Factor the following. 3x^3+49=x^2+147x
To factor the given expression, 3x^3 + 49 = x^2 + 147x, we need to rewrite it in a form where one side is equal to zero.
Rearranging the terms, we get:
3x^3 - x^2 - 147x + 49 = 0
Now, let's try to factor this expression. First, we can look for any common factors among the terms. In this case, we don't see any common factors.
Next, we can check if it is a quadratic trinomial. A quadratic trinomial can be factored into two binomials. However, our expression is a cubic polynomial, so we need to try a different approach.
One approach is to use synthetic division or the Rational Root Theorem to find any possible rational roots. However, in this case, the equation does not have any rational roots.
Therefore, we can conclude that the given expression cannot be factored further using traditional factoring techniques.
3x^3 - x^2 - 147x + 49 = 0
a little inspection and rearranging yields
3x^3-147x - x^2+49
3x(x^2-49) - (x^2-49)
(3x-1)(x+7)(x-7)