Q. Divide. If there is a remainder, include it as a simplified fraction.(4z3+6z2)÷z2
Divide Terms: We have the expression to divide: (4z3+6z2)÷z2First, we will divide each term in the polynomial by the monomial z2.(4z3+6z2)÷z2=z24z3+z26z2
Divide First Term: Now let's divide the first term:(4z3)/(z2)=4z(3−2)=4zWe subtract the exponents because of the division property of exponents.
Divide Second Term: Next, we divide the second term: (6z2)/(z2)=6z2−2=6z0=6Since any non-zero number raised to the power of 0 is 1, z0 is 1.
Combine Results: Combine the results of the division of each term: \(4z^3 + 6z^2) \div z^2 = \frac{4z^3}{z^2} + \frac{6z^2}{z^2} = 4z + 6\
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