SOLUTION: Which polynomial can be factored over the set of polynomials with the integer coefficients? A) x^2+5x+10 B) x^2+5x-14 C) x^2-5x-10 D) x^2+5x+14 I have no idea even after

Question 28105: Which polynomial can be factored over the set of polynomials with the integer coefficients?
A) x^2+5x+10
B) x^2+5x-14
C) x^2-5x-10
D) x^2+5x+14
I have no idea even after reviewing my textbook how to do this? can someone explain how to get the answer?
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
Which polynomial can be factored over the set of polynomials with the integer coefficients?
A) x^2+5x+10
B) x^2+5x-14
C) x^2-5x-10
D) x^2+5x+14
I have no idea even after reviewing my textbook how to do this? can someone explain how to get the answer?
FIRST MAKE COEFFICIENT OF X^2 AS 1 BY TAKING COEFFICIENT OF X^2 AS A COMMON FACTOR.
HERE IT IS ALREADY 1.SO THIS STEP IS NOT NEEDED.
NOW CHECK WHETHER YOU CAN SPLIT THE CONSTANT TERM IN TO 2 FACTORS WHOSE SUM IS THE COEFFICIENT OF X TERM.
A) x^2+5x+10...HERE 10 HAS FACTORS OF 1&10;2&5;NONE OF WHOSE SUM IS 5..SO WE CANNOT FACTORISE THIS INTO 2 POLYNOMIALS OF INTEGER COEFFICIENTS.
B) x^2+5x-14....HERE -14 HAS FACTORS OF +7 AND -2 WHOSE SUM IS +5..SO WE CAN FACTORISE THIS INTO 2 POLYNOMIALS OF INTEGER COEFFICIENTS.
THEY ARE X+7 AND X-2
C) x^2-5x-10.......SAME AS A
D) x^2+5x+14 ......SAME AS A ...+14 CANNOT BE SPLIT AS REQUIRED.

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