Question

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

Answer 1

Given:

`\begin{gathered} x-5\text{ is a factor of} \\ x^2+bx+15 \end{gathered}`
`\begin{gathered} \text{If x-5 is a factor, then} \\ x-5=0 \\ x=0+5 \\ x=5 \\ \\ \text{Then x=5 is a root of the equation.} \end{gathered}`

To find the value of b,

`\begin{gathered} x^2+bx+15=0 \\ \text{Substitute the value of x=5 into the equation to get b;} \\ 5^2+5b+15=0 \\ 25+5b+15=0 \\ 40+5b=0 \\ 5b=0-40 \\ 5b=-40 \\ \text{Dividing both sides by 5,} \\ b=-(40)/(5) \\ b=-8 \end{gathered}`

Therefore, the value of b is -8