Question

Resuelve los siguientes ejercicios del (caso V)

029428b9ccd0916a63d497dfd5cbab6d.pdf

Answer 1

Respuesta:

1) $x^2+7x+10$

$\left(x^2+2x\right)+\left(5x+10\right)$

$x^2+2x=xx+2x=x\left(x+2\right)$

$5x+10=5x+5\cdot \:2=5\left(x+2\right)$

$x\left(x+2\right)+5\left(x+2\right)$

$\left(x+2\right)\left(x+5\right)$

2)$x^2-5x+6$

$\left(x^2-2x\right)+\left(-3x+6\right)$

$x^2-2x=x\left(x-2\right)$

$-3x+6=-3x+3\cdot \:2=-3\left(x-2\right)$

$x\left(x-2\right)-3\left(x-2\right)=\left(x-2\right)\left(x-3\right)$

3) $a^2-4a+3$

$\left(a^2-a\right)+\left(-3a+3\right)$

$a^2-a=a\left(a-1\right)$

$-3a+3=-3\left(a-1\right)$

$a\left(a-1\right)-3\left(a-1\right)=\left(a-1\right)\left(a-3\right)$

4) $y^2-9y+20$

$\left(y^2-4y\right)+\left(-5y+20\right)$

$y^2-4y=y\left(y-4\right)$

$-5y+20=-5y+5\cdot \:4=-5\left(y-4\right)$

$y\left(y-4\right)-5\left(y-4\right)=\left(y-4\right)\left(y-5\right)$

5) $x^2-6-x$

$\left(x^2+2x\right)+\left(-3x-6\right)$

$x^2+2x=x\left(x+2\right)$

$-3x-6=-3\left(x+2\right)$

$x\left(x+2\right)-3\left(x+2\right)=\left(x+2\right)\left(x-3\right)$

6)$x^2-9x+8$

$\left(x^2-x\right)+\left(-8x+8\right)$

$x^2-x=x\left(x-1\right)$

$-8x+8=-8\left(x-1\right)$

$x(x-1) -8\left(x-1\right)=\left(x-1\right)\left(x-8\right)$

8) $a^2+7a+6$

$\left(a^2+a\right)+\left(6a+6\right)$

$a^2+a=a\left(a+1\right)$

$6a+6=6\left(a+1\right)$

$a\left(a+1\right)+6\left(a+1\right)=\left(a+1\right)\left(a+6\right)$

9) $12-8n+n^2$

$\left(n^2-2n\right)+\left(-6n+12\right)$

$n^2-2n=n\left(n-2\right)$

$-6n+12=--6\left(n-2\right)$

$n\left(n-2\right)-6\left(n-2\right)=\left(n-2\right)\left(n-6\right)$

el 7 y 10 no pude resolverlos.