Factor the trinomial 5x^2+21x+4
To factor the trinomial 5x^2 + 21x + 4, we need to find two binomials that multiply together to give us the trinomial.
First, we look for two numbers whose product is equal to the product of the coefficient of the quadratic term and the constant term. In this case, the coefficient of the quadratic term is 5 and the constant term is 4, so the product is 5*4 = 20.
Next, we look for two numbers whose sum is equal to the coefficient of the linear term, which in this case is 21. The two numbers that satisfy these conditions are 1 and 20, since 1*20 = 20 and 1+20 = 21.
Now, we split the linear term into two terms using the two numbers we found: 5x^2 + 1x + 20x + 4.
Next, we group the terms together: (5x^2 + 1x) + (20x + 4).
Now, we factor out the common factors from each group: x(5x + 1) + 4(5x + 1).
Finally, we factor out the common binomial: (x + 4)(5x + 1).
Therefore, the factored form of the trinomial 5x^2 + 21x + 4 is (x + 4)(5x + 1).