Example Question - polynomial simplification
Here are examples of questions we've helped users solve.
Calculating a Limit as x Approaches a Value
<p>\[ \lim_{{x \to 8}} \frac{{3x^2 - 24x}}{{x^2 - 64}} \]</p> <p>Primero, factorizamos el numerador y el denominador.</p> <p>\[ = \lim_{{x \to 8}} \frac{{3x(x - 8)}}{{(x + 8)(x - 8)}} \]</p> <p>Luego cancelamos los términos comunes \(x - 8\).</p> <p>\[ = \lim_{{x \to 8}} \frac{{3x}}{{x + 8}} \]</p> <p>Finalmente, sustituimos \(x = 8\) en la expresión simplificada.</p> <p>\[ = \frac{{3 \cdot 8}}{{8 + 8}} = \frac{{24}}{{16}} = \frac{{3}}{{2}} \]</p> <p>Por lo tanto, el límite es \(\frac{3}{2}\).</p>
Solving Polynomial Subtraction
To solve the question provided in the image, you need to subtract function g(x) from function f(x) and then simplify the result. I'll provide you with the steps for doing so. Given functions: f(x) = 2x + 4 g(x) = -5x + 5 (f - g)(x) means we need to subtract g(x) from f(x): (f - g)(x) = f(x) - g(x) (f - g)(x) = (2x + 4) - (-5x + 5) Now, distribute the negative sign inside the brackets: (f - g)(x) = 2x + 4 + 5x - 5 Combine like terms: (f - g)(x) = 2x + 5x + 4 - 5 (f - g)(x) = 7x - 1 The answer is the polynomial 7x - 1 in its simplest form.
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