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

Mathematics

## Question

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

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

• ### 2. User Answers AkshayG

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 $$\boxed{240}.$$