Question

Divide. Divide \(7 p^{3}+18 p^{2}\) by \(p^{2}\).

Short answer

The quotient of \(7 p^{3}+18 p^{2}\) divided by \(p^{2}\) is \(7 p + 18\).

Step-by-step solution

Divide the first term of the polynomial by the monomial

To begin, let's divide \(7 p^{3}\) by \(p^{2}\). According to the law of exponent, when dividing terms with the same base (in this case \(p\)), we subtract the exponent in the denominator from the exponent in the numerator. Hence, \(7 p^{3}\) divided by \(p^{2}\) simplifies to \(7 p\).

Divide the second term of the polynomial by the monomial

Next, let's divide \(18 p^{2}\) by \(p^{2}\). When the exponents are equal in the division, the resulting exponent will be zero and \(p^0=1\). Hence, \(18 p^{2}\) divided by \(p^{2}\) simplifies to \(18\).

Write the final answer

The result of dividing the polynomial \(7 p^{3}+18 p^{2}\) by the monomial \(p^{2}\) is therefore the sum of the results obtained in step 1 and step 2, i.e. \(7 p + 18\).