Solve for all values of x : x^(2)(x+8)+4x(x+8)+3(x+8)=0 Answer: x=

Factor out common term: First, notice that each term on the left side of the equation has a common factor of (x+8). Factor out (x+8) from each term. x^2(x+8) + 4x(x+8) + 3(x+8) = (x+8)(x^2 + 4x + 3) = 0Apply zero product property: Now, we have a product of two factors equal to zero. According to the zero product property, if a product of two factors is zero, then at least one of the factors must be zero. So we can set each factor equal to zero and solve for x. (x+8) = 0 or (x^2 + 4x + 3) = 0Solve linear equation: First, solve the linear equation (x+8) = 0. x + 8 = 0 x = -8Factor and solve quadratic equation: Next, solve the quadratic equation x^2 + 4x + 3 = 0. This can be factored into (x+1)(x+3) = 0. x^2 + 4x + 3 = (x+1)(x+3) = 0Solve for x: Set each factor of the quadratic equation equal to zero and solve for x. x + 1 = 0 or x + 3 = 0 x = -1 or x = -3

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Solve for all values of
x :

x^(2)(x+8)+4x(x+8)+3(x+8)=0
Answer:
x=

Solve for all values of $x$ : $\newline$ $x^{2}(x+8)+4 x(x+8)+3(x+8)=0$ $\newline$ Answer: $x=$

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Algebra 2

Composition of linear and quadratic functions: find a value

Full solution

Q. Solve for all values of

x

\newline

x^{2}(x+8)+4 x(x+8)+3(x+8)=0

\newline

Answer:

x=

Factor out common term: First, notice that each term on the left side of the equation has a common factor of $(x+8)$ . Factor out $(x+8)$ from each term. $\newline$ $x^2(x+8) + 4x(x+8) + 3(x+8) = (x+8)(x^2 + 4x + 3) = 0$
Apply zero product property: Now, we have a product of two factors equal to zero. According to the zero product property, if a product of two factors is zero, then at least one of the factors must be zero. So we can set each factor equal to zero and solve for $x$ . $(x+8) = 0$ or $(x^2 + 4x + 3) = 0$
Solve linear equation: First, solve the linear equation $(x+8) = 0$ . $\newline$ $x + 8 = 0$ $\newline$ $x = -8$
Factor and solve quadratic equation: Next, solve the quadratic equation $x^2 + 4x + 3 = 0$ . This can be factored into $(x+1)(x+3) = 0$ . $\newline$ $x^2 + 4x + 3 = (x+1)(x+3) = 0$
Solve for x: Set each factor of the quadratic equation equal to zero and solve for $x$ . $x + 1 = 0$ or $x + 3 = 0$ $x = -1$ or $x = -3$