# Determine the factor of a polynomial equation including piecewise functions

• euro94
In summary, the height of a weather balloon can be modeled by the function h(t)=-2t^3 + 3t^2 +149t + 410 and the balloon is exactly 980m above the ground when t=4. Maria needs to increase each dimension of her storage unit by x+1, x+2, and x+4 to produce a storage that is 9 times the volume of her scale model. The value of x can be found by using the same method as finding t=4.
euro94
The height,h, in meters, of a weather balloon above the ground after t seconds can be modeled by the function h(t)=-2t^3 + 3t^2 +149t + 410 for 0< t < 10. When is the balloon exactly 980m above the ground?

980 = -2t3 + 3t2 +149t + 410
0 = -2t3 + 3t2 +149t - 570

hi euro94!

in exam questions like this, it's almost always a whole number,

so try 1, 2, 3 ,4 ,5 ,…

Thanks :)

Maria designed a rectangular storage unit with dimensions 1m by 2m by 4m. By what shoulds he increase each dimension to produce an actual storage that is 9 times the volume of his scale model?

v= (1) (2) (4)
v= 8

v has to be 9 times larger
v= (x+1) (x+2) (x+4)

How do i find the value of x?

erm

same method?

(and I'm off to bed :zzz:)

## 1. What is a polynomial equation?

A polynomial equation is an algebraic equation that contains one or more terms that are composed of variables raised to non-negative integer powers and coefficients. It can also include constants and operators such as addition, subtraction, multiplication, and division.

## 2. How can I determine the factors of a polynomial equation?

To determine the factors of a polynomial equation, you can use various methods such as factoring, the rational roots theorem, or synthetic division. These methods involve identifying common factors, finding roots or zeros of the equation, and simplifying the equation into a product of simpler expressions.

## 3. What are piecewise functions in a polynomial equation?

Piecewise functions are functions that are defined by different expressions or rules for different intervals of the independent variable, typically separated by vertical lines. In a polynomial equation, a piecewise function may appear when the equation has multiple terms with different powers or coefficients for different ranges of the variable.

## 4. Why is it important to determine the factors of a polynomial equation?

Determining the factors of a polynomial equation is important because it allows us to understand the behavior and properties of the equation, such as its roots or zeros, intercepts, and end behavior. It also helps us to graph the equation and solve for unknown variables or unknown terms in real-life applications.

## 5. Can a polynomial equation with piecewise functions have multiple factors?

Yes, a polynomial equation with piecewise functions can have multiple factors. This is because each piece or interval of the function may have different factors, such as different roots or intercepts, that contribute to the overall behavior and shape of the equation. It is important to consider all factors when determining the behavior and properties of the polynomial equation.

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