Final answer:
To factor the trinomial 5x²-21x+4, find two numbers that multiply to 20 (5*4) and add to -21. Rewrite the middle term, group, factor by grouping, and obtain the factored form: (5x - 1)(x - 4).
Step-by-step explanation:
To factor the trinomial 5x²-21x+4, we are looking for two binomials that when multiplied together, give us the original trinomial. We will use the factoring by grouping method, as this is not a simple trinomial where we can apply the reverse FOIL method directly.
First, we need to find two numbers that multiply to a*c (5*4=20) and add up to b (-21). We're looking for factors of 20 that add up to -21. Those numbers are -1 and -20.
Now we rewrite the middle term of the trinomial using -1 and -20:
5x² - 1x - 20x + 4
Next, we group the terms:
(5x² - 1x) + (-20x + 4)
Factor out the greatest common factor from each group:
x(5x - 1) - 4(5x - 1)
Now we see that (5x - 1) is a common factor:
(5x - 1)(x - 4)
This is our factored form of the trinomial 5x²-21x+4.