Find the remainder when \(5x^{3} + 2x^{2} - 7x - 5\) is divided by (x - 2).
Question 1 Report
Find the remainder when \(5x^{3} + 2x^{2} - 7x - 5\) is divided by (x - 2).
Answer Details
To find the remainder when the polynomial \(5x^3 + 2x^2 - 7x - 5\) is divided by \((x-2)\), we can use the Remainder Theorem which states that the remainder of the polynomial division can be found by evaluating the polynomial at the root of the divisor.
In this case, the root of the divisor \((x-2)\) is \(x=2\). So, we evaluate the polynomial at \(x=2\) as follows:
\begin{align*}
5(2)^3 + 2(2)^2 - 7(2) - 5 &= 40 + 8 - 14 - 5 \\
&= 29
\end{align*}
Therefore, the remainder is \(29\), and the correct option is (c).
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