Question

Divide. (x^2+8x+12)/(x+5)

Answer 1

Answer:

$x^2+8x+12=(x+5)(x+3)-3.$

The quotient is $x+3$ and the remainder is -3.

Step-by-step explanation:

Dividing $x^2+8x+12$ by $x+5,$ multiply $x+5$ by x:

$(x+5)x=x^2+5x$ and subtract it from $x^2+8x+12:$

$x^2+8x+12-(x^2+5x)=x^2+8x+12-x^2-5x=3x+12.$

Now multiply $x+5$ by 3:

$(x+5)\cdot 3=3x+15$

and subtract it from $3x+12:$

$3x+12-(3x+15)=3x+12-3x-15=-3.$

Thus,

$x^2+8x+12=(x+5)(x+3)-3.$

The quotient is $x+3$ and the remainder is -3.