Question

which of the following represents the factorization of the trinomial below x^2-17x+30

Answer 1

Hello, if $x_1$ and $x_2$ are two zeroes, we can write

$x^2-17x+30=(x-x_1)(x-x_2)=x^2-(x_1+x_2)x+x_1\cdot x_2$

It means that the coefficients in x must be equal, meaning

$x_1+x_2=17=2+15$

and the constant terms must be equal, meaning

$x_1\cdot x_2=30 = 2 * 15$

So the zeroes are 2 and 15.

$x^2-17x+30=x^2-15x-2x+30\\\\=x(x-15)-2(x-15)\\\\\boxed{=(x-2)(x-15)}$

Thank you