Factor. 3x^2+5x-2 square square

To factor the quadratic expression $3x^2 + 5x - 2$, we need to find two binomials whose product gives us the original expression. The general form of factoring a quadratic expression $ax^2 + bx + c$ is:<br /><br />$ax^2 + bx + c = (dx + e)(fx + g)$<br /><br />where $d \cdot f = a$, $e \cdot g = c$, and $df \cdot eg + de \cdot fg = b$.<br /><br />For the given expression $3x^2 + 5x - 2$, we have $a = 3$, $b = 5$, and $c = -2$. We need to find two numbers whose product is $3 \cdot (-2) = -6$ and whose sum is $5$.<br /><br />The two numbers that satisfy these conditions are $6$ and $-1$ because $6 \cdot (-1) = -6$ and $6 + (-1) = 5$.<br /><br />Now, we $5x$ using these two numbers:<br /><br />$3x^2 + 6x - x - 2$<br /><br />Next, we group the terms:<br /><br />$(3x^2 + 6x) + (-x - 2)$<br /><br />Factor out the greatest common factor from each group:<br /><br />$3x(x + 2) - 1(x + 2)$<br /><br />Now, factor out the common binomial factor $(x + 2)$:<br /><br />$(3x - 1)(x + 2)$<br /><br />So, the factored form of $3x^2 + 5x - 2$ is:<br /><br />$(3x - 1)(x + 2)$