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n200080 [17]
3 years ago
9

If p(x) = 2x^3 - 3x + 5, what is the remainder of p(x) divided by (x - 5)

Mathematics
2 answers:
S_A_V [24]3 years ago
8 0

The remainder of P\left( x \right) = 2{x^3} - 3x + 5 divided by \left( {x - 5}\right) is

Explanation:

If division of a polynomial by a binomial result in a remainder of zero means that the binomial is a factor of polynomial.

The polynomial is P\left( x \right) = 2{x^3} - 3x + 5 and \left( {x - 5} \right).

The numerator of the division is P\left( x \right) = 2{x^3} - 3x + 5 and the denominator is

Solve the given polynomial P\left( x \right) = 2{x^3} - 3x + 5 by the use of synthetic division.

Now obtain the value of x from the denominator.

\begin{aligned}x - 5 &= 0\\x&= 5\\\end{aligned}

Divide the coefficients of the polynomial by 5.

\begin{aligned}5\left| \!{\nderline {\,{2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0\,\,\,\,\,\,\,\,\,\,\,\,\, - 3\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,5} \,}} \right.  \hfill\\\,\,\,\,\underline{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,10\,\,\,\,\,\,\,\,\,\,\,\,\,50\,\,\,\,\,\,\,\,\,\,\,\,\,\,235}\hfill\\\,\,\,\,\,2\,\,\,\,\,\,\,\,\,\,\,\,\,10\,\,\,\,\,\,\,\,\,\,\,\,\,47\,\,\,\,\,\,\,\,\,\,\,\,\,\,240\hfill\\\end{aligned}

The last entry of the synthetic division tells us about remainder and the last entry of the synthetic division is 240.Therefore, the remainder of the synthetic division is 240.

The remainder of p\left( x \right) = 2{x^3} - 3x + 5 divided by \left( {x - 5}\right) is \boxed{240}.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Synthetic Division

Keywords: division, binomial synthetic division, long division method, coefficients, quotients, remainders, numerator, denominator, polynomial, zeros, degree.

Alenkinab [10]3 years ago
4 0

The question is

if p(x)= 2x³-3x+5, what is the remainder of p(x) divided by (x-5)

We use the synthetic division to find the remainder,

x-5=0

x=5

Now, write the coefficients of polynomial.


5 | 2  0  -3    5

   | ↓ 10  50  235

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

     2 10  47  | 240→ is the remainder.

Quotient= 2x²+10x+47


Remainder= 240

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⎡

⎢

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The easiest way to obtain a 1 in row 2 of column 1 is to interchange \displaystyle {R}_{2}R

​2

​​  and \displaystyle {R}_{3}R

​3

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Interchange

R

2

and

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3

→

⎡

⎢

⎣

1

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1

1

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0

1

−

12

−

15

0

5

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0

57

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57

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1

57

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3

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3

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⎢

⎣

1

−

1

1

0

1

−

12

0

0

1

|

8

−

15

1

⎤

⎥

⎦

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−

y

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z

=

8

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−

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⎡

⎢

⎣

1

−

1

1

2

3

−

1

3

−

2

−

9

|

8

−

2

9

⎤

⎥

⎦

Next, we perform row operations to obtain row-echelon form.

−

2

R

1

+

R

2

=

R

2

→

⎡

⎢

⎣

1

−

1

1

0

5

−

3

3

−

2

−

9

|

8

−

18

9

⎤

⎥

⎦

−

3

R

1

+

R

3

=

R

3

→

⎡

⎢

⎣

1

−

1

1

0

5

−

3

0

1

−

12

|

8

−

18

−

15

⎤

⎥

⎦

The easiest way to obtain a 1 in row 2 of column 1 is to interchange \displaystyle {R}_{2}R

​2

​​  and \displaystyle {R}_{3}R

​3

​​ .

Interchange

R

2

and

R

3

→

⎡

⎢

⎣

1

−

1

1

8

0

1

−

12

−

15

0

5

−

3

−

18

⎤

⎥

⎦

Then

−

5

R

2

+

R

3

=

R

3

→

⎡

⎢

⎣

1

−

1

1

0

1

−

12

0

0

57

|

8

−

15

57

⎤

⎥

⎦

−

1

57

R

3

=

R

3

→

⎡

⎢

⎣

1

−

1

1

0

1

−

12

0

0

1

|

8

−

15

1

⎤

⎥

⎦

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x

−

y

+

z

=

8

y

−

12

z

=

−

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