14xe^{\left(x-2\right)}-12e^{\left(x-2\right)}-7x^{3}+20x^{2}-26x+12

asked by guest
on Jan 22, 2025 at 11:04 am



You asked:

Evaluate the expression: 14xex−2−12ex−2−7x3+20x2−26x+1214 x {e}^{x - 2} - 12 {e}^{x - 2} - 7 {x}^{3} + 20 {x}^{2} - 26 x + 12

MathBot Answer:

Evaluated



14xex−2−12ex−2−7x3+20x2−26x+12=−7x3+20x2+14xex−2−26x−12ex−2+12\displaystyle 14 x {e}^{x - 2} - 12 {e}^{x - 2} - 7 {x}^{3} + 20 {x}^{2} - 26 x + 12 = - 7 x^{3} + 20 x^{2} + 14 x e^{x - 2} - 26 x - 12 e^{x - 2} + 12

Expanded

14xex−2−12ex−2−7x3+20x2−26x+12=−7x3+20x2+14xexe2−26x−12exe2+1214 x {e}^{x - 2} - 12 {e}^{x - 2} - 7 {x}^{3} + 20 {x}^{2} - 26 x + 12 = - 7 x^{3} + 20 x^{2} + \frac{14 x e^{x}}{e^{2}} - 26 x - \frac{12 e^{x}}{e^{2}} + 12

Factored

14xex−2−12ex−2−7x3+20x2−26x+12=−(7x−6)(x2−2x−2exe2+2)14 x {e}^{x - 2} - 12 {e}^{x - 2} - 7 {x}^{3} + 20 {x}^{2} - 26 x + 12 = - \left(7 x - 6\right) \left(x^{2} - 2 x - \frac{2 e^{x}}{e^{2}} + 2\right)

ee is Euler's number, a mathematical constant that is approximately 2.718282.71828.

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