Answer:
(x+2)
Step-by-step explanation:
Our expression must be multiplied by another factor to make the needed equation, so lets multiply our factor by another factor where we use [tex]\alpha[/tex] as a variable of the factor we don't know. We can now expand this and compare coefficients to try to determine our value for [tex]\alpha[/tex].
[tex](x-10)(x+\alpha)=x^2-8x-20\\x^2-(10+\alpha)x-10\alpha=x^2-8x-20[/tex]
The terms of the coefficients for each expression must be the same, so we can say that
[tex]-10-\alpha =-8[/tex]
and
[tex]-10\alpha = -20[/tex]
Solving both equations give us the same result,
[tex]\alpha = 2[/tex]
So we can use this to create a factor.
[tex](x+2)(x-10)[/tex]
what does this expand to give us?
[tex]x^2-8x-20[/tex]
this is correct!
