Question

traditional algebra 2 - 7.2 polynomial division
the algebros
know that ( x = - 2 ) is a zero of the function ( f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 9 x - 18 ). find the other zeros.

application!
profit ( p ) (in millions of dollars) for a new algebros t - shirt manufacturer can be
( = - x ^ { 3 } + 4 x ^ { 2 } + x ) where ( x ) is the number of bro - shirts made (in million
luces 4 million shirts and makes a profit of ( $ 4,000,000 ). can the company make a

multiple - choice question
what should you get as your remainder?

Explanation:

Step1: Use the Remainder Theorem

The Remainder Theorem states that if a polynomial \(P(x)\) is divided by \(x - a\), the remainder is \(P(a)\). Here, the company produces \(x = 4\) million shirts. So we need to find \(P(4)\) where \(P(x)=-x^{3}+4x^{2}+x\).

Step2: Substitute \(x = 4\) into the polynomial

Substitute \(x = 4\) into \(P(x)\):

$$
LATEXBLOCK0
$$

Answer:

The remainder is \(4\) (which means the company makes a profit of \(\$4,000,000\) when \(x = 4\) million shirts are produced)