Discussion

Explanation:

Step 1: 
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Step 2:

Step 3:
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The remainder is 25.

Alternately,
If we need to find the remainder when f(x) is divided by (ax + b) 

We first equate ax + b with 0, i.e., ax + b = 0 hence, x = -b/a

Now, remainder of f(x) when divided by (ax + b) = f(-b/a).

Here, f(x) = 𝑥³ + 3𝑥² − 2𝑥 + 9, its remainder when divided by x - 2.

x - 2 = 0, hence, x = 2

∴ The remainder here is f(2) = 2³ + 3(2)² − 2(2) + 9 = 8 + 12 - 4 + 9 = 25

Hence, option (a).

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