1)/5
Let f(d) = 53 - 111 + 59. Suppose -1 = -l + n, -4*l - 14 = 5*n + 9. Let x(z) = -3*z**3 + z**2 - 2. Let h(o) = l*f(o) - x(o). Determine g so that h(g) = 0.
0, 1/3
Let k be ((-16)/(-40))/(2/20). Suppose 3*c**2 - 2*c**2 + 9*c - k*c**2 = 0. Calculate c.
0, 3
Suppose -9 = -3*r + 2*u, u + 12 = 5*u. Suppose -3*p + 1 = -r. Solve -4*i - 3 - 18*i**2 + 15*i**p - 2*i = 0.
-1
Let v be 1 + 11 - (-3660)/976. Determine n so that -15/4*n**2 - 1/4*n**3 - v*n - 49/4 = 0.
-7, -1
Suppose -4*g - o + 85 = 13, 5*o + 58 = 2*g. Factor -3*r + r + 20*r**4 - 3*r**2 - 38*r**4 + g*r**4.
r*(r - 2)*(r + 1)**2
Let x(w) be the second derivative of -w**4/60 + 8*w**2/5 - 245*w. Find r such that x(r) = 0.
-4, 4
Let d(y) be the first derivative of y**5 + 5*y**4/4 - 65*y**3/3 - 125*y**2/2 - 60*y - 72. Factor d(s).
5*(s - 4)*(s + 1)**2*(s + 3)
What is f in -5*f**4 + 93*f + 67*f + 640 - 29*f**2 - 29*f**3 - 91*f**2 - 21*f**3 = 0?
-4, 2
Let u be (0 - -3) + 3 + -4. Factor 8 - 4*t + 4*t**3 - 6*t**3 + 10*t**u + 6*t**3 - 18*t**2.
4*(t - 2)*(t - 1)*(t + 1)
Let q = -2 - -2. Let t = -2250 + 11252/5. Determine w, given that -t*w + q + 2/5*w**2 = 0.
0, 1
Let v(t) be the second derivative of -1/42*t**4 + 0 + 12*t - 1/7*t**2 - 2/21*t**3. Suppose v(p) = 0. Calculate p.
-1
Let b(s) be the first derivative of 0*s - 1/4*s**4 + 1/2*s**2 - 23 + 0*s**3. Determine q, given that b(q) = 0.
-1, 0, 1
Let a(p) be the third derivative of -p**9/9072 + p**8/2520 + p**7/360 + p**6/270 - 11*p**3/3 + 16*p**2. Let f(m) be the first derivative of a(m). Factor f(l).
-l**2*(l - 4)*(l + 1)**2/3
Factor 0*t - 17610*t**2 + 17605*t**2 - 5*t.
-5*t*(t + 1)
Let h(t) be the first derivative of -t**4/4 + 16*t**3/3 + 17*t**2/2 - 238. Factor h(n).
-n*(n - 17)*(n + 1)
Let l(f) be the third derivative of 0 - 5*f**2 - 7/30*f**4 + 8/75*f**5 + 0*f + 4/15*f**3 - 1/75*f**6 + 1/420*f**8 - 4/525*f**7. Find b, given that l(b) = 0.
-2, 1
Let x(s) be the third derivative of s**6/480 + 7*s**5/240 - 5*s**4/96 - 25*s**3/8 - 21*s**2 - 5. Factor x(o).
(o - 3)*(o + 5)**2/4
Let u(k) be the first derivative of k**5/10 + 7*k**4/8 + 5*k**3/2 + 9*k**2/4 - 408. Factor u(c).
c*(c + 1)*(c + 3)**2/2
Suppose x + 11 = -h + 45, 2*x - 2*h = 80. Let s = -19 + x. Let 0 + 4*v - 3*v - 8*v**4 + 22*v**3 - s*v**2 + v + 2 = 0. What is v?
-1/4, 1
Let q be (-5 - (-542)/120) + (-16)/(-32). Let c(j) be the third derivative of q*j**6 + 0 - j**3 - 1/6*j**5 + 7/12*j**4 + 0*j + j**2. Factor c(k).
2*(k - 3)*(k - 1)**2
Let t(a) = a**2 + 29*a + 2. Let r be t(-29). Suppose 0 = 2*y - 11 + 7, r*y = 4*g - 16. Let 0 + 1/3*v**g - 1/3*v**2 - 1/3*v**3 + 1/3*v**4 + 0*v = 0. Calculate v.
-1, 0, 1
Let k be 21/56*-2*(-14)/120. Let h(z) be the third derivative of -2*z**2 - 1/6*z**3 + 0 + 1/120*z**7 - k*z**5 - 1/240*z**6 + 0*z + 5/24*z**4. Factor h(a).
(a - 1)**2*(a + 2)*(7*a - 2)/4
Let u(z) be the second derivative of 1/160*z**5 + 0*z**2 + 0*z**3 + 0 - 1/48*z**4 - 12*z. Solve u(d) = 0 for d.
0, 2
Factor -15/4*p**4 - 33/2*p**3 - 21/4 - 27*p**2 - 39/2*p.
-3*(p + 1)**3*(5*p + 7)/4
Factor 7/2*b**3 + 1/4*b**5 + 4*b**2 + 3/2*b**4 + 1/2 + 9/4*b.
(b + 1)**4*(b + 2)/4
Let p be -4 + 0 + (10 - 4). Factor -4*a**p + 5*a**4 - 2*a**5 - 2*a**3 - 1 - 56*a + 0*a**5 + 60*a.
-(a - 1)**3*(a + 1)*(2*a - 1)
Suppose 3*s + 101 = -367. Let g be (-378)/s + ((-42)/4)/7. Solve -g*b + 2/13*b**2 + 18/13 = 0 for b.
3
Let b(f) = -10*f**4 - 20*f**2 + 12*f + 28. Let g(k) = -7*k**4 - 19*k**2 + 9*k + 29. Let z(x) = 3*b(x) - 4*g(x). Factor z(v).
-2*(v - 2)**2*(v + 2)**2
Suppose -266 = 13*q - 331. Find j such that -1/8*j**q + 1/8*j**3 + 0 + 1/4*j**2 + 0*j - 1/4*j**4 = 0.
-2, -1, 0, 1
Let x(b) be the first derivative of b**6/2 - 12*b**5/5 + 15*b**4/4 - 2*b**3 + 58. Factor x(y).
3*y**2*(y - 2)*(y - 1)**2
Suppose 0 = -p + 3*o + 68, 2*o + 72 = -2*p + 3*p. Let b be (p/(-12))/(-5)*3. Solve 0*f**2 + 0*f**2 + f**2 - 8*f**3 + b*f**3 = 0 for f.
0, 1/4
Let w be 5/2 - (-50)/20*-1. Let g(d) be the third derivative of -1/75*d**6 + w*d + 0 - 2*d**2 + 7/60*d**4 + 2/15*d**3 - 1/30*d**5. Factor g(j).
-2*(j - 1)*(j + 2)*(4*j + 1)/5
Factor 12 + 4*t**4 - 8*t**3 - 35*t + 2*t**2 - 18*t**2 + 43*t.
4*(t - 3)*(t - 1)*(t + 1)**2
Let r = -47 + 50. Factor -k**3 - r*k**4 + k**2 + 5*k**2 - 12*k**3 + 16*k**3.
-3*k**2*(k - 2)*(k + 1)
Factor 11/2*x + 27/2*x**5 - 23*x**2 + 45*x**3 - 1/2 - 81/2*x**4.
(x - 1)**2*(3*x - 1)**3/2
Let j = -9746/3 + 3260. Solve 4/3 - 110/3*z**2 - j*z = 0.
-2/5, 1/11
Let n(l) = 7*l**2 + 844*l + 59643. Let v(t) = 114*t**2 + 13503*t + 954288. Let a(s) = -33*n(s) + 2*v(s). Factor a(c).
-3*(c + 141)**2
Let w(p) = -2*p - 10. Let n be (-273)/(-26)*(-2)/3. Let m be w(n). Factor 15*r - 6 + 57*r**3 + 10*r**2 - 10*r**2 + 15*r**m + 63*r**2.
3*(r + 1)**2*(r + 2)*(5*r - 1)
Suppose 11*w - 9*w - 80 = 0. Suppose 10*v + 0*v = w. Solve 0 - 1/5*j**v + 0*j - 16/5*j**2 - 8/5*j**3 = 0.
-4, 0
Determine m, given that 1/6*m + 2/3*m**2 - 1 + 1/6*m**3 = 0.
-3, -2, 1
Let v = -1/8 + 5/8. Factor -v*u**2 + 1 + 1/2*u.
-(u - 2)*(u + 1)/2
Let l(j) be the second derivative of -7*j**7/18 + 14*j**6/15 - 11*j**5/30 - j**4/3 - j**3/18 + 12*j - 2. Solve l(d) = 0 for d.
-1/7, 0, 1
Let r(k) = k**2 + 4*k - 5. Let y(l) = -l**2 - 8*l + 9. Let d(x) = -x**2 - 9*x + 10. Let p(v) = -5*d(v) + 6*y(v). Let j(b) = 6*p(b) + 5*r(b). Factor j(w).
-(w - 1)**2
Suppose 160 - 55 = 35*d. Let b(k) be the first derivative of -3/8*k**2 - 4 - 3/4*k**d + 3/20*k**5 + 3/16*k**4 + 3/2*k. Factor b(l).
3*(l - 1)**2*(l + 1)*(l + 2)/4
Suppose -3*m**3 + 17*m - 267 + 88*m - 57 - 2*m**2 + 14*m**2 - 126 = 0. Calculate m.
-6, 5
Factor 1/2*f**3 + 5/4 - 39/8*f + 9/2*f**2.
(f + 10)*(2*f - 1)**2/8
Let u(g) = g**3 + 7*g**2 - 8*g. Suppose 32 = -51*o + 47*o. Let h be u(o). Suppose -9/4*r**3 - 3/2*r**2 + 3/4*r + h = 0. What is r?
-1, 0, 1/3
Let u(d) = -d**2 - 11*d + 7. Let l be u(-8). Suppose 7*c**3 - 8*c**5 - 12*c**2 - l*c**3 - 4*c**2 - 4*c - 16*c**4 + 4*c**5 = 0. What is c?
-1, 0
Let i = -32 + 40. Solve -7*p**4 + 5*p**4 - 2*p**3 + i + 7*p + 18*p**2 - 29*p = 0.
-4, 1
Let u = 88 - 25. Suppose -h + 127 = 3*h - 5*f, -5*f = h - u. Solve 8*n - 2 + 33*n**4 - h*n**3 - 12*n**5 + n**4 + 10*n**3 = 0 for n.
-1/2, 1/3, 1
Let c(o) be the first derivative of -o**6/6 + 4*o**5/5 + o**4/4 - 4*o**3/3 - 401. Let c(p) = 0. What is p?
-1, 0, 1, 4
Find z such that 238*z**3 + 3538*z**5 - 3533*z**5 + 47*z**3 - 365*z**2 + 150*z - 75*z**4 = 0.
0, 1, 3, 10
Determine d, given that 155 + 24*d**2 + d**4 + 147 - 302 + 16*d + 9*d**3 = 0.
-4, -1, 0
Let w be 14/(-4) - -4 - (-10)/12. Factor -5/3*i + 1/3*i**2 + w.
(i - 4)*(i - 1)/3
What is o in 1024*o - 2121*o + 1001*o - 99 + 3*o**2 = 0?
-1, 33
Let d = -102 - -102. Let o(p) be the third derivative of 1/120*p**6 + 2*p**2 + 7/240*p**5 + d + 0*p + 0*p**3 - 1/48*p**4. Determine y so that o(y) = 0.
-2, 0, 1/4
Suppose -f = -15 + 10. Let y be 2/f + 64*(-4)/(-60). Solve 8/3*d**5 + 2/3*d - y*d**2 + 0 - 26/3*d**4 + 10*d**3 = 0 for d.
0, 1/4, 1
Suppose 2*w = 2*g + 62, -2*g - 24 = -4*w + 98. Find j, given that -32*j**2 - 6*j**3 + 4*j**3 + w*j**2 + 2*j**4 - 2*j**5 + 4*j**3 = 0.
-1, 0, 1
Let h = 17 + -13. Let 8*y**4 + 8*y**h - 17*y**4 + 2*y**2 - 3*y**3 + 2*y**3 = 0. What is y?
-2, 0, 1
Let p(q) = q**2 + q + 1. Let t(k) = -8*k**2 - 8*k - 5. Let w be (-2)/8 + 2442/(-88). Let j(l) = w*p(l) - 4*t(l). Factor j(i).
4*(i - 1)*(i + 2)
Let x(z) be the third derivative of 6*z**2 + 0 - 1/150*z**5 + 0*z + 4/15*z**3 + 0*z**4. Factor x(q).
-2*(q - 2)*(q + 2)/5
Let y(h) be the second derivative of 2/15*h**6 + 0 + 3/5*h**5 + h**4 + 2/3*h**3 + 0*h**2 - 4*h. Factor y(a).
4*a*(a + 1)**3
Factor -2/17*i**2 - 32/17*i - 56/17.
-2*(i + 2)*(i + 14)/17
Let r(p) = -p**2 - 8*p + 3. Let i be r(-8). Solve 3*f**4 + 3*f**4 - 2*f**5 - 14*f**i + 12*f**3 - 2*f**4 = 0 for f.
0, 1
Suppose 32*v = 3*s + 31*v - 55, 4*s = 2*v + 74. Let n(t) be the first derivative of 4/3*t**3 - s*t - 12*t**2 - 7 - 2/5*t**5 + 2*t**4. Factor n(l).
-2*(l - 3)**2*(l + 1)**2
Let c(h) be the third derivative of -h**7/2520 - h**6/240 + h**5/30 - h**4/8 + 2*h**2. Let i(o) be the second derivative of c(o). Factor i(y).
-(y - 1)*(y + 4)
Let t(m) be the first derivative of -12*m**3 + 220*m**2 - 96*m + 106. Solve t(n) = 0.
2/9, 12
Let v(m) be the third derivative of m**8/1680 - m**7/75 + 11*m**6/200 + 28*m**5/75 + 8*m**4/15 - 139*m**2. Determine w, given that v(w) = 0.
-1, 0, 8
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