factorise 8x^2+14x+3

Sure, here is the step-by-step factorization of the expression 8x^2+14x+3:

Step 1: Multiply the coefficient of x^2 (which is 8) with the constant term (which is 3). So, 8*3 = 24.

Step 2: Now, we need to find two numbers that multiply to 24 (from step 1) and add up to 14 (the coefficient of x). The numbers are 12 and 2 because 12*2 = 24 and 12+2 = 14.

Step 3: Rewrite the middle term (14x) as the sum of 12x and 2x. So, the expression becomes 8x^2 + 12x + 2x + 3.

Step 4: Factor by grouping. The first two terms can be grouped together and the last two terms can be grouped together. This gives us 4x(2x + 3) + 1(2x + 3).

Step 5: Notice that (2x + 3) is a common factor. So, the expression can be written as (4x + 1)(2x + 3).

So, the factorization of 8x^2 + 14x + 3 is (4x + 1)(2x + 3).