Respuesta :
Answer:
[tex]x^2-7x-10[/tex] is consider prime (also known as not factorable over the rationals)
Step-by-step explanation:
[tex]x^2-7x-10[/tex] is consider prime.
[tex]x^2-7x-10[/tex] comparing to [tex]ax^2+bx+c[/tex] gives you [tex]a=1,b=-7,c=-10[/tex].
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 [tex]x^2-7x+10[/tex], 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 [tex]x^2-7x+10[/tex] is [tex](x-2)(x-5)[/tex].
