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Solve the equation by factoring:Answer:
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Q. Solve the equation by factoring:Answer:
- Factor GCF: Factor out the greatest common factor (GCF)Identify the GCF of the terms in the equation.The GCF of , , and is .Factor out from each term.
- Rewrite Quadratic: Rewrite the quadratic in standard formThe quadratic part of the factored expression is currently in the form . We need to rewrite it in standard form, which is .So, we have .Rewrite it as .
- Factor Expression: Factor the quadratic expressionNow we need to factor the quadratic expression -x^2 + x + 56＂).\(\newlineWe are looking for two numbers that multiply to \$-56\) and add up to \(1\).\(\newline\)The numbers are \(8\) and \(-7\).\(\newline\)So, the factored form is \(3x(-(x - 8)(x + 7)) = 0\).
- Set Equal: Set each factor equal to zero\(\newline\)Now we have the factored form of the equation: \(3x(x - 8)(x + 7) = 0\).\(\newline\)Set each factor equal to zero to find the solutions for \(x\).\(\newline\)\(3x = 0\), \(x - 8 = 0\), and \(x + 7 = 0\).
- Solve for x: Solve for x\(\newline\)Solve each equation for x.\(\newline\)For \(3x = 0\), \(x = 0\).\(\newline\)For \(x - 8 = 0\), \(x = 8\).\(\newline\)For \(x + 7 = 0\), \(x = -7\).
