Question

Can someone help me with this

Answer 1

By illegal I'm guessing it means undefined, so when the denominator is equal to 0 because you can't divide by 0
you can either use the quadratic equation or sub the values from the multiple choice to find it. in this case it's easier to use the values given in the multiple choice
b^2-2b-8=0
b^2-2b=8
(-2)^2-2 (-2)=8
4--4=8
4+4=8
so -2 is one of the values
(-4)^2-2 (-4)=8
16+8=8
16+8=24
so -4 isnt one of the values
(4)^2-2 (4)=8
16-8=8
so 4 is one of the values
(-5)^2-2 (-5)=8
25+10=8
25+10=35
so -5 isn't one of the values
So because we know that the values are -2 and 4, and -5 and -4 aren't values, we can conclude the answer is B

Answer 2

As this is a fraction, we need to find values where the denominator is equal to 0.

$b^2-2b-8=0$
$(b-4)(b+2)$
$b=4 \vee b=-2$

So the answer is B.