Question

Factor the trinomial below 14x2 - 39x - 35

Answer 1

Answer:

$(2x -7)(7x + 5)$

Step-by-step explanation:

We have a trinomial of the form $ax ^ 2 + bx + c$

Use the formula $-b + \frac{\sqrt{b^2 -4ac}}{2a}\\\\-b - \frac{\sqrt{b^2 -4ac}}{2a}$

Where a, b, c are constants belonging to real numbers.

So in the equation $14x^2 - 39x - 35$ we have

$\frac{39 + \sqrt{(-39)^2 -4(14)(-35)}}{2(14)} \\\\\frac{39 - \sqrt{(-39)^2 -4(14)(-35)}}{2(14)}$

Then the solutions are:

$x_1 = \frac{7}{2} --> 2x = 7 -->(2x-7) = 0\\\\x_2 =\frac{-5}{7} --> 7x = -5 -->(7x+5) = 0$

Then the polynomial is factorized in the following way:

$(2x -7)(7x + 5)$