How do you find the missing number or term to make a perfect square trinomial. x^2 + 10x + c ?

1 Answer
Jun 7, 2015

A perfect square trinomial would be color(blue)(a^2)+color(purple)(2ab)+color(red)(b^2)

Here : color(blue)(a=x)
color(purple)(2ab=10x)
And color(red)(b^2=c)

Thus :

color(blue)acolor(red)b=5x ( we divide by 2 on bothside )
color(blue)x*color(red)b=5x ( since color(blue)(a=x) )
cancelx*color(red)b=cancelx*5
color(red)(b=5)

And thus :

color(red)(c=b^2=5^2=25