Answer :
Final answer:
The greatest common factor (GCF) from the polynomial 7x⁴−21x³+35x² is 7x². After factoring out the GCF, the polynomial becomes 7x²(x²−3x+5). By distributing it back, we can confirm this is correct.
Explanation:
The student is asking to factor the greatest common factor (GCF) from the polynomial 7x⁴−21x³+35x². In this case, you inspect each term in the polynomial and find the GCF.
Here, the GCF is 7x² as it is the highest factor common to all the terms. When you factor 7x² out of each term, the expression becomes:
7x²(x²−3x+5).
The factored expression can be distributed back to the original expression to verify its accuracy. In effect, when you do 7x² * x², you get 7x⁴, when you do 7x² * -3x, you get -21x³, and when you do 7x² * 5, you get 35x², which confirms the factoring is correct.
Learn more about Factoring Polynomials here:
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