Solve the equation by factoring: 2x^(3)-18x^(2)+16 x=0 Answer: x=

Factor GCF: Factor out the greatest common factor (GCF) from the given equation. The GCF of 2x^3, -18x^2, and 16x is 2x. So we factor 2x out of each term. 2x(x^2 - 9x + 8) = 0Factor Quadratic: Factor the quadratic expression inside the parentheses. We need to find two numbers that multiply to 8 and add up to -9. These numbers are -1 and -8. 2x(x - 1)(x - 8) = 0Solve GCF: Set each factor equal to zero and solve for x. First, set the GCF 2x equal to zero: 2x = 0 x = 0Solve Factor 1: Set the first factor inside the parentheses equal to zero and solve for x. x - 1 = 0 x = 1Solve Factor 2: Set the second factor inside the parentheses equal to zero and solve for x. x - 8 = 0 x = 8

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Solve the equation by factoring:

2x^(3)-18x^(2)+16 x=0
Answer:
x=

Solve the equation by factoring: $\newline$ $2 x^{3}-18 x^{2}+16 x=0$ $\newline$ Answer: $x=$

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Algebra 1

Transformations of quadratic functions

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Q. Solve the equation by factoring:

\newline

2 x^{3}-18 x^{2}+16 x=0

\newline

Answer:

x=

Factor GCF: Factor out the greatest common factor (GCF) from the given equation. $\newline$ The GCF of $2x^3$ , $-18x^2$ , and $16x$ is $2x$ . So we factor $2x$ out of each term. $\newline$ $2x(x^2 - 9x + 8) = 0$
Factor Quadratic: Factor the quadratic expression inside the parentheses. $\newline$ We need to find two numbers that multiply to $8$ and add up to $-9$ . These numbers are $-1$ and $-8$ . $\newline$ $2x(x - 1)(x - 8) = 0$
Solve GCF: Set each factor equal to zero and solve for $x$ . $\newline$ First, set the GCF $2x$ equal to zero: $\newline$ $2x = 0$ $\newline$ $x = 0$
Solve Factor $1$ : Set the first factor inside the parentheses equal to zero and solve for $x$ . $x - 1 = 0$ $x = 1$
Solve Factor $2$ : Set the second factor inside the parentheses equal to zero and solve for $x$ . $x - 8 = 0$ $x = 8$