Expand (2x + 3)^5 using the Binomial Theorem and Pascal’s triangle. Show all steps.
1 answer:
Answer:
32x⁵ + 240x⁴ + 720x³ + 1080x² + 810x + 243
Step-by-step explanation:
(2x + 3)⁵
₅C₀ (2x)⁵ (3)⁰ + ₅C₁ (2x)⁴ (3)¹ + ₅C₂ (2x)³ (3)² + ₅C₃ (2x)² (3)³ + ₅C₄ (2x)¹ (3)⁴ + ₅C₅ (2x)⁰ (3)⁵
Use Pascal's triangle to find nCr.
1 (2x)⁵ (3)⁰ + 5 (2x)⁴ (3)¹ + 10 (2x)³ (3)² + 10 (2x)² (3)³ + 5 (2x)¹ (3)⁴ + 1 (2x)⁰ (3)⁵
(2x)⁵ + 15 (2x)⁴ + 90 (2x)³ + 270 (2x)² + 405 (2x)¹ + 243
32x⁵ + 240x⁴ + 720x³ + 1080x² + 810x + 243
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Step-by-step explanation:
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Answer:
Step-by-step explanation:
a) x = 1.786 & -1.120
Explanation:
Turning points are points where the derivative equals zero. Solving the derivative for the values of X will give the answer to part a.
The derivative of this equation .
Solving the equation using the quadratic formula we get 1.786 & -1.120
b) x = -3, x=0 and x=2
Explanation:
The solution to this equation are the points where the graph intersects with the x axis. Looking at the graph we can see that these points are -3 , 0 and 2