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DESCARGA

CAPITULO X

Descomposición Factorial

Ejercicio 90

Factorar o descomponer en dos factores:

$a (x + 1) + b (x + 1) = (x + 1) (a + b)$
$x (a + 1) - 3 (a + 1) = (a + 1) (x - 3)$
$2 (x - 1) + y (x - 1) = (x - 1) (2 + y)$
$m (a - b) + (a - b) n = (a - b) (m + n)$
$2 x (n - 1) - 3 y (n - 1) = (n - 1) (2 x - 3 y)$
$\begin{matrix} a (n + 2) + n + 2 & = a (n + 2) + (n + 2) \\ = (n + 2) (a + 1) \end{matrix}$
$\begin{matrix} x (a + 1) - a - 1 & = x (a + 1) - (a + 1) \\ = (a + 1) (x - 1) \end{matrix}$
$\begin{matrix} a^{2} + 1 - b (a^{2} + 1) & = (a^{2} + 1) - b (a^{2} + 1) \\ (a^{2} + 1) (1 - b) \end{matrix}$
$3 x (x - 2) - 2 y (x - 2) = (x - 2) (3 x - 2 y)$
$\begin{matrix} 1 - x + 2 a (1 - x) & = (1 - x) + 2 a (1 - x) \\ = (1 - x) (1 + 2 a) \end{matrix}$
$\begin{matrix} 4 x (m - n) + n - m & = 4 x (m - n) - m + n \\ = 4 x (m - n) - (m - n) \\ = (m - n) (4 x - 1) \end{matrix}$
$\begin{matrix} - m - n + x (m + n) & = - (m + n) + x (m + n) \\ = (m + n) (x - 1) \end{matrix}$
$a^{3} (a - b + 1) - b^{2} (a - b + 1) = (a - b + 1) (a^{3} - b^{2})$
$\begin{matrix} 4 m (a^{2} + x - 1) + 3 n (x - 1 + a^{2}) & = 4 m (x - 1 + a^{2}) + 3 n (x - 1 + a^{2}) \\ = (x - 1 + a^{2}) (4 m + 3 n) \end{matrix}$
$\begin{matrix} x (2 a + b + c) - 2 a - b - c & = x (2 a + b + c) - (2 a + b + c) \\ = (2 a + b + c) (x - 1) \end{matrix}$
$\begin{matrix} (x + y) (n + 1) - 3 (n + 1) & = (n + 1) [(x + y) - 3] \\ = (n + 1) (x + y - 3) \end{matrix}$
$\begin{matrix} (x + 1) (x - 2) + 3 y (x - 2) & = (x - 2) [(x + 1) + 3 y] \\ = (x - 2) (x + 3 y + 1) \end{matrix}$
$\begin{matrix} (a + 3) (a + 1) - 4 (a + 1) & = (a + 1) [(a + 3) - 4] \\ = (a + 1) (a - 1) \end{matrix}$
$\begin{matrix} (x^{2} + 2) (m - n) + 2 (m - n) & = (m - n) [(x^{2} + 2) + 2] \\ = (m - n) (x^{2} + 2 + 2) \\ = (m - n) (x^{2} + 4) \end{matrix}$
$\begin{matrix} a (x - 1) - (a + 2) (x - 1) & = (x - 1) [a - (a + 2)] \\ = (x - 1) (a - a - 2) \\ = - 2 (x - 1) \\ = 2 (1 - x) \end{matrix}$
$\begin{matrix} 5 x (a^{2} + 1) + (x + 1) (a^{2} + 1) & = (a^{2} + 1) [5 x + (x + 1)] \\ = (a^{2} + 1) (6 x + 1) \end{matrix}$
$\begin{matrix} (a + b) (a - b) - (a - b) (a - b) & = (a + b) (a - b) - {(a - b)}^{2} \\ = (a - b) [(a + b) - (a - b)] \\ = (a - b) (a + b - a + b) \\ = 2 b (a - b) \end{matrix}$
$\begin{matrix} (m + n) (a - 2) + (m - n) (a - 2) & = (a - 2) [(m + n) + (m - n)] \\ = (a - 2) (m + n + m - n) \\ = 2 m (a - 2) \end{matrix}$
$\begin{matrix} (x + m) (x + 1) - (x + 1) (x - n) & = (x + 1) [(x + m) - (x - n)] \\ = (x + 1) (x + m - x + n) \\ = (x + 1) (m + n) \end{matrix}$
$\begin{matrix} (x - 3) (x - 4) + (x - 3) (x + 4) & = (x - 3) [(x - 4) + (x + 4)] \\ = (x - 3) (x - 4 + x + 4) \\ = 2 x (x - 3) \end{matrix}$
$\begin{matrix} (a + b - 1) (a^{2} + 1) - a^{2} - 1 & = (a + b - 1) (a^{2} + 1) - (a^{2} + 1) \\ = (a^{2} + 1) [(a + b - 1) - 1] \\ = (a^{2} + 1) (a + b - 2) \end{matrix}$
$\begin{matrix} (a + b - c) (x - 3) - (b - c - a) (x - 3) & = (x - 3) [(a + b - c) - (b - c - a)] \\ = (x - 3) [a + b - c - b + c + a] \\ = 2 a (x - 3) \end{matrix}$
$3 x (x - 1) - 2 y (x - 1) + z (x - 1) = (x - 1) (3 x - 2 y + z)$
$\begin{matrix} a (n + 1) - b (n + 1) - n - 1 & = a (n + 1) - b (n + 1) - (n + 1) \\ = (n + 1) (a - b - 1) \end{matrix}$
$\begin{matrix} x (a + 2) - a - 2 + 3 (a + 2) & = x (a + 2) - (a + 2) + 3 (a + 2) \\ = (a + 2) (x - 1 + 3) \\ = (a + 2) (x + 2) \end{matrix}$
$\begin{matrix} (1 + 3 a) (x + 1) - 2 a (x + 1) + 3 (x + 1) & = (x + 1) [(1 + 3 a) - 2 a + 3] \\ = (x + 1) (1 + 3 a - 2 a + 3) \\ = (x + 1) (a + 4) \end{matrix}$
$\begin{matrix} (3 x + 2) (x + y - z) - (3 x + 2) - (x + y - 1) (3 x + 2) & = (3 x + 2) [(x + y - z) - 1 - (x + y - 1)] \\ = (3 x + 2) [x + y - z - 1 - x - y + 1] \\ = - z (3 x + 2) \end{matrix}$