Question

What values for b make the 16z^2+bz+25 a perfect square trinomial?

Option 1: b = 10
Option 2: b = −5
Option 3: b = −10
Option 4: b = 5

Answer 1

To make the expression a perfect square trinomial, the value of b should be 40z.

Step-by-step explanation:

A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial. In order for the expression 16z^2+bz+25 to be a perfect square trinomial, the coefficient of the linear term (bz) should be twice the product of the square root of the constant term (25) and the square root of the quadratic term (16z^2).

Plugging in the values we have, b = 2(√(16z^2) * √(25))

b = 2(4z * 5) = 40z

So, the value of b needed to make the given expression a perfect square trinomial is b = 40.