Question

Pemfaktoran dari 2x²+5x-18​

Answer 1

We can factor a polynomial by finding its roots. In particular, a quadratic equation has (at most) two roots $x_1,\ x_2$, which would allow us to write the polynomial as

$p(x)=a(x-x_1)(x-x_2)$

To find the solutions, we can use the quadratic formula

$x_{1,2} = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a} = \dfrac{-5\pm\sqrt{169}}{4} = \dfrac{-5\pm13}{4}$

So, the two solutions are

$\dfrac{-5+13}{4} = 2\quad\text{and}\quad\dfrac{-5-13}{4} =-\dfrac{9}{2}$

And so we can factor the polynomial as follows:

$2x^2+5x-18=2(x-2)\left(x+\dfrac{9}{2}\right)$