Final answer:
To factor the equation b^2 - 10b + 90 completely, we can use the method of factoring by grouping. The factored form of the equation is (b - 6)(b - 4).
Step-by-step explanation:
When factoring a quadratic equation, we look for two binomials that, when multiplied together, give us the original quadratic equation. In this case, the equation is b^2 - 10b + 90.
To factor this equation, we need to find two numbers that add up to -10 (the coefficient of the b term) and multiply to give us 90 (the constant term).
The numbers -6 and -4 satisfy these conditions, so the factored form of the equation is (b - 6)(b - 4).