To find the quotient of the expression (-25x^4 - 5z^3) divided by (-5x^2), we can perform polynomial division. Let’s break it down step by step:
Divide the leading terms:
Divide the coefficient of the highest power of (x) in the numerator by the coefficient of the highest power of (x) in the denominator: (\frac{-25x4}{-5x2} = 5x^{4-2} = 5x^2).
Multiply the divisor by the result from step 1:
Multiply (-5x^2) by the entire denominator (-5x^2): ((-5x^2) \cdot (-5x^2) = 25x^4).
Subtract the result from step 2 from the numerator:
Subtract (25x^4) from the original numerator (-25x^4 - 5z^3): (-25x^4 - 5z^3 - 25x^4 = -5z^3).
Write down the result:
The quotient is (-5z^3).
Therefore, the quotient of (-25x^4 - 5z^3) divided by (-5x^2) is (-5z^3).
