Final answer:
To factor the GCF from the expression 32a⁵b⁷c³+12a¹b²-36a⁶bc⁴, identify the numerical GCF and the lowest powers of each variable in all terms, which leads to factoring out 4a¹b²c³.
Step-by-step explanation:
The subject of this question is factoring the greatest common factor (GCF) out of a polynomial expression in Mathematics. To factor out the GCF of the expression 32a⁵b⁷c³+12a¹b²-36a⁶bc⁴, first identify the GCF of the numerical coefficients (32, 12, -36), and then look for the lowest powers of each variable present in all the terms.
The numerical GCF is 4. For the variables, the lowest power of a is a¹, for b it's b², and for c it's c³. Factoring out 4a¹b²c³, we get:
4a¹b²c³(8a⁴b⁵+3a⁸-9a⁵bc)