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Answer :
Final answer:
To factor the greatest common factor from 14x⁵ - 28x⁴ + 35x³, we find that 7x³ is the GCF. Factoring it out leaves us with the expression 7x³(2x² - 4x + 5).
Explanation:
To factor the greatest common factor (GCF) from the expression 14x⁵ - 28x⁴ + 35x³, we first need to find the common factors of the numerical coefficients (14, 28, and 35) and the variable terms (x⁵, x⁴, x³). The GCF of the numerical coefficients is 7, and the GCF of the variable terms is x³, since that is the highest power of x that divides each term.
Therefore, factoring out the GCF 7x³, the expression becomes:
7x³(2x² - 4x + 5).
Each term in the original expression is now divisible by 7x³, and after dividing each term by 7x³, we are left with the factors inside the parentheses, which cannot be simplified further.
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