In order to determine the factors of the given trinomials, use the quadratic formula:
[tex]x=\frac{-b\pm\sqrt[]{b^{2}-4ac}}{2a}[/tex]where a, b and c are the coefficients of the polynomial:
ax² + bx + c
Replace the values of the coefficients of the given trinomials into the quadratic formula.
1) 5x² + 17x + 6
a = 5, b = 17, c = 6
[tex]\begin{gathered} x=\frac{-17\pm\sqrt[]{17^{2}-4(5)(6)}}{2(5)} \\ x=\frac{-17\pm13}{10} \end{gathered}[/tex]the two solutions for x are:
x1 = (-17-13)/10 = -30/10 = -3
x2 = (-17+13)/10 = -4/10 = -2/5
The factors are given by the following expression:
(x - x1)(x - x2)
Then, you have:
5x² + 17x + 6 = (x - (-3))(x - (-2/5)) = (x + 3)(x + 2/5)
