Question

factor each trinomial. if the trinomial cannot be factored write prime. show ALL work1.) 5x^2+17x+62.) 2x^2+5x-12

Answer 1

In order to determine the factors of the given trinomials, use the quadratic formula:

`x=\frac{-b\pm\sqrt[]{b^(2)-4ac}}{2a}`

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

`\begin{gathered} x=\frac{-17\pm\sqrt[]{17^(2)-4(5)(6)}}{2(5)} \\ x=(-17\pm13)/(10) \end{gathered}`

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)