Final answer:
To factor the trinomial 4x³-7x+1, we can find two binomials that multiply to give the trinomial. By trying different combinations of factors, we find that (-4x+1)(x-1) is the correct factorization.
Step-by-step explanation:
To factor the trinomial 4x³-7x+1, we need to find two binomials whose product equals the trinomial. We can start by looking for factors of the constant term (1) and the leading coefficient (4). In this case, the factors of 1 are 1 and -1, and the factors of 4 are 4 and 1. We can now try different combinations of these factors to see which ones add up to the middle term (-7x). After some trial and error, we find that (-4x+1)(x-1) is the correct factorization of the trinomial.