(a³-64)÷(a-4) dividing polynomials

Mathematics

1 answer:

AnnZ [28]3 years ago

7 0

Answer:

$\textbf{$a^2 + 4a + 16$}\\$

Step-by-step explanation:

$\textup{Given:}\\$$ \frac{a^3 - 64}{a - 4} $$\\\textup{This can be written as:}\\$ (a - 4)(a^2 + 4a + 16) $ \hspace{25mm} $[ (a^3 - b^3) = (a - b)(a^2 + ab + b^2)]$\\$

$\textup{Here $b = 4$}\\\textup{Now, it can be written as}\\$$ \frac{(a - 4)(a^2 + 4a + 16)}{a - 4} $$\\\textup{which renders us}\\$

$a^2 + 4a + 16$

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Therefore the curve start falling and it goes up and down until $x=3$ and from this point it rises without a bound as shown in the figure below