How would you factor this (3x^2+x)+ (3x+1).... Can you please show ur steps on how u get the answer so I understand how to do the problem. Thank You
To factor the expression (3x^2 + x) + (3x + 1), you can follow these steps:
Step 1: Recognize that this is a polynomial expression with two terms inside parentheses.
Step 2: Begin by factoring each term separately.
For the first term (3x^2 + x), we look for the greatest common factor (GCF) between the coefficients and variables. The common factor between 3 and 1 (coefficient of x^2 and x) is 1. For the variables, we can factor out x since it is common to both terms. Factoring out the GCF gives us:
(3x^2 + x) = x(3x + 1)
For the second term (3x + 1), there is no common factor to factor out, so we leave it as is.
Step 3: Combine the factored terms.
Now that we have factored each term individually, we can combine them:
(x(3x + 1)) + (3x + 1)
At this point, notice that both terms inside the parentheses are (3x + 1). We can factor out this common binomial factor, resulting in:
(3x + 1)(x + 1)
Therefore, the fully factored form of the expression (3x^2 + x) + (3x + 1) is (3x + 1)(x + 1).