Question

Factors of x^2-7x-10

Answer 1

Answer:

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

Step-by-step 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 $(x-2)(x-5)$.