Q. 471 - Intermediate Algebra

Question

In the following exercise, divide each polynomial by the monomial
$(54y^4-24y^3)÷(-6y^2)$

Step-by-Step Solution

Answer

The solution is $4y-9y^2$.

Step 1. Given information.

The given expression is $(54y^4-24y^3)÷(-6y^2)$

Step 2. Separating each terms.

$(54y^4-24y^3)÷(-6y^2)=\frac{54y^4}{(-6y^2)}-\frac{24y^3}{(-6y^2)}$

Step 3. Simplify the expression.

Using quotient property, $\frac{a^m}{a^n}=a^{m-n}$

$$\begin{gathered} \frac{54y^4}{(-6y^2)}-\frac{24y^3}{(-6y^2)}=\frac{54}{-6}{y}^{(4-2)}-\frac{24}{-6}{y}^{(3-2)} \\ \Rightarrow -9y^2+4y \end{gathered}$$

Step 4. Simplified answer.

Hence, the simplified expression is $4y-9y^2$.