What value of b makes the trinomal below a perfect square x2 bx 16?

To make the trinomial ( x^2 + bx + 16 ) a perfect square, we need it to be expressible in the form ( (x + p)^2 ), where ( p ) is a constant. Expanding ( (x + p)^2 ) gives us ( x^2 + 2px + p^2 ). To match the constant term, we set ( p^2 = 16 ), which gives ( p = 4 ) or ( p = -4 ). Thus, ( 2p = 8 ) or ( -8 ), meaning ( b ) must be ( 8 ) or ( -8 ).