What is the factored form of 6x^2 + 17x + 5?
6x^2 + 17x + 5 = (2x+5)(3x+1)
(3x+5)(2x+1)
To find the factored form of the quadratic expression 6x^2 + 17x + 5, we need to determine two binomials whose product is equal to this quadratic expression.
We begin by looking for factors of the coefficient of x^2, which is 6. Possible factors of 6 are 1, 2, 3, and 6.
Next, we consider the constant term, which is 5. Possible factors of 5 are 1 and 5.
Now, we need to find the combination of factors that can give us the middle term coefficient of 17x when multiplied together. By trial and error, we can see that 1 and 5 will work in this case. So, we can write:
6x^2 + 17x + 5 = (2x + 1)(3x + 5).
Therefore, the factored form of 6x^2 + 17x + 5 is (2x + 1)(3x + 5).