+2653 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:
+84 \( f(x) \cdot g(x) f(x) = -7x^4-3x^2 + 2,\space g(x) = 2x^8 - 3x^7 + 5x^6 + 3x^5 - 11x^4 + 3x^3 - 18x^2 + 17x - 5.\)
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)_/¯
+84 \( f(x) \cdot g(x) f(x) = -7x^4-3x^2 + 2,\space g(x) = 2x^8 - 3x^7 + 5x^6 + 3x^5 - 11x^4 + 3x^3 - 18x^2 + 17x - 5.\)
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)_/¯
