Question

efectúa la siguiente división : (x² + 14x + 45) entre (x + 5)​

Answer 1

Respuesta:

(x+5)(x+9)\(x+5)=se simplifican x+5 y x+5 y te queda x+9

Explicación paso a paso:

Answer 2

Respuesta:

Explicación paso a paso:

Usando la division sintetica en los polinomios

$\frac{x^2+14x+45}{x+5}$

Sacamos los coeficientes del tercer termino que es 45

Queda  45 = 1, 14 , 45

$\mathrm{Encontrar\:los\:ceros\:del\:\:denominador}:\quad x=-5$

$x+5=0$

$x+5-5=0-5$

$x+5-5=0-5$

x=-5

Se escribe en forma de division normal

$\begin{matrix}\texttt{\space\space-5¦\space\space\space1\space\space14\space\space45}\\ \texttt{\space\space\space\space¦\underline{\space\space\space\space\space\space\space\space\space\space\space\space}}\\ \texttt{\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space}\end{matrix}$

$\begin{matrix}\texttt{\space\space-5¦\space\space\space1\space\space14\space\space45}\\ \texttt{\space\space\space\space¦\underline{\space\space\space\space\space\space\space\space\space\space\space\space}}\\ \texttt{\space\space\space\space\space\space\space\space1\space\space\space\space\space\space\space\space}\end{matrix}$

$\begin{matrix}\texttt{\space\space-5¦\space\space\space1\space\space14\space\space45}\\ \texttt{\space\space\space\space¦\underline{\space\space\space\space\space\space-5\space\space\space\space}}\\ \texttt{\space\space\space\space\space\space\space\space1\space\space\space\space\space\space\space\space}\end{matrix}$

$\begin{matrix}\texttt{\space\space-5¦\space\space\space1\space\space14\space\space45}\\ \texttt{\space\space\space\space¦\underline{\space\space\space\space\space\space-5\space\space\space\space}}\\ \texttt{\space\space\space\space\space\space\space\space1\space\space\space9\space\space\space\space}\end{matrix}$

$\begin{matrix}\texttt{\space\space-5¦\space\space\space1\space\space14\space\space45}\\ \texttt{\space\space\space\space¦\underline{\space\space\space\space\space\space-5\space-45}}\\ \texttt{\space\space\space\space\space\space\space\space1\space\space\space9\space\space\space0}\end{matrix}$

Al final da un binomio con su tercer termino cero 0 (45-45 = 0)

Por tanto el cocientes es la letra x mas el valor del segundo termino o sea el 9

Por tanto

$\frac{x^2+14x+45}{x+5} = \quad x+9$