\( \left(y^{2}-y-12\right) \) by \( (y-4) \)

To divide \( y^{2} - y - 12 \) by \( y - 4 \), you can use synthetic division or polynomial long division. Let’s use polynomial long division. 1. The leading term of the dividend \( y^2 \) divided by the leading term of the divisor \( y \) gives \( y \). 2. Multiply \( y \) by \( y - 4 \) to get \( y^2 - 4y \). 3. Subtract \( (y^2 - 4y) \) from \( (y^2 - y - 12) \): \((y^2 - y - 12) - (y^2 - 4y) = 3y - 12\). 4. Now divide \( 3y \) by \( y \) to get \( 3 \). 5. Multiply \( 3 \) by \( y - 4 \) to get \( 3y - 12 \). 6. Subtract \( (3y - 12) \) from \( (3y - 12) \) to find the remainder, which is \( 0 \). So, the result is \( y + 3 \) with no remainder.