Answer: 2s²(39 - 74s - 280s)(s - 2)(s + 7/2)
Explanation:
To factor the polynomial 78s - 148s³ - 560s² completely, we can first factor out a common factor of 2s²:
2s²(39 - 74s - 280s)
Then, we can factor the quadratic expression inside the parentheses using the quadratic formula:
s = [-(-74) ± √((-74)² - 4(39)(-280))] / 2(39)
s = [74 ± √(54724)] / 78
s = [74 ± 2√13681] / 78
s = [74 ± 2×117] / 78
Therefore, the roots of the quadratic expression are:
s = 2 or s = -7/2
Substituting these values back into the factored expression, we get:
2s²(39 - 74s - 280s) = 2s²(39 - 74(2) - 280(2)) = -1240s²
2s²(39 - 74s - 280s) = 2s²(39 - 74(-7/2) - 280(-7/2)) = 2450s²
So the completely factored form of the polynomial is:
2s²(39 - 74s - 280s)(s - 2)(s + 7/2)