multiply to outside number 1(-1/3)=-1/3.

This goes under the 2 inside.

-1/3   |   3      -5          -1          2

       |             -1          2          -1/3

         -------------------------------------

           3        -6          1

The last number we are fixing to be put is the remainder of (3x^3-5x^2-x+2)/(x+1/3) or you could say it is the value of p(-1/3) since:

P(x)/(x-c)=Q(x)+R/(x-c)

Multiply both sides by (x-c):

P(x)=Q(x)(x-c)+R

If you evaluate P at x=c, we get R:

P(c)=Q(c)(c-c)+R

P(c)=Q(c)*0+R

P(c)=R.

Let's finish:

-1/3   |   3      -5          -1          2

       |             -1          2          -1/3

         -------------------------------------

           3        -6          1         5/3

This means p(-1/3)=5/3.

We could have also got this by directly plugging in (-1/3) for x into 3x^3-5x^2-x+2.

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Let us revise some transformation

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∵ The quadrilateral PUMA has coordinates at:

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Learn more:

You can learn more about transformation in brainly.com/question/5563823

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