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2. Which binomial I is a factor of x^2+4x-12 Prime (x-2) (x-3) (x+3)

Pergunta

2. Which binomial I is a factor of x^2+4x-12
Prime
(x-2)
(x-3)
(x+3)

2. Which binomial I is a factor of x^2+4x-12 Prime (x-2) (x-3) (x+3)

Solução

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JoséElite · Tutor por 8 anos

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To determine which binomial is a factor of the quadratic expression \(x^2 + 4x - 12\), we need to factor the quadratic expression.<br /><br />First, we look for two numbers that multiply to \(-12\) (the constant term) and add up to \(4\) (the coefficient of the linear term).<br /><br />The numbers that satisfy these conditions are \(6\) and \(-2\), because:<br />\[ 6 \times (-2) = -12 \]<br />\[ 6 + (-2) = 4 \]<br /><br />So, we can factor the quadratic expression as:<br />\[ x^2 + 4x - 12 = (x + 6)(x - 2) \]<br /><br />Therefore, the binomial \((x - 2)\) is a factor of \(x^2 + 4x - 12\).<br /><br />The correct answer is:<br />\((x-2)\)
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