Question 1176238



To factor a trinomial in the form {{{x^2 + bx + c}}}, find two integers, {{{r}}} and {{{s}}}, whose product is {{{c}}} and whose sum is {{{b}}}.

 {{{x^2 + bx +24}}}

{{{c=24}}}
{{{rs=c}}}
{{{rs=24}}}......eq.1

1.

{{{24=3*8}}}
{{{r=3}}}
{{{s=8}}}
{{{r+s=b=11}}}

{{{x^2 + 11x +24}}}
{{{x^2 + 3x+8x +24}}}
{{{(x^2 + 3x)+(8x +24)}}}
{{{x(x+ 3)+8(x +3)}}}
{{{(x+8)(x +3)}}}

2.

{{{24=2*12}}}
{{{r=2}}}
{{{s=12}}}
{{{r+s=14}}}

{{{x^2 + 14x +24}}}
{{{x^2 + 2x+12x +24}}}
{{{(x^2 + 2x)+(12x +24)}}}
{{{x(x+ 2)+12(x +2)}}}
{{{(x+2)(x +12)}}}

3.

{{{24=4*6}}}
{{{r=4}}}
{{{s=6}}}
{{{r+s=10}}}

{{{x^2 + 10x +24}}}
{{{x^2 + 4x+6x +24}}}
{{{(x^2 + 4x)+(6x +24)}}}
{{{x(x+ 4)+6(x +4)}}}
{{{(x+4)(x +6)}}}