Consider the expression 3x (x-2) + 2 and 2x^2 + 3x - 12.

A. Evaluate each expression for x = 2 and for x = 7. Based on your results, do you know whether the two expressions are equivalent? Explain.

B. Evaluate each expression for x = 5. Based on your results, do you know whether the two expressions are equivalent? Explain.

Lets begin by doing part a, then part b.

A) 2x^2 + 3x - 12

2 (2^2) + 3 (2) - 12

2 (4) + 6 - 12

8 + 6 - 12

14 - 12 = 2

2

3x (x-2) + 2

3 (2) * (3-2) + 2

6 * 1 + 2

6 + 2 = 8

Nope, these are not equivalent.

Next one, x = 7

2x^2 + 3x - 12

2 (7^2) + 3 (7) - 12

2 (49) + 21 - 12

98 + 21 - 12

119 - 12 = 107

3x (x-2) + 2

3 (7) (7-2) + 2

21 (5) + 2

105 + 2 = 107

Yes! When x = 7, these expressions are equal.

B) 2x^2 + 3x - 12

Apply the value for x.

2 (5^2) + 3 (5) - 12

2 (25) + 15 - 12

50 + 15 - 12

55 - 12 = 43

3x (x-2) + 2

3 (5) * (5-2) + 2

15 * 3 + 2

45 + 2

47

When x = 5, these expressions are not equivalent.