Question

Consider the expressions 3x(x − 2) + 2 and 2x2 + 3x − 18.

Part 1
Evaluate each expression for x = 4 and for x = 5. Based on your results, do you know whether the two expressions are equivalent? Complete the explanation.

For x = 4, each expression has a value of
26
. For x = 5, each expression has a value of
47
. These results suggest that the expressions
may be
equivalent, but
do not prove that
the expressions are equivalent.

Part 2 out of 2
Evaluate each expression for x = 3. Based on your results, do you know whether the two expressions are equivalent? Complete the explanation.

For x = 3, the first expression has a value of
, and the second expression has a value of
. Since these values are
(select)
, the expressions
(select)
equivalent.

Answer 1

Part 1:
For x = 4, the first expression evaluates to:
3(4)(4-2) + 2 = 26
For x = 5, the first expression evaluates to:
3(5)(5-2) + 2 = 47
For x = 4, the second expression evaluates to:
2(4)^2 + 3(4) - 18 = 18
For x = 5, the second expression evaluates to:
2(5)^2 + 3(5) - 18 = 37
Based on these results, we cannot definitively determine whether the two expressions are equivalent, although they may be.

Part 2:
For x = 3, the first expression evaluates to:
3(3)(3-2) + 2 = 11
For x = 3, the second expression evaluates to:
2(3)^2 + 3(3) - 18 = 9
Since these values are not equal, we can conclude that the expressions are not equivalent.