Find the Excluded Values (7b^3)/(b^2-7b+10)

$\frac{7 b^{3}}{b^{2} - 7 b + 10}$

Step 1

Set the denominator in $\frac{7 b^{3}}{b^{2} - 7 b + 10}$ equal to $0$ to find where the expression is undefined.

$b^{2} - 7 b + 10 = 0$

Step 2

Solve for $b$ .

Factor $b^{2} - 7 b + 10$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $10$ and whose sum is $- 7$ .

$- 5, - 2$

Write the factored form using these integers.

$(b - 5) (b - 2) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$b - 5 = 0$

$b - 2 = 0$

Set $b - 5$ equal to $0$ and solve for $b$ .

Set $b - 5$ equal to $0$ .

$b - 5 = 0$

Add $5$ to both sides of the equation.

$b = 5$

Set $b - 2$ equal to $0$ and solve for $b$ .

Set $b - 2$ equal to $0$ .

$b - 2 = 0$

Add $2$ to both sides of the equation.

$b = 2$

The final solution is all the values that make $(b - 5) (b - 2) = 0$ true.

$b = 5, 2$

Step 3

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

$b = 2, b = 5$

Step 4

Find the Excluded Values (7b^3)/(b^2-7b+10)

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