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Find the remainder when 3x³ + 6x - 1 is divided by x - 3.

March 23, 2026Mathematics

ScanSolve AI Answer

Answer

98

4 steps

Identify the polynomial and the divisor.
The polynomial is $P(x) = 3x^3 + 6x - 1$ .
The divisor is $x - 3$ .
Apply the Remainder Theorem.
According to the Remainder Theorem, if a polynomial $P(x)$ is divided by $x - c$ , the remainder is $P(c)$ .
In this case, $c = 3$ . So, we need to find $P(3)$ .
Substitute $x = 3$ into the polynomial.
$P(3) = 3(3)^3 + 6(3) - 1$
Calculate the value.
$P(3) = 3(27) + 18 - 1$ $P(3) = 81 + 18 - 1$ $P(3) = 99 - 1$ $P(3) = 98$
The remainder is 98.

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