What is the factored form of 6x2 + 17x + 5?
the product of 5 and sum 17 there is no number.
6x^2 : 3x * 2x
5: 5 *1
factor = (2x+5)(3x+1)
Good luck
To find the factored form of the quadratic expression 6x^2 + 17x + 5, we need to factorize it by identifying two binomial factors.
Step 1: Write down the expression: 6x^2 + 17x + 5
Step 2: Look for two numbers that multiply to give the product of the coefficient of x^2 (6) and the constant term (5). In this case, 6 * 5 = 30. We need to find two numbers whose product is 30 and whose sum is the coefficient of x (17).
The numbers that fit these conditions are 15 and 2. 15 * 2 = 30, and 15 + 2 = 17.
Step 3: Split the middle term (17x) into two terms using the two numbers (15 and 2) we found in the previous step. Write the quadratic expression as follows:
6x^2 + 15x + 2x + 5
Step 4: Group the terms and factor by grouping:
(6x^2 + 15x) + (2x + 5)
3x(2x + 5) + 1(2x + 5)
Step 5: Notice that we now have a common binomial factor (2x + 5). Factor it out:
(3x + 1)(2x + 5)
Therefore, the factored form of 6x^2 + 17x + 5 is (3x + 1)(2x + 5).