Questions: Which expression has the greatest value when (x=3) ? (2 x^3) (2 x^3+5) ((2 x)^3) ((x-1)^3)

Transcript text: Which expression has the greatest value when $x=3$ ? $2 x^{3}$ $2 x^{3}+5$ $(2 x)^{3}$ $(x-1)^{3}$

Solution

Step 1: Substitute $ x = 3 $ into each expression

We need to evaluate each expression by substituting $ x = 3 $.

Step 2: Evaluate $ 2x^2 $

\[ 2x^2 = 2(3)^2 = 2 \times 9 = 18 \]

Step 3: Evaluate $ 2x^2 + 5 $

\[ 2x^2 + 5 = 2(3)^2 + 5 = 2 \times 9 + 5 = 18 + 5 = 23 \]

Step 4: Evaluate $ (2x)^3 $

\[ (2x)^3 = (2 \times 3)^3 = 6^3 = 216 \]

Step 5: Evaluate $ (x - 1)^3 $

\[ (x - 1)^3 = (3 - 1)^3 = 2^3 = 8 \]

The expression $ (2x)^3 $ has the greatest value when $ x = 3 $, which is 216.

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