Question

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

Answer 1

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`