+1610 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:
+1622 \(f(x)\cdot{g(x)} = (-7x^4 - 3x^2 + 2)(2x^8-3x^7+5x^6+3x^5-11x^4+3x^3-18x^2+17x-5)\)
Leading term is the term with the highest degree:\(-7x^4\cdot{2x^8}=-14x^{12}\)
Thus, the leading coefficient is -14
The (highest) degree of the function is 12
We know that the constant term must stem from the product of the constants of the original function. 2 * -5 = -10
Coefficient of x^6 would be -3x^2 * 3x^3 + 2*5x^6 + -7x^4 *-18x^2 = 7*18 - 9 + 10 = 127
