Question

The polynomial x2-6x-40 can be factoring into (x+a)(x-b)

Answer 1

Answer: (x + a) (x - b) = (x + 4) (x - 10)

Given the below polynomial expression

x^2 - 6x - 40

`\begin{gathered} x^2\text{ - 6x - 40} \\ \text{The standard quadratic function is ax}^2\text{ + bx + c = 0} \\ \text{let a = 1, b = -6 and c = -40} \\ \text{ find ac} \\ ac\text{ = 1 x (-40) = -40} \\ \text{The factor of ac (-40) that will give -6 is -10 and 4} \\ \text{Hence, the above polynomial function can be factor as follows} \\ x^2\text{ + 4x - 10x - 40} \\ x(x\text{ + 4) - 10(x + 4)} \\ (x\text{ + 4) (x- 10)} \end{gathered}`

Therefore, (x + a) (x - b) = (x + 4) (x - 10)