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