SOLUTION: Which of the following trinomials is prime over the set of rational numbers? A x2 – 9x + 12 B x2 – x – 12 C x2 + 4x – 12 D x2 + 7x + 12

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Question 416193: Which of the following trinomials is prime over the set of rational numbers?
A x2 – 9x + 12
B x2 – x – 12
C x2 + 4x – 12
D x2 + 7x + 12
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

Note: trinomials that are prime over the set of rational numbers will NOT factor.

A Tinomial ax^2 + bx + c 'will factor' if (b^2-4ac)is a perfect square or zero.



A. x2 – 9x + 12   81-48 = 33  Prime  ( 33 is NOT a perfect square)

B. x2 – x – 12    1+48  = 49 (49 is a perfect square)  factoring results:  (x-4)(x+3)

C. x2 + 4x – 12  16+48  = 64 (64 is a perfect square)  factoring results:   (x+6)(x-2)

D. x2 + 7x + 12   49-48 = 1  (1 is a perfect square)   factoring results:   (x+3)(x+4)