Ejercicio 100 – Solucionario Baldor

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DESCARGA

CAPITULO X

Descomposición Factorial

Ejercicio 100

Factorar:

$\begin{matrix} 2 x^{2} + 3 x - 2 & = 2 x^{2} + 4 x - x - 2 & . \begin{matrix} 4 \\ 1 \end{matrix} | \begin{matrix} 4 \end{matrix} \\ = 2 x (x + 2) - (x + 2) \\ = (x + 2) (2 x - 1) \end{matrix}$
$\begin{matrix} 3 x^{2} - 5 x - 2 & = 3 x^{3} - 6 x + x - 2 & . \begin{matrix} 6 \\ 1 \end{matrix} | \begin{matrix} 6 \end{matrix} \\ = 3 x (x - 2) + (x - 2) \\ = (x - 2) (3 x + 1) \end{matrix}$
$\begin{matrix} 6 x^{2} + 7 x + 2 & = 6 x^{2} + 3 x + 4 x + 2 & . \begin{matrix} 12 \\ 6 \\ 3 \\ 1 \end{matrix} | \begin{matrix} 2 \\ 2 \\ 3 \end{matrix} \\ = 3 x (2 x + 1) + 2 (2 x + 1) \\ = (2 x + 1) (3 x + 2) \end{matrix}$
$\begin{matrix} 5 x^{2} + 13 x - 6 & = 5 x^{2} + 15 x - 2 x - 6 & . \begin{matrix} 30 \\ 15 \\ 1 \end{matrix} | \begin{matrix} 2 \\ 15 \end{matrix} \\ = 5 x (x + 3) - 2 (x + 3) \\ = (x + 3) (5 x - 2) \end{matrix}$
$\begin{matrix} 6 x^{2} - 6 - 5 x = 6 x^{2} - 5 x - 6 & = 6 x^{2} - 9 x + 4 x - 6 & . \begin{matrix} 36 \\ 18 \\ 9 \\ 1 \end{matrix} | \begin{matrix} 2 \\ 2 \end{matrix} \\ = 3 x (2 x - 3) + 2 (2 x - 3) \\ = (2 x - 3) (3 x + 2) \end{matrix}$
$\begin{matrix} 12 x^{2} - x - 6 & = 12 x^{2} + 8 x - 9 x - 6 & . \begin{matrix} 72 \\ 36 \\ 18 \\ 9 \\ 1 \end{matrix} | \begin{matrix} 2 \\ 2 \\ 2 \\ 9 \end{matrix} \\ = 4 x (3 x + 2) - 3 (3 x + 2) \\ = (3 x + 2) (4 x - 3) \end{matrix}$
$\begin{matrix} 4 a^{2} + 15 a + 9 & = 4 a^{2} + 12 a + 3 a + 9 & . \begin{matrix} 36 \\ 18 \\ 9 \\ 3 \\ 1 \end{matrix} | \begin{matrix} 2 \\ 2 \\ 3 \\ 3 \end{matrix} \\ = 4 a (a + 3) + 3 (a + 3) \\ = (a + 3) (4 a + 3) \end{matrix}$
$\begin{matrix} 3 + 11 a + 10 a^{2} & = 3 + 6 a + 5 a + 10 a^{2} & . \begin{matrix} 30 \\ 15 \\ 5 \\ 1 \end{matrix} | \begin{matrix} 2 \\ 3 \\ 5 \end{matrix} \\ = 3 (1 + 2 a) + 5 a (1 + 2 a) \\ = (1 + 2 a) (3 + 5 a) \end{matrix}$
$\begin{matrix} 12 m^{2} - 13 m - 35 & = 12 m^{2} - 28 m + 15 m - 35 & . \begin{matrix} 420 \\ 210 \\ 105 \\ 35 \\ 7 \\ 1 \end{matrix} | \begin{matrix} 2 \\ 2 \\ 3 \\ 5 \\ 7 \end{matrix} \\ = 4 m (3 m - 7) + 5 m (3 m - 7) \\ = (3 m - 7) (4 m + 5 m) \end{matrix}$
$\begin{matrix} 20 y^{2} + y - 1 & = 20 y^{2} + 5 y - 4 y - 1 & . \begin{matrix} 20 \\ 10 \\ 5 \\ 1 \end{matrix} | \begin{matrix} 2 \\ 2 \\ 5 \end{matrix} \\ = 5 y (4 y + 1) - (4 y + 1) \\ = (4 y + 1) (5 y - 1) \end{matrix}$
$\begin{matrix} 8 a^{2} - 14 a - 15 & = 8 a^{2} + 6 a - 20 a - 15 & . \begin{matrix} 120 \\ 60 \\ 30 \\ 15 \\ 5 \\ 1 \end{matrix} | \begin{matrix} 2 \\ 2 \\ 2 \\ 3 \\ 5 \end{matrix} \\ = 2 a (4 a + 3) - 5 (4 a + 3) \\ = (4 a + 3) (2 a - 1) \end{matrix}$
$\begin{matrix} 7 x^{2} - 44 x - 35 & = 7 x^{2} - 49 x + 5 x - 35 & . \begin{matrix} 245 \\ 49 \\ 1 \end{matrix} | \begin{matrix} 5 \\ 49 \end{matrix} \\ = 7 x (x - 7) + 5 (x - 7) \\ = (x - 7) (7 x + 5) \end{matrix}$
$\begin{matrix} 16 m + 15 m^{2} - 15 = 15 m^{2} + 16 m - 15 & = 15 m^{2} + 25 m - 9 m - 15 & . \begin{matrix} 225 \\ 75 \\ 25 \\ 1 \end{matrix} | \begin{matrix} 3 \\ 3 \\ 25 \end{matrix} \\ = 5 m (3 m + 5) - 3 m (3 m + 5) \\ = (3 m + 5) (5 m - 3 m) \end{matrix}$
$\begin{matrix} 2 a^{2} + 5 a + 2 & = 2 a^{2} + 4 a + a + 2 & . \begin{matrix} 4 \\ 1 \end{matrix} | \begin{matrix} 4 \end{matrix} \\ = 2 a (a + 2) + (a + 2) \\ = (a + 2) (2 a + 1) \end{matrix}$
$\begin{matrix} 12 x^{2} - 7 x - 12 & = 12 x^{2} - 16 x + 9 x - 12 & . \begin{matrix} 144 \\ 72 \\ 36 \\ 18 \\ 9 \\ 1 \end{matrix} | \begin{matrix} 2 \\ 2 \\ 2 \\ 2 \\ 9 \end{matrix} \\ = 4 x (3 x - 4) + 3 (3 x - 4) \\ = (3 x - 4) (4 x + 3) \end{matrix}$
$\begin{matrix} 9 a^{2} + 10 a + 1 & = 9 a^{2} + 9 a + a + 1 & . \begin{matrix} 9 \\ 1 \end{matrix} | \begin{matrix} 9 \end{matrix} \\ = 9 a (a + 1) + (a + 1) \\ = (a + 1) (9 a + 1) \end{matrix}$
$\begin{matrix} 20 n^{2} - 9 n - 20 & = 20 n^{2} - 25 n + 16 n - 20 & . \begin{matrix} 400 \\ 200 \\ 100 \\ 50 \\ 25 \\ 1 \end{matrix} | \begin{matrix} 2 \\ 2 \\ 2 \\ 2 \\ 25 \end{matrix} \\ = 5 n (4 n - 5) + 4 (4 n - 5) \\ = (4 n - 5) (5 n + 4) \end{matrix}$
$\begin{matrix} 21 x^{2} + 11 x - 2 & = 21 x^{2} + 14 x - 3 x - 2 & . \begin{matrix} 42 \\ 21 \\ 7 \\ 1 \end{matrix} | \begin{matrix} 2 \\ 3 \\ 7 \end{matrix} \\ = 7 x (3 x + 2) - (3 x + 2) \\ = (3 x + 2) (7 x - 1) \end{matrix}$
$\begin{matrix} m - 6 + 15 m^{2} = 15 m^{2} + m - 6 & = 15 m^{2} + 10 m - 9 m - 6 & . \begin{matrix} 90 \\ 45 \\ 15 \\ 5 \\ 1 \end{matrix} | \begin{matrix} 2 \\ 3 \\ 3 \\ 5 \end{matrix} \\ = 5 m (3 m + 2) - 3 (3 m + 2) \\ = (3 m + 2) (5 m - 3) \end{matrix}$
$\begin{matrix} 15 a^{2} - 8 a - 12 & = 15 a^{2} + 10 a - 18 a - 12 & . \begin{matrix} 180 \\ 90 \\ 45 \\ 15 \\ 5 \\ 1 \end{matrix} | \begin{matrix} 2 \\ 2 \\ 3 \\ 3 \\ 5 \end{matrix} \\ = 5 a (3 a + 2) + 6 a (3 a + 2) \\ = (3 a + 2) (5 a + 6 a) \end{matrix}$
$\begin{matrix} 9 x^{2} + 37 x + 4 & = 9 x^{2} + 36 x + x + 4 & . \begin{matrix} 36 \\ 1 \end{matrix} | \begin{matrix} 36 \end{matrix} \\ = 9 x (x + 4) + (x + 4) \\ = (x + 4) (9 x + 1) \end{matrix}$
$\begin{matrix} 44 n + 20 n^{2} - 15 & = 20 n^{2} + 4 n - 15 = 20 n^{2} + 50 n - 6 n - 15 & . \begin{matrix} 300 \\ 150 \\ 75 \\ 25 \\ 5 \\ 1 \end{matrix} | \begin{matrix} 2 \\ 2 \\ 3 \\ 5 \\ 5 \end{matrix} \\ = 10 n (2 n + 5) - 3 (2 n + 5) \\ = (2 n + 5) (10 n - 3) \end{matrix}$
$\begin{matrix} 14 m^{2} - 31 m - 10 = & 14 m^{2} + 4 m - 35 m - 10 & . \begin{matrix} 140 \\ 70 \\ 35 \\ 1 \end{matrix} | \begin{matrix} 2 \\ 2 \\ 35 \end{matrix} \\ = 2 m (7 m + 2) - 5 (7 m + 2) \\ = (7 m + 2) (2 m - 5) \end{matrix}$
$\begin{matrix} 2 x^{2} + 29 x + 90 & = 2 x^{2} + 20 x + 9 x + 90 & . \begin{matrix} 180 \\ 90 \\ 45 \\ 15 \\ 5 \\ 1 \end{matrix} | \begin{matrix} 2 \\ 2 \\ 3 \\ 3 \\ 5 \end{matrix} \\ = 2 x (x + 10) + 9 (x + 10) \\ = (x + 10) (2 x + 9) \end{matrix}$
$\begin{matrix} 20 a^{2} - 7 a - 40 & = 20 a^{2} + 25 a - 32 a - 40 & . \begin{matrix} 800 \\ 400 \\ 200 \\ 100 \\ 50 \\ 25 \\ 1 \end{matrix} | \begin{matrix} 2 \\ 2 \\ 2 \\ 2 \\ 2 \\ 25 \end{matrix} \\ = 5 a (4 a + 5) - 8 a (4 a + 5) \\ = (4 a + 5) (5 a - 8 a) \end{matrix}$
$\begin{matrix} 4 n^{2} + n - 33 & = 4 n^{2} + 12 n - 11 n - 33 & . \begin{matrix} 132 \\ 66 \\ 33 \\ 11 \\ 1 \end{matrix} | \begin{matrix} 2 \\ 2 \\ 3 \\ 11 \end{matrix} \\ = 4 n (n + 3) - 11 (n + 3) \\ = (n + 3) (4 n - 11) \end{matrix}$
$\begin{matrix} 30 x^{2} + 13 x - 10 & = 30 x^{2} + 25 x - 12 x - 10 & . \begin{matrix} 300 \\ 150 \\ 75 \\ 25 \\ 1 \end{matrix} | \begin{matrix} 2 \\ 2 \\ 3 \\ 25 \end{matrix} \\ = 5 x (6 x + 5) - 2 (6 x + 5) \\ = (6 x + 5) (5 x - 2) \end{matrix}$