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

1. User Answers asadullahgiki
The question is
if p(x)= 2x³3x+5, what is the remainder of p(x) divided by (x5)
We use the synthetic division to find the remainder,
x5=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

2. User Answers 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.