Solve the equation by factoring: 2x^(3)+2x^(2)-112 x=0 Answer: x=

Factor GCF: Factor out the greatest common factor (GCF) Identify the GCF of the terms in the equation. The GCF of 2x^3, 2x^2, and -112x is 2x. Factor out 2x from each term. 2x^3 + 2x^2 - 112x = 0 2x(x^2 + x - 56) = 0Identify GCF: Factor the quadratic expression Factor the quadratic expression x^2 + x - 56. We need to find two numbers that multiply to -56 and add up to 1. The numbers 8 and -7 satisfy these conditions. x^2 + x - 56 = (x + 8)(x - 7)Factor Quadratic: Write the factored form of the equation Combine the GCF factored out in Step 1 with the factored quadratic from Step 2. 2x(x + 8)(x - 7) = 0Write Factored Form: Solve for x using the zero product property Set each factor equal to zero and solve for x. 2x = 0, x + 8 = 0, x - 7 = 0 Solving each equation gives us: x = 0, x = -8, x = 7

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Solve the equation by factoring:

2x^(3)+2x^(2)-112 x=0
Answer:
x=

Solve the equation by factoring: $\newline$ $2 x^{3}+2 x^{2}-112 x=0$ $\newline$ Answer: $x=$

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Math Problems

Algebra 2

Sum of finite series not start from 1

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Q. Solve the equation by factoring:

\newline

2 x^{3}+2 x^{2}-112 x=0

\newline

Answer:

x=

Factor GCF: Factor out the greatest common factor (GCF) $\newline$ Identify the GCF of the terms in the equation. $\newline$ The GCF of $2x^3$ , $2x^2$ , and $-112x$ is $2x$ . $\newline$ Factor out $2x$ from each term. $\newline$ $2x^3 + 2x^2 - 112x = 0$ $\newline$ $2x(x^2 + x - 56) = 0$
Identify GCF: Factor the quadratic expression $\newline$ Factor the quadratic expression $x^2 + x - 56$ . $\newline$ We need to find two numbers that multiply to $-56$ and add up to $1$ . $\newline$ The numbers $8$ and $-7$ satisfy these conditions. $\newline$ $x^2 + x - 56 = (x + 8)(x - 7)$
Factor Quadratic: Write the factored form of the equation $\newline$ Combine the GCF factored out in Step $1$ with the factored quadratic from Step $2$ . $\newline$ $2x(x + 8)(x - 7) = 0$
Write Factored Form: Solve for $x$ using the zero product property $\newline$ Set each factor equal to zero and solve for $x$ . $\newline$ $2x = 0$ , $x + 8 = 0$ , $x - 7 = 0$ $\newline$ Solving each equation gives us: $\newline$ $x = 0$ , $x = -8$ , $x = 7$