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Answer:
(x+4)(x-5)
Step-by-step explanation:
Second order polynomial in the following format:
ax² + bx + c = 0
Has roots x¹ and x².
Can be factored as:
(x - x¹)(x - x²)
So, we have to find the roots.
Finding the roots:
Bhaskara formula, which is:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]In the polynomial given in this question:
a = 1, b = -1, c = -20
So
[tex]x=\frac{-(-1)\pm\sqrt{(-1)^2-4\ast1\ast(-20)}}{2}=\frac{1\pm\sqrt{81}}{2}[/tex]The roots are:
[tex]x^1=\frac{1+9}{2}=5,x^2=\frac{1-9}{2}=-4[/tex]The factored form is:
(x - x¹)(x - x²) = (x - (-4))(x - 5) = (x+4)(x-5)