Question

If x – 10 is a factor of x2 - 8x - 20. what is the other factor?

Answer 1

Answer:

The other factor is (x+2)

Step-by-step explanation:

x²- 8x - 20 =  (x + 2)(x - 10)

let me know if you need any other help:)

Answer 2

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 $\alpha$ 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 $\alpha$.

$(x-10)(x+\alpha)=x^2-8x-20\\x^2-(10+\alpha)x-10\alpha=x^2-8x-20$

The terms of the coefficients for each expression must be the same, so we can say that

$-10-\alpha =-8$

and

$-10\alpha = -20$

Solving both equations give us the same result,  

$\alpha = 2$

So we can use this to create a factor.

$(x+2)(x-10)$

what does this expand to give us?

$x^2-8x-20$

this is correct!