Evaluate: (24x^6 -12 x^3) \text{ divided by } 4x^3.

Question:

Evaluate: {eq}(24x^6 -12 x^3) \text{ divided by } 4x^3. {/eq}

Division of Polynomial by a Monomial:

To divide a polynomial by a monomial, we divide each and every term of the polynomial by the monomial. While doing this, we divide the numbers by numbers and the variables by variables. To divide the variables of the same bases, we use the following property:

$$\dfrac{a^m}{a^n}=a^{m-n} $$

Answer and Explanation:

We will evaluate the given division:

$$\begin{align} \dfrac{24x^6 -12 x^3}{4x^3} &= \dfrac{24x^6 }{4x^3}- \dfrac{12 x^3}{4x^3} \\[0.4cm] &= \dfrac{24}{4} \cdot \dfrac{x^6}{x^3} - \dfrac{12}{4} \cdot \dfrac{x^3}{x^3} \\[0.4cm] &= 6 x^{6-3} - 3 x^{3-3} & [ \because \dfrac{a^m}{a^n}=a^{m-n} ]\\[0.4cm] &= 6x^3 - 3x^0 \\[0.4cm] &= \boxed{\mathbf{6x^3 -3 }}& [ \because x^0=1] \end{align} $$


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What Are Monomials & Polynomials?

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