ax^(3)+bx^(2)+cx+d=0 In the equation above, a,b,c, and d are constants. If the equation has roots -1,-3, and 5 , which of the following is a factor of ax^(3)+bx^(2)+cx+d ? A) x-1 B) x+1 C) x-3 D) x+5

Identify Relationship: Identify the relationship between roots and factors of a polynomial. If a polynomial has roots at x = r, then (x - r) is a factor of the polynomial.Determine Factors: Given the roots -1, -3, and 5, determine the corresponding factors. The factors corresponding to these roots are (x - (-1)), (x - (-3)), and (x - 5), which simplify to (x + 1), (x + 3), and (x - 5) respectively.Match with Choices: Match the given factors with the choices provided. The factors we found are (x + 1), (x + 3), and (x - 5). We need to find which one of these is listed in the choices.Identify Correct Factor: Identify the correct factor from the choices. Choice A is (x - 1), which does not match any of our factors. Choice B is (x + 1), which matches one of our factors. Choice C is (x - 3), which does not match any of our factors. Choice D is (x + 5), which does not match any of our factors.

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$ax^{3}+bx^{2}+cx+d=0$ $\newline$ In the equation above, $\newline$ $a,b,c,$ and $\newline$ $d$ are constants. $\newline$ If the equation has roots $\newline$ $-1,-3,$ and $5$ , which of the following is a factor of $\newline$ $ax^{3}+bx^{2}+cx+d$ ? $\newline$ A) $x-1$ $\newline$ B) $x+1$ $\newline$ C) $x-3$ $\newline$ D) $x+5$

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Algebra 1

Compare linear and exponential growth

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ax^{3}+bx^{2}+cx+d=0

\newline

In the equation above,

\newline

a,b,c,

and

\newline

d

are constants.

\newline

If the equation has roots

\newline

-1,-3,

and

5

, which of the following is a factor of

\newline

ax^{3}+bx^{2}+cx+d

\newline

x-1

\newline

x+1

\newline

x-3

\newline

x+5

Identify Relationship: Identify the relationship between roots and factors of a polynomial. $\newline$ If a polynomial has roots at $x = r$ , then $(x - r)$ is a factor of the polynomial.
Determine Factors: Given the roots $-1$ , $-3$ , and $5$ , determine the corresponding factors. $\newline$ The factors corresponding to these roots are $(x - (-1))$ , $(x - (-3))$ , and $(x - 5)$ , which simplify to $(x + 1)$ , $(x + 3)$ , and $(x - 5)$ respectively.
Match with Choices: Match the given factors with the choices provided. $\newline$ The factors we found are $(x + 1)$ , $(x + 3)$ , and $(x - 5)$ . We need to find which one of these is listed in the choices.
Identify Correct Factor: Identify the correct factor from the choices. $\newline$ Choice A is $(x - 1)$ , which does not match any of our factors. $\newline$ Choice B is $(x + 1)$ , which matches one of our factors. $\newline$ Choice C is $(x - 3)$ , which does not match any of our factors. $\newline$ Choice D is $(x + 5)$ , which does not match any of our factors.