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# Algebra

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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.

Degree:

Constant term:

Coefficient of x^6:

Jun 23, 2024

#1
+85
+1

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

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
+85
+1

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

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