Question

The expression b² +8b-48 can be written in factored form as (b+12)(b+c), wher c represents a number. What is the value of c ?

Answer 1

The value of c in the factored form of the expression b² + 8b - 48 is -4.

Step-by-step explanation:

This expression is a quadratic equation of the form at² + bt + c = 0, where the constants are a = 1, b = 8, and c = -48. To find the value of c, we can expand the factored form (b+12)(b+c) by multiplying the two binomials.

Expanding (b+12)(b+c), we get b² + bc + 12b + 12c. Comparing this with the given expression b² + 8b - 48, we can see that the constant term in the expanded form is -48, which means 12c = -48.

Solving this equation, we can divide both sides by 12 to get c = -4.