1. **State the problem:** We need to write the equation of the polynomial Line #2 given by $$y = a(x + 15)(x + 8)(x - 1)(x - 8)$$ with the coefficient $a = 0.9$. 2. **Recall the formula:** The polynomial is expressed in factored form with roots at $x = -15, -8, 1, 8$. 3. **Substitute the value of $a$:** $$y = 0.9(x + 15)(x + 8)(x - 1)(x - 8)$$ 4. **Expand the factors step-by-step:** First, multiply the pairs: $$(x + 15)(x + 8) = x^2 + 8x + 15x + 120 = x^2 + 23x + 120$$ $$(x - 1)(x - 8) = x^2 - 8x - x + 8 = x^2 - 9x + 8$$ 5. **Multiply the two quadratics:** $$ (x^2 + 23x + 120)(x^2 - 9x + 8) $$ Multiply term-by-term: $$x^2 \cdot x^2 = x^4$$ $$x^2 \cdot (-9x) = -9x^3$$ $$x^2 \cdot 8 = 8x^2$$ $$23x \cdot x^2 = 23x^3$$ $$23x \cdot (-9x) = -207x^2$$ $$23x \cdot 8 = 184x$$ $$120 \cdot x^2 = 120x^2$$ $$120 \cdot (-9x) = -1080x$$ $$120 \cdot 8 = 960$$ 6. **Combine like terms:** $$x^4 + (-9x^3 + 23x^3) + (8x^2 - 207x^2 + 120x^2) + (184x - 1080x) + 960$$ $$= x^4 + 14x^3 - 79x^2 - 896x + 960$$ 7. **Multiply by $a = 0.9$:** $$y = 0.9(x^4 + 14x^3 - 79x^2 - 896x + 960)$$ $$= 0.9x^4 + 12.6x^3 - 71.1x^2 - 806.4x + 864$$ **Final answer:** $$\boxed{y = 0.9x^4 + 12.6x^3 - 71.1x^2 - 806.4x + 864}$$