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Determine all of the following for f(x) \cdot g(x), where f(x) = -7x^4-3x^2 + 2 and g(x) = 2x^8 - 3x^7 + 5x^6 + 3x^5 - 11x^4 + 3x^3 - 18x^2 + 17x - 5.

 

Leading term:

Leading coefficient:

Degree:

Constant term:

Coefficient of x^6:

 Jun 23, 2024

Best Answer 

 #1
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\( f(x) \cdot g(x) f(x) = -7x^4-3x^2 + 2,\space g(x) = 2x^8 - 3x^7 + 5x^6 + 3x^5 - 11x^4 + 3x^3 - 18x^2 + 17x - 5.\) 

a) the leading term would be \(-7x^4 * 2x^8\) or -\(14x^{12}\)

b) the coefficient of that would be -14

c) degree of 12 since its x^12

d) the constant term would be \(2*-5\) or -10

e) well to get \(x^6\) you would need either \(x^5*x\),  \(x^4*x^2\),or \(x^3*x^3\). g(x) has an x^5 but f(x) has no x term. so no \(x^5*x\). for the second case you have either -7*-18 or -3*-11, adding gets you 159. f(x) has no x^3 term so final answer \(\boxed{159}\). at least i think so :P  ¯\_(ツ)_/¯

 Jun 23, 2024
 #1
avatar+85 
+1
Best Answer

\( f(x) \cdot g(x) f(x) = -7x^4-3x^2 + 2,\space g(x) = 2x^8 - 3x^7 + 5x^6 + 3x^5 - 11x^4 + 3x^3 - 18x^2 + 17x - 5.\) 

a) the leading term would be \(-7x^4 * 2x^8\) or -\(14x^{12}\)

b) the coefficient of that would be -14

c) degree of 12 since its x^12

d) the constant term would be \(2*-5\) or -10

e) well to get \(x^6\) you would need either \(x^5*x\),  \(x^4*x^2\),or \(x^3*x^3\). g(x) has an x^5 but f(x) has no x term. so no \(x^5*x\). for the second case you have either -7*-18 or -3*-11, adding gets you 159. f(x) has no x^3 term so final answer \(\boxed{159}\). at least i think so :P  ¯\_(ツ)_/¯

shmewy Jun 23, 2024

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