Answer: A
Step-by-step explanation:
The most direct method to factor the polynomial is to factor by grouping. All we have to do is the split the polynomial in half, and then factor each half. Be sure to carry the signs and to insert a plus in the middle.
[tex](25x^3-25x^2)+(-x+1)[/tex] [factor each polynomial separately]
[tex]25x^2(x-1)+-1(x-1)[/tex] [pair together the separate factors]
[tex](25x^2-1)(x-1)[/tex] [the first factor is factorable by difference of squares]
[tex](5x+1)(5x-1)(x-1)[/tex] [multiply last 2 factors]
[tex](5x+1)(5x^2-5x-1x+1)[/tex] [combine like terms]
[tex](5x+1)(5x^2-6x+1)[/tex]
The only option that has this option is A.
The expression 25x³-25x²-x+1 cannot be factored any further. Therefore the correct answer is D) (5x+1)(5x²+6x-1).
To factor the expression 25x³-25x²-x+1, we can first try to find any common factors among the terms. In this case, we can factor out a common factor of 1, resulting in 1(25x³-25x²-x+1).
Next, we can try to factor out a common factor among the remaining terms. Unfortunately, there are no common factors among them.
Therefore, the given expression cannot be factored any further, and the answer is option D) (5x+1)(5x²+6x-1).
The question asks us to factor the expression 25x³-25x²-x+1. Factoring is a mathematical process that involves breaking down complicated expressions into products of simpler ones. When factoring expressions, it's important to look for common factors and to apply different factoring techniques such as grouping, the difference of squares, or the sum and difference of cubes.
