Question

Factor.

16x² + 40x + 25
A) (4x - 5)(4x + 5)
B) (4x - 5)(4x - 5)
C) (4x + 5)(4x + 5)
D) (5x + 4)(5x - 4)

Answer 1

Factor 16x² + 40x + 25.
First take the square root of a & c, where ax² + bx + c

`√(16) = 4... \: √(25) = 5`
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:

`{( √(a) + √(c))}^(2) \\ =( √(a) + √(c))( √(a) + √(c)) \\ = ( √(16) + √(25))( √(16) + √(25)) \\ = (4 + 5) (4 + 5)`
C) (4x + 5)(4x + 5)

Answer 2

The answer is C; (4x + 5)(4x + 5) although you can factor it further to (4x-5)²