Question

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

Part 1 out of 2
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
. These results suggest that the expressions
(select)
equivalent, but
(select)
the expressions are equivalent.

Answer 1

See answer below

Explanation:

For the first expression

3 x (x - 2) + 2 = 3 x^2 - 6 x + 2

evaluated at x= 4 we get: 26

and for x = 5 we get 47.

For the second expression

2 x^2 + 3 x - 18

we get the exact same values when doing the evaluation at these two points.

Based on those results, one may think the expressions may be equivalent, but they are not equivalent. Because at any other x-value, their results are different. See for example that for x = 0 the first one gives "2" while the second one gives -18.