Find the illegal values of b in the fraction 2b2+3b-10/ b2-2b-8

-2 and 4

Step-by-step explanation:

When you look for values that make an expression “illegal” the first step is to look for 3 things.

1) a variable in a denominator

- we have b, a variable, in the denominator of this expression

- values in the denominator cannot be 0

2) variables under even roots

- variables under even roots are a restriction because even roots are undefined when there are negative values under them

- there are no roots in this case so we dont have to worry about that

3) the literal letters: “log” in the expression

- there’s no “log” in the expression so we dont have to worry about that

—moving on—

We have a variable in the denominator, b.

The expression is a quadratic:

b^2 - 2b - 8

You have to find values that make this quadratic 0.

So you can make an equation setting the quadratics equal to 0.

b^2 - 2b - 8 = 0

Solve for b

Factor:

(b - 4)(b + 2) = 0

Because of zero product property we can say:

b = -2, b = 4.

If these values are plugged into your expression, it will be “illegal,” or “undefined,”

4 + 5 7/9= 9 7/9

step-by-step explanation:

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.