20. finance the break - even point for a business occurs when the revenues equal the cost. a local…

20. finance the break - even point for a business occurs when the revenues equal the cost. a local children’s museum studied their costs and revenues from paid admission. they found that their break - even point is given by the expression 2h² - 2h - 24, where h is the number of hours the museum is open per day. factor the expression.

20. finance the break - even point for a business occurs when the revenues equal the cost. a local children’s museum studied their costs and revenues from paid admission. they found that their break - even point is given by the expression 2h² - 2h - 24, where h is the number of hours the museum is open per day. factor the expression.

Answer

Explanation:

Step1: Factor out the GCF

First, find the greatest - common factor of the coefficients 2, - 2, and - 24. The GCF of 2, - 2, and - 24 is 2. $2h^{2}-2h - 24=2(h^{2}-h - 12)$

Step2: Factor the quadratic expression

For the quadratic expression $h^{2}-h - 12$, we need to find two numbers that multiply to - 12 and add up to - 1. The numbers are - 4 and 3 since $(-4)\times3=-12$ and $-4 + 3=-1$. $h^{2}-h - 12=(h - 4)(h+3)$

Answer:

$2(h - 4)(h + 3)$