Questions: Factor 3x^2+2x-8

Transcript text: Factor $3 x^{2}+2 x-8$

Solution

Step 1: Identify the Coefficients

The coefficients are $a = 3$, $b = 2$, and $c = -8$.

Step 2: Calculate the Discriminant

The discriminant $D$ is calculated as $D = b^2 - 4ac = 2^2 - 4_3_-8 = 100$.

Step 3: Factorization Method

Since $D > 0$, the quadratic equation has two distinct real roots.

Step 4: Finding Roots

Using the quadratic formula, the roots are $x = \frac{-b \pm \sqrt{D}}{2a}$, which gives us $x_1 = 1.33$ and $x_2 = -2$.

The factorized form is $(x - 1.33)(x + 2)$.

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