 - 19. Let n(o) be the first derivative of x(o). Suppose n(g) = 0. What is g?
-5, 3
Let o = -428 + 431. Suppose 3*k**3 - 80*k**2 + 8*k**4 - 23*k**o - 30*k**3 + 14*k**4 - 27*k**4 = 0. Calculate k.
-8, -2, 0
Suppose -98*v + 0*v - 244*v = -1026. Let 0*u - 9/5*u**5 + 0 - 4/5*u**2 - 6*u**4 + 23/5*u**v = 0. What is u?
-4, 0, 1/3
Let s(p) be the second derivative of p**7/273 - 6*p**6/65 + 109*p**5/130 - 42*p**4/13 + 196*p**3/39 + 1450*p. Factor s(q).
2*q*(q - 7)**2*(q - 2)**2/13
Let f(s) = -s**2 - 3*s + 4. Let r be f(-4). Let c(p) = -p**3 + 2*p**2 + 6*p - 7. Let i be c(3). Factor -4/11*b + r - 1/11*b**i.
-b*(b + 4)/11
Suppose -8*b = -22*b + 42. Suppose -i = -b - 3. Determine j, given that -6*j**4 + 60*j**2 - 31*j**3 - 12*j - i*j**3 - 26*j**3 + 22*j**5 - j**5 = 0.
-2, 0, 2/7, 1
Suppose 22 = 10*c - 28, -3*c + 30 = 5*h. Let f(p) be the first derivative of -p**2 + 8 - h*p + 1/3*p**3. Factor f(s).
(s - 3)*(s + 1)
Let u(n) = 3*n + 46. Let j be u(-15). Let o be (3 + 14)/(-1*(-1)/j). Factor 5*y**5 - o*y**3 + 31*y - 15 - 6*y + 10*y**2 + 8*y**3 + 5*y**4 - 21*y**3.
5*(y - 1)**3*(y + 1)*(y + 3)
Let g(j) be the first derivative of -j**4 - 28*j**3/3 - 28*j**2 - 32*j - 5707. Factor g(r).
-4*(r + 1)*(r + 2)*(r + 4)
Let i(u) = -u**3 + 35*u**2 + 17*u + 686. Let o be i(36). Factor -s - 1/3*s**o + 0.
-s*(s + 3)/3
Suppose 0 = 10*f - 37 - 43. Determine d, given that 9*d**2 - d**2 + 10*d**5 + 12*d**4 + 18*d**3 - f*d**5 = 0.
-4, -1, 0
Let l(g) be the second derivative of -g**5/80 + 15*g**4/16 - 29*g**3/8 - 253*g**2/2 - 120*g. Let y(d) be the first derivative of l(d). Factor y(s).
-3*(s - 29)*(s - 1)/4
Let p = 894 + -889. Suppose p*g - 26 = -7*z + 4*z, 0 = 2*z - g. Factor -2*x - 1/2*x**z + 0.
-x*(x + 4)/2
Factor 2/15*o**2 + 44/5 + 10/3*o.
2*(o + 3)*(o + 22)/15
Suppose 0 = 228*w - 468 - 672. Let n(p) be the third derivative of -1/24*p**4 + 1/420*p**7 + 0*p + 0*p**6 - 1/40*p**w + 0*p**3 + 14*p**2 + 0. Factor n(u).
u*(u - 2)*(u + 1)**2/2
Suppose 424*z + 913/2*z**2 + 11/2 + 38*z**3 = 0. Calculate z.
-11, -1, -1/76
Let v(w) be the third derivative of w**5/20 - 9*w**4/8 + 7*w**3 + 30*w**2 + 11. Solve v(h) = 0.
2, 7
Let b = -562255 + 9008561/16. Let l = b + -4669/16. Solve 31*w + 567*w**4 + 363/2*w**2 + 729/4*w**5 + l*w**3 + 2 = 0 for w.
-2, -1/3, -2/9
What is u in 4374 + 4050*u**2 + 96*u**4 + 1032*u**3 + 13851/2*u = 0?
-4, -9/4
Suppose 6 = -l - 3*b + 17, -l - b + 7 = 0. Let g(r) = 3*r**2 + 1. Let p be g(-1). Factor -4*d**3 - d**2 - 3*d**p - 5*d**3 - l*d**2.
-3*d**2*(d + 1)*(d + 2)
Find q, given that -16/15*q**4 - 375086/15*q - 462/5*q**3 - 13282/5*q**2 + 48778/5 = 0.
-29, 3/8
Let i(y) = -3*y**4 - y**2 + y. Let s(b) = b**5 - 39*b**4 - 8*b**3 - 19*b**2 + 20*b + 6. Let l(h) = 39*i(h) - 3*s(h). Find n such that l(n) = 0.
-2, -1, 1, 3
Let s(w) be the second derivative of -w**7/315 + w**6/60 + 8*w**5/45 + w**4/3 - 64*w**2 - 4*w - 1. Let o(m) be the first derivative of s(m). Factor o(h).
-2*h*(h - 6)*(h + 1)*(h + 2)/3
Let k(y) be the second derivative of 3*y**5/100 - 27*y**4/4 - 137*y**3/5 + 12095*y. Factor k(g).
3*g*(g - 137)*(g + 2)/5
Suppose -7824 - 2116 = -35*z. Let s = z - 282. Determine w so that 0*w**3 - 6/7*w**s + 0 + 2/7*w**4 + 4/7*w = 0.
-2, 0, 1
Let q = 1310 - 41919/32. Let y(n) be the second derivative of 1/8*n**3 - 3/160*n**5 + 0*n**2 - q*n**4 - 17*n + 0. Solve y(t) = 0.
-2, 0, 1
Let l(q) be the first derivative of 18*q**5/35 + 51*q**4/4 + 575*q**3/7 - 300*q**2/7 - 1500*q/7 + 5241. Let l(i) = 0. What is i?
-10, -5/6, 1
Let p(d) = -d + 10. Suppose 0 = -3*f + 15 + 6. Let h be p(f). Let y**4 - 24*y**2 - 23*y**2 + 49*y**2 - h*y**3 = 0. Calculate y.
0, 1, 2
Let k be 1/(-2)*(-53 - -43). Let v(p) be the second derivative of 0 - 33*p - 8/5*p**2 + 1/5*p**4 - 2/25*p**k + 8/15*p**3 - 2/75*p**6. Factor v(i).
-4*(i - 1)**2*(i + 2)**2/5
Let v be 96/(-144) + (-5)/((-195)/31046). Let s = 796 - v. Factor -4/13 - s*c**2 + 10/13*c + 2/13*c**3.
2*(c - 2)*(c - 1)**2/13
Let i(p) = -p + 2. Let l be i(0). Factor -147*q**4 + 10*q**2 - 14*q**3 - 4*q - 4*q + 150*q**4 + 10*q**l.
q*(q - 2)**2*(3*q - 2)
Let g(k) be the second derivative of -k**7/70 + k**6/20 + k**5/20 - k**4/4 + 99*k**2/2 - 19*k. Let b(j) be the first derivative of g(j). Factor b(u).
-3*u*(u - 2)*(u - 1)*(u + 1)
Let j(v) = -v**3 + 5*v**2 + 2*v - 42. Suppose 5 + 25 = 5*i. Let o(q) = q**3 - 5*q**2 - 3*q + 43. Let y(u) = i*o(u) + 5*j(u). Suppose y(m) = 0. Calculate m.
-3, 4
Let j(n) = 996*n**2 + 3985*n + 6. Let x be j(-4). Suppose -2/9 + 0*h + 2/9*h**x = 0. Calculate h.
-1, 1
Let l = 2187 + -2154. Let g be ((-632)/3318)/((-4)/l). Factor g*p + 1/7*p**2 + 10/7.
(p + 1)*(p + 10)/7
Let w(j) = -4*j + 39. Let r be w(12). Let d(n) = -n**3 - 5*n**2 + 5*n - 38. Let q be d(r). Determine m so that 6*m + 2*m + 243*m**2 + 6 - q*m**2 = 0.
-3, -1
Let g(z) be the second derivative of -z**5/60 + 13*z**4/4 + z**3/18 - 39*z**2/2 + 96*z + 2. Factor g(d).
-(d - 117)*(d - 1)*(d + 1)/3
Determine o, given that 114*o + 2/3*o**2 + 340/3 = 0.
-170, -1
Let n(a) be the first derivative of -2*a**6/9 - 4*a**5/3 - 7*a**4/3 - 4*a**3/3 + 36. Factor n(w).
-4*w**2*(w + 1)**2*(w + 3)/3
Let j(m) = -39*m**2 + 504*m + 531. Let l(h) = -3*h**2 - h + 1. Let w(q) = j(q) - 12*l(q). Determine i, given that w(i) = 0.
-1, 173
Let i(q) = 9*q**3 - 6465*q**2 - 2786499*q - 400314941. Let k(o) = 8*o**3 - 6465*o**2 - 2786493*o - 400314942. Let s(j) = 13*i(j) - 14*k(j). Factor s(w).
5*(w + 431)**3
Let b = 141 - 105. Solve -b*g**2 - 60*g**3 + 107*g**3 + 84*g - 44 - 51*g**3 = 0 for g.
-11, 1
Let z be 54/24 - (4/18 + (-51)/108). Let n(g) be the first derivative of -20*g - 20*g**2 + z*g**4 + 9 - 5*g**3 + g**5. Solve n(s) = 0 for s.
-2, -1, 2
Let v(u) be the first derivative of -735*u**4/4 + 4270*u**3/3 + 1250*u**2/3 + 40*u - 2107. Factor v(c).
-5*(c - 6)*(21*c + 2)**2/3
Suppose -18*l = -u - 19*l + 114, 2*l - 341 = -3*u. Factor 4*q**3 + 9 - u*q**2 - q**3 - q + 104*q**2 - 2*q.
3*(q - 3)*(q - 1)*(q + 1)
Let b(z) be the third derivative of z**6/120 + z**5/6 + 3*z**4/8 - 1871*z**2. Factor b(t).
t*(t + 1)*(t + 9)
Let s(w) be the second derivative of -w**5/20 - 157*w**4/12 - 1040*w**3 - 3042*w**2 - w + 171. Factor s(j).
-(j + 1)*(j + 78)**2
Let k(g) be the first derivative of -g**3/9 - 7*g**2/3 - 13*g/3 - 2299. Factor k(z).
-(z + 1)*(z + 13)/3
Let m(h) = h**3 + 3*h**2 - 2*h - 4. Let p be m(-3). Factor -2*z**p + 6*z**2 + 2*z - z**2 + z**3 + 0*z**3.
z*(z + 1)*(z + 2)
Let l(v) = -v**3 + 11*v**2 + 59*v + 18. Let m be l(15). Suppose 3*u = -5*s + 4, 5 = m*u + 3*s - 1. Factor -2*y + 3*y**2 + 1/2*y**4 - 2*y**u + 1/2.
(y - 1)**4/2
Let b(q) be the third derivative of q**8/2184 + 4*q**7/39 + 1537*q**6/260 - 3384*q**5/65 + 1296*q**4/13 - 378*q**2 - 14. Solve b(o) = 0.
-72, 0, 1, 3
Let f = -11721 + 11721. Let d(s) be the second derivative of 1/28*s**4 + f + 3/7*s**3 + 12/7*s**2 - 14*s. Determine a so that d(a) = 0.
-4, -2
Let d(k) be the first derivative of k**4/66 + 5*k**3/33 - 63*k - 99. Let p(a) be the first derivative of d(a). Factor p(q).
2*q*(q + 5)/11
Let p(s) be the third derivative of -s**7/42 - 61*s**6/10 - 8979*s**5/20 - 5329*s**4/12 + 620*s**2 + 5*s + 1. Factor p(r).
-r*(r + 73)**2*(5*r + 2)
Let p(b) be the third derivative of b**6/480 - b**5/60 - 11*b**4/96 - b**3/4 - 1739*b**2. Factor p(x).
(x - 6)*(x + 1)**2/4
Let r(w) = 3*w - 27. Let m be r(15). Factor -4*g + 16*g - g**2 - 2*g**2 + 5*g**2 + m.
2*(g + 3)**2
Let p be (-4 + 5416/(-1))*(-24)/60. Suppose -10*h = -2208 + p. Factor -3/2*z**3 + 3/2*z + 0*z**2 + 3/4*z**h - 3/4.
3*(z - 1)**3*(z + 1)/4
Let x = 89996/5 + -17998. Determine g so that 8/5 - 14/5*g**2 - x*g**4 + 8/5*g - 4*g**3 = 0.
-2, -1, 2/3
Determine k so that 772/3*k - 1/3*k**3 - 776/3 - 190/3*k**2 = 0.
-194, 2
Suppose -2/3*a**4 + 14*a**3 - 48*a - 100/3*a**2 + 0 = 0. What is a?
-1, 0, 4, 18
Factor -303*v + 1141*v**2 + 1298*v**2 + 2*v**3 - 450 - v**3 - 2291*v**2.
(v - 3)*(v + 1)*(v + 150)
Let o = -15/7 - -93/14. Factor -15/2*t**2 + 0 + 3/2*t**5 - 3*t + 3/2*t**4 - o*t**3.
3*t*(t - 2)*(t + 1)**3/2
Let d(m) be the first derivative of m**6/72 + 5*m**5/12 + 15*m**4/8 - 40*m**3 + 22. Let q(w) be the third derivative of d(w). Factor q(g).
5*(g + 1)*(g + 9)
Suppose 0 = 1097*b - 1094*b + 18. Let k be 47/6 + b + (-3)/(-18). Determine j, given that 0 - 5/2*j + 1/2*j**k = 0.
0, 5
Let z(k) = -k**3 + k**2 +