Question

review (1–2 minutes) evaluate each expression for x = 2 and x = -3. 1 ( x^4 ) 2 ( -x^2 + 1 ) 3 ( (-x)^2 - 1 ) 4 ( x^8 ) © carnegie learning, inc.

Explanation:

Problem 1: \( x^4 \)

Step 1: Evaluate for \( x = 2 \)

Substitute \( x = 2 \) into \( x^4 \).
\( 2^4 = 2 \times 2 \times 2 \times 2 = 16 \)

Step 2: Evaluate for \( x = -3 \)

Substitute \( x = -3 \) into \( x^4 \).
\( (-3)^4 = (-3) \times (-3) \times (-3) \times (-3) = 81 \)

Step 1: Evaluate for \( x = 2 \)

Substitute \( x = 2 \) into \( -x^2 + 1 \). First, calculate \( x^2 \): \( 2^2 = 4 \). Then, \( -4 + 1 = -3 \)

Step 2: Evaluate for \( x = -3 \)

Substitute \( x = -3 \) into \( -x^2 + 1 \). First, calculate \( x^2 \): \( (-3)^2 = 9 \). Then, \( -9 + 1 = -8 \)

Step 1: Evaluate for \( x = 2 \)

Substitute \( x = 2 \) into \( (-x)^2 - 1 \). First, calculate \( (-2)^2 = 4 \). Then, \( 4 - 1 = 3 \)

Step 2: Evaluate for \( x = -3 \)

Substitute \( x = -3 \) into \( (-x)^2 - 1 \). First, calculate \( (-(-3))^2 = 3^2 = 9 \). Then, \( 9 - 1 = 8 \)

Answer:

For \( x = 2 \): \( 16 \)
For \( x = -3 \): \( 81 \)

Problem 2: \( -x^2 + 1 \)