To factor the expression completely, let’s first simplify it. We start by combining like terms.
The expression is:
49x² + 81 – 7x + 92 – 7x + 92 – 7x + 97x + 9 – 7x + 9
First, combine all the linear terms (-7x, -7x, -7x, 97x, -7x):
-7x – 7x – 7x + 97x – 7x = 97x – 35x = 62x
Now, combine constant terms (81, 92, 92, 9, 9):
81 + 92 + 92 + 9 + 9 = 283
Now, we have:
49x² + 62x + 283
This expression does not factor neatly into integers, so we consider using the quadratic formula to find the roots or attempting to find any common factors directly.
We could check for factors of 49 and 283 but since they don’t seem to lend themselves to simple factoring, we determine that:
This expression is already in its simplified form as 49x² + 62x + 283, and cannot be factored into simpler terms with rational coefficients.
In summary, the factored form remains as:
49x² + 62x + 283