0*v + 5*r = 9*v - 15, 5*v - 3*r - 37 = 0. Let b(c) be the second derivative of 0*c**v + 0 + 0*c**2 + 0*c**3 + 0*c**4 - 9*c + 1/75*c**6. Factor b(a).
2*a**4/5
Factor 0*c - 486/5*c**4 - 1976/5*c**2 - 1968/5*c**3 + 0 + 2/5*c**5.
2*c**2*(c - 247)*(c + 2)**2/5
Suppose -9 - 11 = -5*f. Suppose -3*i = 2*m - 9, -i = -m - 2*i + f. Solve -m*c**2 + 20*c + 17*c**2 + 5*c**3 - 34*c**2 = 0 for c.
0, 2
Let t(k) be the first derivative of -5*k**4/4 - 10*k**3/3 + 2035*k**2/2 - 14520*k - 1247. Suppose t(g) = 0. What is g?
-24, 11
Let l(j) be the third derivative of 187*j**6/40 + 181*j**5/60 - 47*j**4/3 + 2*j**3/3 - 784*j**2. Solve l(b) = 0 for b.
-1, 2/187, 2/3
Suppose 32/5 + 0*a**2 - 2/15*a**5 + 8/3*a**3 - 128/15*a - 2/5*a**4 = 0. What is a?
-6, -2, 1, 2
Let b be (-44299)/(-20006) + 6/(-28). Factor 2/3 + 2/15*y**3 - 2/3*y**b - 2/15*y.
2*(y - 5)*(y - 1)*(y + 1)/15
Let t(o) be the second derivative of 3 + o + 23/20*o**5 + 54*o**2 + 15/2*o**4 + 27*o**3 + 11/120*o**6 + 1/336*o**7. Determine u so that t(u) = 0.
-6, -2
Suppose 0 = -3*o - 0*o + 9*o - 18. Find n, given that 0*n - 3/4*n**o + 0 + 3/4*n**2 = 0.
0, 1
Factor -57600/7 - 960/7*s - 4/7*s**2.
-4*(s + 120)**2/7
Let k be -7 + 8 + 1 + 1. Suppose 0 = k*f + i - 10, 4*i + 7 - 20 = -3*f. Let 2 - c**2 + c**f - 3*c + c**2 = 0. What is c?
-2, 1
Let p(l) be the second derivative of 6*l + 0*l**6 + 1/105*l**7 - 3/50*l**5 - 6 + 0*l**2 + 0*l**3 - 1/15*l**4. Factor p(w).
2*w**2*(w - 2)*(w + 1)**2/5
Factor -5802*l**2 - 210 + 2923*l**2 - l**3 + 43*l + 2891*l**2.
-(l - 14)*(l - 3)*(l + 5)
Let j be ((69/9)/(2/(-9)))/(1125/(-4000)). Suppose -j*f - 2/3*f**2 - 16928/3 = 0. What is f?
-92
Let w be (9/(-21))/((-1320)/308) + (-111)/(-90). Factor 10/9*r**2 - 2/9*r**3 - w*r + 0.
-2*r*(r - 3)*(r - 2)/9
Let k(h) = -2*h**4 - 10*h**3 + 9*h**2 - 13*h. Let x(v) = 2*v**4 + 10*v**3 - 4*v**2 + 12*v. Let m(d) = -4*k(d) - 5*x(d). Solve m(t) = 0 for t.
-2, -1, 0
Solve -149/5*i**3 - 2/5*i**4 + 381/5*i**2 + 77/5 - 307/5*i = 0.
-77, 1/2, 1
Let n(o) = -o**3 - 40*o**2 + 157*o + 223. Let b(i) = -i**3 - 84*i**2 + 317*i + 445. Let t(p) = 3*b(p) - 5*n(p). Determine c so that t(c) = 0.
-1, 5, 22
Let m(j) be the first derivative of j**7/42 - j**5/20 - 55*j - 61. Let o(l) be the first derivative of m(l). Factor o(a).
a**3*(a - 1)*(a + 1)
Let n be ((-306)/(-6885))/((-78)/20 - (0 - (-1 - -5))). Factor -8/9*v + n*v**2 + 4/9.
4*(v - 1)**2/9
Let t be (-288 - (-6)/1)/(-2). Let h be 188/t - -10*(-2)/(-12). Factor 1/4*k**h + k + 0 + k**2.
k*(k + 2)**2/4
Determine q so that 90*q**3 + 691*q**2 - 1633*q**2 + 686*q**2 + 168*q - 2*q**4 = 0.
0, 1, 2, 42
Factor -22/3 - 2/21*h**2 - 52/7*h.
-2*(h + 1)*(h + 77)/21
Let s(t) be the third derivative of t**5/160 + t**4/16 - 45*t**3/16 + 3*t**2 + 33. Factor s(i).
3*(i - 5)*(i + 9)/8
Determine a, given that 79/6*a - 27/2*a**2 + 1/2*a**4 - 3 + 17/6*a**3 = 0.
-9, 1/3, 1, 2
Suppose 339*k + 4044 = 1687*k. Factor -10/3 - 1/6*o**2 + 1/3*o**k - 41/6*o.
(o - 5)*(o + 4)*(2*o + 1)/6
Factor 29000/3 + 1/3*i**4 - 9700/3*i + 390*i**2 - 59/3*i**3.
(i - 29)*(i - 10)**3/3
Let d be 2 + 11/((-154)/(-2220)) - (-197 - -193). Let -2400/7*g + 1346/7*g**2 + d - 100/7*g**3 + 2/7*g**4 = 0. Calculate g.
1, 24
Let k = -228026 + 228029. Let u = 12 - 7. Factor -2/7*x**u + 0*x**k + 2/7*x + 4/7*x**4 + 0 - 4/7*x**2.
-2*x*(x - 1)**3*(x + 1)/7
Let o = -4/69913 - -2377054/209739. What is z in 16/3*z**2 + 0*z + 2/3*z**5 + 0 + 20/3*z**4 + o*z**3 = 0?
-8, -1, 0
Let r(a) = -81*a - 79. Let l be 144/(-80) - 8/(-10). Let n be r(l). Factor -5/2*i**4 - 5/2*i**3 + 5/2*i + 0 + 5/2*i**n.
-5*i*(i - 1)*(i + 1)**2/2
Let z = -431/7 - -2617/35. Let q = -127/10 + z. Factor y**4 + 1/2*y**5 + 0 - q*y**3 + 0*y - y**2.
y**2*(y - 1)*(y + 1)*(y + 2)/2
Let s(z) be the third derivative of 5*z**7/189 - z**6/108 - 16*z**5/135 + z**4/9 + 622*z**2. Find t, given that s(t) = 0.
-6/5, 0, 2/5, 1
Let o(u) = 63*u**3 - 195*u**2 + 204*u - 66. Let d(b) = b**4 - b**3 - b**2 - 1. Let p(c) = 3*d(c) + o(c). Determine h, given that p(h) = 0.
-23, 1
Let u(g) be the second derivative of -g**5/30 - 11*g**4/6 - 32*g**3 - 256*g**2/3 + 59*g - 14. Suppose u(z) = 0. What is z?
-16, -1
Suppose u = -3*n + 4386, -2*n - 3*n = 4*u - 17579. Solve u*k**2 - k**4 - 4407*k**2 - 2*k**4 + 9*k**3 = 0.
0, 1, 2
Let a(p) = 2*p**5 + 3*p**4 - p**3 + 1. Let n(v) = -4*v**5 + 56*v**4 - 548*v**3 + 544*v**2 - 112*v - 16. Let q(o) = 16*a(o) + n(o). Let q(s) = 0. Calculate s.
-7, 0, 2/7, 1, 2
Factor 763*q - 17*q**3 + 108*q**2 + 695*q + 14*q**3 + 5*q**3.
2*q*(q + 27)**2
Let o be (3 - (-105)/(-20))/(3/(-2)). Let p = 958 + -946. Suppose 3*h**3 + p*h**2 - o*h**4 + 0 + 0*h = 0. What is h?
-2, 0, 4
Let j(y) be the third derivative of -2*y**7/105 - y**6/10 + y**5/5 + 11*y**4/6 + 4*y**3 + y**2 + 2*y + 27. Suppose j(t) = 0. Calculate t.
-3, -1, 2
Suppose 5*u - 40 = -3*u. Factor -3266*m**5 - 784*m - 1012*m**3 + 1325*m**2 + 355*m**2 + 120*m**4 + 3262*m**u.
-4*m*(m - 14)**2*(m - 1)**2
Let g(c) be the third derivative of c**8/168 + 187*c**7/105 + 4417*c**6/30 + 4231*c**5/15 - 2945*c**4/4 - 2883*c**3 + 5660*c**2. Solve g(v) = 0.
-93, -1, 1
Let i(c) = -c**3 + 11*c**2 - 29*c + 19. Let j = 84 + -37. Let q(w) = -46 - j + w + 92. Let o(h) = -i(h) + 6*q(h). Factor o(a).
(a - 5)**2*(a - 1)
Suppose 6*u = -59 + 41. Let b(g) = -7*g**2 + 26*g - 25. Let i(q) = -20*q**2 + 80*q - 76. Let t(m) = u*i(m) + 8*b(m). Suppose t(k) = 0. What is k?
1, 7
Let l(w) be the first derivative of -w**4/34 + 650*w**3/51 - 26243*w**2/17 - 53138*w/17 + 829. Factor l(o).
-2*(o - 163)**2*(o + 1)/17
Let w = 11205 - 11200. Let p(n) be the third derivative of 0 - 2/39*n**3 - 1/390*n**w + 0*n - 1/52*n**4 + 4*n**2. Find o, given that p(o) = 0.
-2, -1
Let m(q) = -8 - 90 + 35 + 2*q - 13*q. Let j be m(-16). Factor -4*c**2 + c**4 - j*c**3 + 36*c**3 + 42*c**3 - 4*c + 36*c**3.
c*(c - 2)*(c + 1)*(c + 2)
Let o(v) be the second derivative of v**5/180 - 7*v**4/72 - v**3 - 31*v**2/2 - 15*v. Let m(b) be the first derivative of o(b). Factor m(u).
(u - 9)*(u + 2)/3
Let w be 6/(-15) + 30 + (-2048)/80. Determine q so that 0 - 3/2*q + q**3 + 1/2*q**5 + 2*q**2 - 2*q**w = 0.
-1, 0, 1, 3
Factor 348*c + 6675*c**2 - 3338*c**2 - 3336*c**2.
c*(c + 348)
Let f(l) be the second derivative of -l**6/30 + 17*l**5/15 - 21*l**4/2 - 54*l**3 + 11*l**2/2 + 9*l. Let n(w) be the first derivative of f(w). Factor n(d).
-4*(d - 9)**2*(d + 1)
Let u(z) be the second derivative of 3*z**5/20 + 4*z**4 + 41*z**3/2 + 39*z**2 - 7884*z. Find h such that u(h) = 0.
-13, -2, -1
Let l(w) be the second derivative of -1/6*w**4 + 6*w + 3 - 5/6*w**3 + 1/80*w**5 + 0*w**2. Factor l(m).
m*(m - 10)*(m + 2)/4
Suppose -20*n = -118*n + 686. Let t(i) be the second derivative of 6*i + 0*i**4 - 5/42*i**n + 0*i**2 - 5/6*i**3 + 0 + 0*i**6 + 1/2*i**5. Factor t(y).
-5*y*(y - 1)**2*(y + 1)**2
Let u = 93606 + -93603. Factor -1/2*q**4 - 4*q + 2*q**2 + 0 + q**u.
-q*(q - 2)**2*(q + 2)/2
Let c = 17171/2547 + -1845/283. Suppose c*p**4 + 0*p**2 + 8/9*p**3 - 32/9 - 32/9*p = 0. What is p?
-2, 2
Suppose 5 = 4*c + 17, -2*c = 5*d - 24. Let i = d + -5. What is u in -2*u - 3 + 1 + 2*u**3 + 2*u**4 + i - u**4 = 0?
-1, 1
Suppose -4*n - 39 = -5*y, 5*y = 2*n + 54 - 7. Suppose 0*x + y*x = 231. Factor x*b**2 - 2*b**2 - 3*b**2 - b**3 - 4*b**2 - 36*b.
-b*(b - 6)**2
Let f = 1/79 + -379/48664. Let j = 459/616 + f. Solve 3/4*v + j*v**3 + 3/2*v**2 + 0 = 0 for v.
-1, 0
Factor -8450/3 + 1495*x + 1/3*x**3 - 44*x**2.
(x - 65)**2*(x - 2)/3
Let b(c) be the third derivative of -41/75*c**5 + 0*c + 2/525*c**7 - 13/50*c**6 + 0 + 13/10*c**4 + 223*c**2 + 16/3*c**3. Solve b(z) = 0 for z.
-1, 1, 40
Let k(b) = -3*b**3 + 7*b**2 + 8*b - 10. Let c be k(3). Let x be (-28 - -22)*2/c. Factor 7/4*n**2 - 1/4*n - 1/2 + 3/2*n**x.
(n + 1)*(2*n - 1)*(3*n + 2)/4
Let s be 932/14*869/(-21032) - -3. Let j = 1/1673 + s. Let -1/2*w**2 + 2 + j*w**3 - w = 0. What is w?
-2, 2
Suppose 10*t - 4 - 36 = 0. Suppose 0*y + y**5 - 22*y**2 + 15*y**2 - 7*y**4 + 15*y**3 - 6*y**2 + t*y = 0. What is y?
0, 1, 4
Suppose 196*c - 3071 = -131. Factor c + 3/2*f**2 + 21/2*f.
3*(f + 2)*(f + 5)/2
Let d(l) = -4*l**2 + 86*l - 24. Let n be d(21). Let m be (-10)/90 + 56/n. Let -3/2*w**m - 3/4 + 3/4*w**4 + 3/2*w + 0*w**2 = 0. What is w?
-1, 1
Suppose -5*g + 28 = 12*s, -s + 952*g - 947*g = -24. Solve -88/5*o + 24/5*o**s - 18/5*o**5 + 118/5*o**3 - 12*o**2 