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What is the coefficient of $x^2$ in $(x^3 + x^2 + x + 1)(5x^4 - 8x^3 + 17x^2 + 4x - 18)$?

 Dec 4, 2023
 #1
avatar+259 
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. Let's simplify the given expression: (x3+x2+x+1)(5x4−8x3+17x2+4x−18)

We can use the distributive property to multiply the two polynomials.

Steps to solve:

1. Distribute the first polynomial: 5x7−8x6+17x5+4x4−18x3+x2(5x4−8x3+17x2+4x−18)+x(5x4−8x3+17x2+4x−18)+1(5x4−8x3+17x2+4x−18)

 

2. Distribute the second polynomial: 5x7−8x6+17x5+4x4−18x3+5x6−8x5+17x4+4x3−18x2+x(5x4−8x3+17x2+4x−18)+1(5x4−8x3+17x2+4x−18)

 

3. Distribute the third polynomial: 5x7−8x6+17x5+4x4−18x3+5x6−8x5+17x4+4x3−18x2+5x5−8x4+17x3+4x2−18x+1(5x4−8x3+17x2+4x−18)

 

4. Distribute the fourth polynomial: 5x7−8x6+17x5+4x4−18x3+5x6−8x5+17x4+4x3−18x2+5x5−8x4+17x3+4x2−18x+5x4−8x3+17x2+4x−18

 

5. Combine like terms: 5x7−3x6+14x5+18x4−5x3+3x2−18x+4x−18

 

6. Combine like terms: 5x7−3x6+14x5+18x4−5x3+3x2−14x−18

 

7. Combine like terms: 5x7−3x6+14x5+18x4−5x3+3x2−14x−18

 

Answer: 5x7−3x6+14x5+18x4−5x3+3x2−14x−18

 Dec 4, 2023

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