Question

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

Answer 1

(x+2)

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!

Answer 2

The other factor is (x+2)

Explanation:

x²- 8x - 20 = (x + 2)(x - 10)

let me know if you need any other help:)