Write Prime if the expression cannot be factored:?

Question

s^2-s-6 : Is the answer (s+3)(s-2)
y^2-4y-5:Is the answer prime
6f^2+5f+2: Is the answer prime


Ok so I did these and got them wrong. Well my teacher said two are wrong but he didn't tell me which ones. I read the chapter over and over and I keep coming up with the same answers can someone just show me the procedure rather then the answers that would be great!!

Answer 1

y^2-4y-5=(y-5)(y+1) not irreducible
6t^2+5t+2 is irreducible

Answer 2

s^2-s-6 = (s-3)(s+2)
Do you see that -3s +2s =-s which is what you need for middle term. If you had (s+3)(s-2) you would get +3s + (-2s) = +s for the middle term which would be wrong.

y^2 -4y -5 = (y-5)(y+1)
Take a quick check -5*y+1*y = -4y which is the correct middle term. So above factoring is correct.

6f^2 +5f +2 This can not be factored using real numbers because the roots are imaginary. In the given equation a= 6, b=-4 and c= 2. If b^2-4ac is negative, there are no real roots. In this case 5^2-4*6*2 = 25-48 = -23. So no real roots. This is prime.

Answer 3

(s^2) - s - 6 = (s - 3)(s + 2)
-3 + 2 = -1 which is the number for -s
-3*2 = -6
use FOIL (First, Outside, Inside, Last) to check

(y^2) - 4y - 5 = (y - 5)(y + 1)
-5 + 1 = -4 which is the number for -4y
-5*1 = -5

(6f^2) + 5f + 2
using the quadratic equation, this is found to be unfactorable which means it is prime, so this is the one you got right

Answer 4

s^2-s-6
-6
Factors are (2,3) (1,6), negative, therefore terms have different signs.
-1
combination of above factors that add to -1 (-3, 2)
(s-3)(s+2)
Wrong Signs




y^2-4y-5
-5
The factors for -5 are (1,5)
-4
Negative, so the signs for the two terms must be different.
Need them to add up to -4
-5, +1
Therefore (y+1)(y-5)

6f^2+5f+2

+6f
Factors of 6 are 1,6 or 3,2
+5,+2
Both positive, therefore both terms must be positive and add to 5 somehow, not possible with 1,6 only 3,2
+2, Factors are (1,2)
(3y+1)(2y+2)....doesn't add...check with quadratic and it doesn't work. PRIME

Answer 5

y^2-4y-5=(y-5)(y+1) not irreducible
6t^2+5t+2 is irreducible

Answer 6

y^2-4y-5: (y-5)(y+1)

6f^2+5f+2: (3f+1)(2f+1)