Factor completely. If a polynomial is prime, state this
9 + 8t^2 - 18t
8 t^2 -18 t + 9
probably has (4 3)(2 3) because 12+6=18
so
(4t - 3)(2t - 3)
To factor the given polynomial, we will look for common factors among the terms and then apply the techniques for factoring quadratic expressions.
The given polynomial is:
9 + 8t^2 - 18t
Step 1: Group the terms:
(9) + (8t^2 - 18t)
Step 2: Factor out common factors:
The terms (8t^2 - 18t) have a common factor of 2t:
(9) + 2t(4t - 9)
Now, we have factored out the common factor of 2t.
Step 3: Check for further factoring:
The expression (4t - 9) cannot be factored further using integer coefficients. Therefore, it is a prime expression.
So, the completely factored form of the polynomial 9 + 8t^2 - 18t is:
2t(4t - 9)
Note: If the expression (4t - 9) could be factored further, we would continue factoring until we obtain irreducible factors.