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

• asadullahgiki:

  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

• AkshayG:

  The remainder of [tex]P\left( x \right) = 2{x^3} - 3x + 5[/tex] divided by [tex]\left( {x - 5}\right)[/tex] 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 [tex]P\left( x \right) = 2{x^3} - 3x + 5[/tex] and [tex]\left( {x - 5} \right).[/tex]

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

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

  Now obtain the value of [tex]x[/tex] from the denominator.

  [tex]\begin{aligned}x - 5 &= 0\\x&= 5\\\end{aligned}[/tex]

  Divide the coefficients of the polynomial by [tex]5.[/tex]

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

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

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

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  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.