[size=150]The polynomial function [math]p(x)=x^3-3x^2-10x+24[/math] has a known factor of [math](x-4)[/math].[/size][br][br]Rewrite [math]p(x)[/math] as the product of linear factors.

[size=150]Tyler thinks he knows one of the linear factors of [math]P(x)=x^3-9x^2+23x-15[/math]. After finding that [math]P(1)=0[/math], he suspects that[math]x-1[/math] is a factor of [math]P(x)[/math]. [/size][br][img]data:image/png;base64,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[/img][br]Here is the diagram he made to check if he’s right, but he set it up incorrectly. What went wrong? 

The polynomial function [math]q(x)=2x^4-9x^3-12x^2+29x+30[/math] has known factors [math](x-2)[/math] and [math](x+1)[/math]. Which expression represents [math]q(x)[/math] as the product of linear factors?

[size=150]Each year a certain amount of money is deposited in an account which pays an annual interest rate of [math]r[/math] so that at the end of each year the balance in the account is multiplied by a growth factor of [math]x=1+r[/math]. $1,000 is deposited at the start of the first year, an additional $300 is deposited at the start of the next year, and $500 at the start of the following year.[/size][br][br]Write an expression for the value of the account at the end of three years in terms of the growth factor [math]x[/math].[br]

Determine (to the nearest cent) the amount in the account at the end of three years if the interest rate is 4%.[br]

[size=150]State the degree and end behavior of [math]f(x)=5+7x-9x^2+4x^3[/math].[/size]

[size=150]Describe the end behavior of [math]f(x)=1+7x+9x^3+6x^4-2x^5[/math].[/size][br]

[size=150]What are the points of intersection between the graphs of the functions [math]f(x)=(x+3)(x-1)[/math] and [math]g(x)=(x+1)(x-3)[/math]?[/size]