Solve each equation in Exercises 1 - 14 by factoring. $3 x^{2} - 2 x = 8$

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First, rewrite the equation so that all terms are on one side, setting the equation equal to zero: $3x^2 - 2x - 8 = 0$.

Next, look for two numbers that multiply to the product of the coefficient of $x^2$ term and the constant term (i.e., $3 \times (-8) = -24$) and add up to the coefficient of the $x$ term (which is $-2$).

Use these two numbers to split the middle term $-2x$ into two terms, then group the terms in pairs to factor by grouping.

Factor out the greatest common factor (GCF) from each group, which should give you a common binomial factor.

Set each factor equal to zero and solve for $x$ to find the solutions of the equation.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Rearranging Equations to Standard Form

To solve quadratic equations by factoring, first rewrite the equation so that one side equals zero. This involves moving all terms to one side, resulting in a standard form ax² + bx + c = 0, which is essential for applying factoring techniques.

Factoring Quadratic Expressions

Factoring involves expressing a quadratic polynomial as a product of two binomials. This step simplifies solving the equation by setting each factor equal to zero, allowing us to find the roots of the quadratic.

Zero Product Property

The zero product property states that if the product of two factors is zero, then at least one of the factors must be zero. This principle is used after factoring to set each factor equal to zero and solve for the variable.

Solve each equation in Exercises 1 - 14 by factoring. 3x2−2x=83x^2 - 2x = 8