Question

if x-5 is a factor of x^2 + bx + 15 what is the value of b

Answer 1

b = -8

Explanation:$\begin{gathered} x^2\text{ + bx + 15} \\ x\text{ - 5 is a factor} \\ \text{equate the factor to zero:} \\ x\text{ -5 = 0} \\ x\text{ = 5} \end{gathered}$

For x - 5 to be a factor of the function, it means when x = 5, the function will be zero

$\begin{gathered} \text{equate the function to zero, then replace x with 5:} \\ x^2\text{ + bx + 15 = 0} \\ (5)^2\text{ + b(5) + 15 = 0} \\ 25\text{ + 5b + 15 = 0} \end{gathered}$$\begin{gathered} \text{collect like terms:} \\ 25\text{ + 15 + 5b = 0} \\ 40\text{ + 5b = 0} \\ 5b\text{ = -40} \\ \end{gathered}$$\begin{gathered} \text{Divide both sides by 5:} \\ \frac{5b}{5}\text{ = }\frac{-40}{5} \\ b\text{ = -8} \end{gathered}$