Answer:
Explanation:
You want the expressions that are factors of 12x² +51x -15.
GCF
We notice that all of the coefficients are divisible by 3, and the smallest difference between coefficients is 15-12=3. This means 3 is the greatest common factor of the coefficients. With that factored out, we have ...
3(4x² +17x -5)
Factors
To factor the quadratic, we need factors of (4)(-5) = -20 that have a sum of +17. Divisors of -20 are 20, 10, 5, 4, 2, 1, -1, -2, -4, -5, -10, -20. No pair of these has a sum of +17, so there are no integer factors of the quadratic.
A graph confirms the roots are irrational.
3 is the only factor of the given quadratic seen on the list.
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Additional comment
Euclid's algorithm for finding the GCF looks at the remainder of division of the larger of two numbers by the smaller. If that remainder is a divisor of both numbers, it is the GCF. Here, 15/12 = 1 remainder 3, and 3 divides both 12 and 15. Hence 3 is their GCF.