Factor the following polynomial.

28x^3+59x^2+13x

x (28 x^2 + 59 x + 13)

x (4 x + 1)(7 x + 13)

To factor the polynomial 28x^3 + 59x^2 + 13x, we can use the common factor method.

First, we look for any common factors among the coefficients of the terms. In this case, all the coefficients are prime numbers, so there are no common factors.

Next, we can try to factor out a common variable factor. Looking at the polynomial, we can see that x appears in every term. So, we can factor out x:

x(28x^2 + 59x + 13)

Now, we need to factor the quadratic expression 28x^2 + 59x + 13. We can try to find two binomials that multiply together to give this quadratic expression.

To do this, we need to find two numbers that multiply to give 28 * 13 = 364 and add up to 59.

The factors of 364 are: 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364.

Among these factors, we can see that 7 and 52 add up to 59.

So, we can rewrite the quadratic expression as:

x(28x^2 + 7x + 52x + 13)

Now, we group the terms:

x((28x^2 + 7x) + (52x + 13))

We can factor out the common factor from each grouped term:

x(7x(4x + 1) + 13(4x + 1))

Notice that we have a common binomial factor of (4x + 1) in both terms. We can factor it out:

x(4x + 1)(7x + 13)

So, the factored form of the polynomial 28x^3 + 59x^2 + 13x is:

x(4x + 1)(7x + 13)