Factor 16x² + 40x + 25.
First take the square root of a & c, where ax² + bx + c
[tex] \sqrt{16} = 4... \: \sqrt{25} = 5[/tex]
Now see if b (40) = 2×those roots multiplied:
2×4×5 = 2×20 = 40. YES! ✔
Now is b + or -?? b = +40, so we know that the factors will be:
[tex]{( \sqrt{a} + \sqrt{c})}^{2} \\ =( \sqrt{a} + \sqrt{c})( \sqrt{a} + \sqrt{c}) \\ = ( \sqrt{16} + \sqrt{25})( \sqrt{16} + \sqrt{25}) \\ = (4 + 5) (4 + 5)[/tex]
C) (4x + 5)(4x + 5)
