+262 (a) Let b be a constant. What is the smallest possible degree of the polynomial \(f(x)+b\cdot g(x)\), where \(f(x) = 2x^5 - 6x^4 - 4x^3 + 12x^2 + 7x - 5 \)and \(g(x) = x^5 - 3x^4 - 2x^3 - 6x^2 + 14x - 10\)?
(b) Let f be a cubic polynomial such that f(0) = 5, f(1) = -5, f(2) = 8, and f(3)=13. What is the sum of the coefficients of f?
(c) What is the coefficient of x in \((x^3 + x^2 + x + 1)^7\)?
(d) There exists a polynomial f(x) and a constant k such that
\((x^2 - 2x - 5) f(x) = 2x^4 - x^3 + kx^2 - 19x - 10.\)What is k?
+129771 (a)
If b = -2 the addition of the polynomials = 24x^2 -21x + 15 = the smallest possible polynomial
(d)
2x^2 + 3x + (16 + k)
x^2 - 2x - 5 [ 2x^4 - x^3 + kx^2 -19x -10 ]
2x^4 -4x^3 -10x^2
_________________________________
3x^3 + (10 + k)x^2 -19x
3x^3 -6 x^2 -15x
_______________________________
(16+ k)x^2 - 4x - 10
(16 + k)x^2 - (32 - 2k)x - 80 - 5k
_____________________________
(28 + 2k)x + (70 + 5k)
(28 + 2k) + (70 + 5k) = 0
98 = -7k
-98/7 = -14 = k
