
Let q(n) = -n**5 + 3*n**2 - n. Let u(k) = 40*k**5 + 290*k**4 + 405*k**3 - 5*k**2 - 85*k. Let f(l) = -15*q(l) - u(l). Solve f(r) = 0.
-10, -1, 0, 2/5
Let w be (1 + 1)*2717/1760 + -3. Let h(o) be the second derivative of -17/24*o**3 + 0 + w*o**5 - o + 3/4*o**2 - 1/3*o**4. Suppose h(q) = 0. Calculate q.
-1, 2/7, 3
Determine p so that -4/5*p**3 - 548/5*p**2 + 19044/5 - 18492/5*p = 0.
-69, 1
Let u = -262/335 + 13894/2345. Factor u*y**2 - 4*y + 4/7*y**4 - 20/7*y**3 + 8/7.
4*(y - 2)*(y - 1)**3/7
Let j = -572907 - -572907. Let -966/5*r**3 + j + 882/5*r**2 + 0*r - 2/5*r**5 + 86/5*r**4 = 0. Calculate r.
0, 1, 21
Let y(g) be the first derivative of g**8/19320 - g**7/2415 - g**6/345 + 20*g**3/3 - g - 103. Let v(z) be the third derivative of y(z). Factor v(a).
2*a**2*(a - 6)*(a + 2)/23
Let i(p) be the third derivative of p**7/525 + 2*p**6/75 + 7*p**5/50 + 11*p**4/30 + 8*p**3/15 + 5498*p**2. Factor i(b).
2*(b + 1)**2*(b + 2)*(b + 4)/5
Let z be ((-153)/(-85))/((-3)/(-5)). Suppose z*w - 4*w + 5 = j, -2*j + 10 = -w. Solve -1/8*p + w + 1/4*p**3 + 0*p**4 - 1/8*p**5 + 0*p**2 = 0 for p.
-1, 0, 1
Let f(w) = 20*w**3 - 20*w**2 + 5. Let j be (1/(-1))/(2/10). Let h(c) = c**3 + c**2 + 1. Let q be -1 - (208/13 + -18). Let o(l) = j*h(l) + q*f(l). Factor o(z).
5*z**2*(3*z - 5)
Let t(j) be the first derivative of 2*j**3/21 - 220*j**2/7 + 24200*j/7 + 876. Factor t(n).
2*(n - 110)**2/7
Let 4/9*s**2 + 1/9*s**3 - 55/3*s + 0 = 0. What is s?
-15, 0, 11
Let l(x) = x**2 - 7*x + 20. Let a be l(6). Suppose 3*m + 2*s + 2 = 1, s + a = 3*m. Factor -u**3 + 5*u**2 - 4*u**3 - 3 + 2*u**m + 4*u + u**3.
-(u - 3)*(u + 1)*(2*u - 1)
Let m = 9 + -12. Let k be (m + 1)/((-20)/150). Suppose 54 - 51*g**3 - 30 - k*g**4 - 18*g**2 + 6*g + 54*g = 0. What is g?
-2, -2/5, 1
Suppose q - 27 = -2*q. Suppose q = 4*z + 1. Suppose -2*k**z - 6*k + 2*k**2 - 2*k**2 = 0. Calculate k.
-3, 0
Suppose 2936/5*i**2 - 1077512/5*i - 2/5*i**3 + 0 = 0. What is i?
0, 734
Let p(a) be the first derivative of 79*a + a**5 + 68*a - 100*a**2 + 2833*a**4 - 2823*a**4 - 22*a + 10*a**3 + 127. Solve p(j) = 0.
-5, 1
Let c(g) = -2*g**2 + 4*g - 1. Let k be c(3). Let d(q) = 2*q**3 + 13*q**2 - 2*q + 39. Let p be d(k). Factor 19/4*z**2 - 3/2*z + 21/4*z**3 - z**p + 0.
-z*(z - 6)*(z + 1)*(4*z - 1)/4
Let u(o) = 2*o**2 + 65*o + 80. Let j be u(-31). Let v be (-6)/(-10) + (336/(-35) - j). Suppose 27/4*n**2 - 13/2*n**3 - 1 - n + 7/4*n**v = 0. What is n?
-2/7, 1, 2
Suppose 6*t = -4*v + 2*t + 20, 3*t = 4*v - 13. Let -202*x**4 - 2*x**3 + 801*x**5 - 773*x**5 + 56*x**v + 166*x**2 - 20 - 26*x = 0. What is x?
-1, -2/7, 1/2, 1, 5
Let t(i) be the third derivative of i**10/604800 + i**9/34560 + i**8/13440 + i**5/60 + 3*i**3 - i**2 - 2. Let l(h) be the third derivative of t(h). Factor l(y).
y**2*(y + 1)*(y + 6)/4
Let s(y) be the third derivative of -y**5/20 + 9*y**4/2 + 80*y**3 - 13*y**2. Find o such that s(o) = 0.
-4, 40
Let y(d) = 3*d - 1. Suppose k - n = 3, n = 3*k - 3*n - 6. Let o be y(k). What is q in 3*q**2 - 5*q**2 - 2*q**3 - 17*q + o*q = 0?
-1, 0
Let v be (-12 + 410/35)/((-5)/7). Let p = -4 + 4. Factor v*a**4 - 2/5*a**2 + p - 2/5*a + 2/5*a**3.
2*a*(a - 1)*(a + 1)**2/5
Let t(r) be the second derivative of 3/4*r**4 - 11/60*r**5 + 0 - 2*r**2 - 2/9*r**3 - 31*r. Find k such that t(k) = 0.
-6/11, 1, 2
Let v be 1*(-1)/84*-140. Let -37/3*j**3 - v*j**4 - 16/3 - 68/3*j - 28*j**2 = 0. What is j?
-4, -2, -1, -2/5
Suppose -327 = -248*i + 139*i. Let s(b) be the first derivative of 18 + 0*b - 1/18*b**i - 1/3*b**2. Factor s(q).
-q*(q + 4)/6
Let x be (-2)/(9/60*4/12). Let z be (-5 + 5)/(x/4). Factor z + 1/2*m**3 - 1/2*m + 1/4*m**4 - 1/4*m**2.
m*(m - 1)*(m + 1)*(m + 2)/4
Suppose -f = -5*n - 13, f - 7 = -5*n + 6. Suppose 3*h = -g + f, -5*g - 2*h + 26 = -0*h. Factor -3*p**3 + 34*p + g*p**2 - 26*p - p**3.
-4*p*(p - 2)*(p + 1)
Let q(g) be the first derivative of g**4/3 + 332*g**3/9 + 1510*g**2/3 + 7300*g/3 - 2547. Determine m, given that q(m) = 0.
-73, -5
Factor 356/5*z + 4/5*z**2 + 696/5.
4*(z + 2)*(z + 87)/5
Let i be -18*(-3 - 14/(-6)). Suppose 4*r**3 - 10*r**2 - 2*r**3 + 162*r - i*r**2 + 5*r**2 - 19*r**2 = 0. Calculate r.
0, 9
Let m = -4022 - -2256. Let s = m - -1766. Factor 1/2*t**4 + 0*t**2 + s*t + 1/2*t**5 - t**3 + 0.
t**3*(t - 1)*(t + 2)/2
Suppose 3*t - 4*t = 5*v - 115, 0 = -2*t. Find c such that 3*c**4 - c + c**5 + 22*c**3 + 5*c - v*c**3 - 3*c**2 - 4*c = 0.
-3, -1, 0, 1
Let d be 6/(-5)*(260/104 + (-12)/4). Factor 0*z + d*z**2 + 8/5*z**3 - 3/5*z**4 + 0.
-z**2*(z - 3)*(3*z + 1)/5
Let z(c) be the third derivative of c**6/1080 - 49*c**5/540 + 667*c**4/216 - 529*c**3/18 - 4*c**2 + 74*c + 2. What is b in z(b) = 0?
3, 23
Let m be ((-18)/(-16))/3 + (-9588)/(-544). Suppose -m*a - 4*o = -20*a - 12, 0 = -a + 3*o - 10. Factor 2/5*p**a - 8/5 + 0*p.
2*(p - 2)*(p + 2)/5
Let w be -13 + 187/308*48 + -15. Let -4/7*l + 10/7*l**2 + 0 + 22/7*l**3 + w*l**4 = 0. Calculate l.
-2, -1, 0, 1/4
Let a(c) be the second derivative of c**6/195 + 2*c**5/65 + c**4/26 + 3840*c. Solve a(l) = 0.
-3, -1, 0
Let s = -52 - -56. Solve -26*n**2 + 31*n**2 - s*n - 46*n = 0 for n.
0, 10
Let r(t) = -3*t**2 - 2*t + 5. Let l(b) = 40*b**2 - 4204*b - 2238798. Let x(z) = -2*l(z) - 28*r(z). Let x(v) = 0. Calculate v.
-1058
Let m(y) be the first derivative of -y**5/270 - 2*y**4/27 - 16*y**3/27 + 2*y**2 - 5*y + 45. Let d(i) be the second derivative of m(i). Factor d(w).
-2*(w + 4)**2/9
Let u = 165 - 405. Let n be -2 + u/(-105) - (-316)/70. What is c in 2/5*c**4 + 0 + n*c**2 - 13/5*c**3 - 9/5*c = 0?
0, 1/2, 3
Let t(o) be the first derivative of o**4/4 - 3*o**3 + 15*o**2/2 - 3*o - 35. Let m be t(7). Factor m - 7*z**3 + 3*z**2 + 7*z**4 - 8*z**4 + 5*z**3 + 8*z.
-(z - 2)*(z + 1)**2*(z + 2)
Determine v, given that -342*v**2 + 2/7*v**3 + 136458*v - 18148914 = 0.
399
Let b be 26 + (-832)/520*351/24. Factor -22/5 - 1/5*v**2 + b*v.
-(v - 11)*(v - 2)/5
Suppose 0 = 2*j - 4*v - 20, -6*j + v = -5. Let m(y) be the first derivative of j*y - 19 + 10/9*y**3 + 0*y**2 - 1/6*y**4. Factor m(o).
-2*o**2*(o - 5)/3
Let s = 34/3 - 11. Let h be 1*(-29 - -39) + -10. Factor -1/3*m**2 + h + s*m.
-m*(m - 1)/3
Let l be (-4)/((-3)/(1 + 2)). Suppose 4 = 3*j - l*v, 4*j + 3*v - 2 = -5. Factor -1/2*h**2 + j - 3/2*h.
-h*(h + 3)/2
Let q(v) = -44*v**2 - 21*v + 23. Let b be q(1). Let j be (-96)/b*11/44. Factor -12/7*h**3 - 12/7*h**2 - j*h**4 + 0 - 4/7*h.
-4*h*(h + 1)**3/7
Let p(n) be the third derivative of n**8/84 - 2*n**7/7 - 17*n**6/30 + n**5 + 8*n**4/3 - 1972*n**2. Determine v, given that p(v) = 0.
-1, 0, 1, 16
Suppose 6*v - 42 + 18 = 0. Let j be (v/(-6) - 0)*(-81)/324. Factor -8/3*y + 0*y**3 + 0 - 8/3*y**2 + 2/3*y**4 + j*y**5.
y*(y - 2)*(y + 2)**3/6
Let a(x) be the second derivative of 1/35*x**5 + 0 + 0*x**2 - 5/84*x**4 + 61*x - 1/210*x**6 + 1/21*x**3. Factor a(j).
-j*(j - 2)*(j - 1)**2/7
Let x(d) be the first derivative of -d**4/4 - 2*d**3/3 + d**2/2 - 4*d + 2. Let a be x(-3). Find l such that -24*l**4 - a*l**5 + 11*l**4 + 15*l**4 = 0.
0, 1
Let n(x) be the first derivative of 3*x**4/4 - 22*x**3 + 114*x**2 - 216*x + 179. Factor n(t).
3*(t - 18)*(t - 2)**2
Let u(o) = 2*o**2 - 27*o + 90. Let m be u(8). Let g be m/(-8) + (-370)/(-200). Suppose -g*y**2 + 2/5*y**3 + 36/5 - 6/5*y = 0. What is y?
-2, 3
Let c = -1/7174 + 3714339/3587. Let b = c - 1035. Determine w so that 0 - 1/2*w**2 - b*w = 0.
-1, 0
Find k such that -47/2*k**2 + 651/2*k - 2205/2 + 1/2*k**3 = 0.
5, 21
Suppose -1144 = -661*t + 1768 - 929. Factor -5324 - 726*h - 1/2*h**t - 33*h**2.
-(h + 22)**3/2
Let h(y) be the first derivative of -2*y**3/3 + 78*y**2 - 154*y + 2050. Factor h(p).
-2*(p - 77)*(p - 1)
Let w be (-19)/(-7) + -3 - (-66)/(-14). Let t be (42/(-18) + 1)/(w/10). Solve 16/3*r + 2/3*r**3 - t - 10/3*r**2 = 0 for r.
1, 2
Let q(b) be the second derivative of 11/20*b**4 + 9/50*b**5 - b - 54 + 1/50*b**6 + 0*b**2 + 3/5*b**3. Factor q(t).
3*t*(t + 1)*(t + 2)*(t + 3)/5
Let q(w) = -w**3 + w + 1. Let a(l) = 21*l**3 - 32*l**2 - 121*l + 109. Let k(h) = 2*a(h) + 46*q(h). Determine n, given that k(n) = 0.
-11, -6, 1
Let y be (5 - 2) + (-1739826)/579906. Let l = y + 1299431/64434. Suppose l*g**2 + 22/3*g + 2/3 = 0. Calculate g.
-2/11
Let m = 2890 - 1938. Let p = -950 + m. Solve -16/3*i + 2/3*i**p + 32/3 = 0 for i.
4
Let n = 15150 + -15146. Find q, given that 123/2*q**3 + 9*q**n - 363/4 - 495/8*q + 327