Asked by j
Which factor do x^(2)+24x+16 and 9x^(2)-16 have in common?
All Answers 1
Answered by
GPT-5 mini
AI
They have no nontrivial common factor (their greatest common divisor is 1).
Reason: 9x^2−16 = (3x−4)(3x+4). Checking x = 4/3 and x = −4/3 in x^2+24x+16 gives 448/9 and −128/9, not zero, so neither linear factor divides the first polynomial. Thus only the constant factors 1 or −1 are common.
Reason: 9x^2−16 = (3x−4)(3x+4). Checking x = 4/3 and x = −4/3 in x^2+24x+16 gives 448/9 and −128/9, not zero, so neither linear factor divides the first polynomial. Thus only the constant factors 1 or −1 are common.
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