Question

Factors of x^2-7x-10

Answer 1

`x^2-7x-10` is consider prime (also known as not factorable over the rationals)

Explanation:

`x^2-7x-10` is consider prime.

`x^2-7x-10` comparing to
`ax^2+bx+c` gives you
`a=1,b=-7,c=-10`.

Since a=1, all you have to do is find two numbers that multiply to be -10 and add up to be -7.

Here are all the integer pairs that multiply to be -10:

-1(10)

1(-10)

2(-5)

-2(5)

Now you will see none of those pairs adds to be -7:

-1+10=9

1+(-10)=-9

2+(-5)=-3

-2+5=3

So this is not factorable over the real numbers.

Now if you had something like
`x^2-7x+10`, that would be a different story. You can find two numbers that multiply to be 10 and add up to be -7. Those numbers are -2 and -5 since -2(-5)=10 and -2+(-5)=-7. So the factored form of
`x^2-7x+10` is
`(x-2)(x-5)`.