Algebra \( 2 \rightarrow \) L. Divide polynomials using long division YN5 Divide. If the polynomial does not divide evenly, include the remainder as a fraction. \( \left(z^{2}-34\right) \div(z-7) \)

To divide \( z^2 - 34 \) by \( z - 7 \) using long division, start by setting up the division. Place \( z^2 - 34 \) under the division symbol and \( z - 7 \) outside. 1. Divide the first term \( z^2 \) by \( z \) to get \( z \). 2. Multiply \( z \) by \( z - 7 \) to get \( z^2 - 7z \). 3. Subtract \( z^2 - 7z \) from \( z^2 - 34 \): \[ (z^2 - 34) - (z^2 - 7z) = 7z - 34 \] 4. Now, divide \( 7z \) by \( z \) to get \( 7 \). 5. Multiply \( 7 \) by \( z - 7 \): \[ 7(z - 7) = 7z - 49 \] 6. Subtract \( 7z - 49 \) from \( 7z - 34 \): \[ (7z - 34) - (7z - 49) = 15 \] You cannot divide \( 15 \) by \( z - 7 \) anymore, so you conclude the division. Thus, the result is: \[ z + 7 + \frac{15}{z - 7} \]