Question

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.

Answer 1

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.