Answer :
Final answer:
The expression 7x^5-21x^4+14x^3 factors completely to 7x^3(x^2 - 3x + 2) by first identifying and pulling out the greatest common factor, 7x^3.
Explanation:
We are trying to factor completely the polynomial 7x^5-21x^4+14x^3. Factoring completely means expressing an algebraic expression as a product of its simplest factors.
The first step in factoring any expression is to identify the greatest common factor. In our problem, the greatest common factor is 7x^3. We can write out all of the terms divided by 7x^3:
7x^5 ÷ 7x^3 = x^2
-21x^4 ÷ 7x^3 = -3x
14x^3 ÷ 7x^3 = 2
We use the above results as the terms for a new polynomial and multiply it by our factor. Here's our completely factored equation:
7x^3(x^2 - 3x + 2)
Learn more about Factoring here:
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Answer:
7x³ (x-2) (x-1)
Step-by-step explanation:
7x⁵-21x⁴+14³
= 7x³ (x²-3x+2) <----- factor out the gcf
= 7x³ (x-2) (x-1)
