3, -1, 1
Suppose 4*h + 2*s - 6 = 0, 44*h - 46*h = -5*s - 9. What is i in -31/3*i + 2 + 50/3*i**h - 25/3*i**3 = 0?
2/5, 3/5, 1
Let c(j) be the second derivative of j**7/112 + j**6/16 + 3*j**5/20 + j**4/8 - 19*j. Determine s so that c(s) = 0.
-2, -1, 0
Let v(c) be the third derivative of -c**5/420 + c**4/28 - 5*c**3/42 + 2*c**2 - 18*c. Find b such that v(b) = 0.
1, 5
Suppose 0 = -3*w + 6*w + t - 5, 2*w = -3*t + 15. Let s(y) be the second derivative of 1/12*y**4 + 3*y + w*y**3 + 0*y**2 + 0. Determine x, given that s(x) = 0.
0
Let x(u) = -2*u**2 - 96*u - 182. Let s be x(-46). Let c(t) be the second derivative of -2/3*t**3 - t + 4*t**s + 0 - 1/3*t**4. Find n, given that c(n) = 0.
-2, 1
Suppose 4*s = 3*o - 11, 4*s + 13 = -4*o - 19. Let p be (-2)/o*81/108. Suppose -p*g + 1/4*g**2 + 0 = 0. Calculate g.
0, 2
Let p(n) = -2*n**2 - 2. Let r(m) = 33*m**2 + 6*m + 36. Let d(h) = 18*p(h) + r(h). Determine y, given that d(y) = 0.
0, 2
Find p such that -15 + 85/6*p + 5/6*p**2 = 0.
-18, 1
Let a(o) be the first derivative of -2*o**3/33 + 26*o**2/11 - 50*o/11 - 269. Factor a(r).
-2*(r - 25)*(r - 1)/11
Let f = 6 - 6. Let i = f + 3. Determine b so that 2/3*b**i + 8/3 - 2*b**2 + 0*b = 0.
-1, 2
Let t(y) be the first derivative of -10 - 28/3*y**3 - 18/5*y**5 + 6*y**2 - 2*y + 2/3*y**6 + 8*y**4. Find o, given that t(o) = 0.
1/2, 1
Let m = 2/215 + 416/1505. Let c = -505/8 + 3551/56. Factor -2/7*x + 2/7*x**3 - c*x**2 + m.
2*(x - 1)**2*(x + 1)/7
Let v(u) be the third derivative of -u**8/8960 - u**7/560 - u**6/80 - u**5/20 - 5*u**4/8 + 14*u**2. Let k(n) be the second derivative of v(n). Solve k(p) = 0.
-2
Let v(h) be the second derivative of h**4/6 + 8*h**3/3 + 15*h**2 + 313*h. Solve v(c) = 0.
-5, -3
What is u in -1/8*u**4 + 0 - 3/8*u**3 + 9/8*u**2 - 5/8*u = 0?
-5, 0, 1
Let r(h) be the first derivative of 0*h**3 + 4/17*h**2 + 5 + 0*h - 1/34*h**4. Factor r(y).
-2*y*(y - 2)*(y + 2)/17
Solve 0*n**4 - 2/7 - 1/7*n**5 + 4/7*n**3 - 3/7*n + 2/7*n**2 = 0.
-1, 1, 2
Let d(u) = u**3 + u**2 - u - 1. Let m(n) = -9*n**3 - 21*n**2 + 9*n + 21. Let g(f) = -24*d(f) - 3*m(f). Factor g(q).
3*(q - 1)*(q + 1)*(q + 13)
Let q = 7/3 - 1. Let l be ((-12)/(-27))/(4/18). Factor 5/3*d**l - 8/3*d - q.
(d - 2)*(5*d + 2)/3
Let d(s) = -25*s**5 + 115*s**4 + 195*s**3 - 145*s**2 - 110*s. Let v(y) = y**5 + y**4 - 2*y**3 - y. Let m(b) = -d(b) - 30*v(b). Determine n, given that m(n) = 0.
-28, -1, 0, 1
Let h(w) be the third derivative of 0*w**3 + 0*w**4 - 1/240*w**6 + 0 - 40*w**2 + 0*w + 1/1260*w**7 + 1/180*w**5. Solve h(n) = 0 for n.
0, 1, 2
Let g(d) be the first derivative of -2*d**2 + 14/3*d**3 - 1/3*d**6 - 9/2*d**4 - 8 + 2*d**5 + 0*d. Factor g(p).
-2*p*(p - 2)*(p - 1)**3
Factor -44/5*c - 1/10*c**2 + 89/10.
-(c - 1)*(c + 89)/10
Let a(z) be the third derivative of z**8/6720 - z**6/1440 + 4*z**3/3 + 6*z**2. Let l(q) be the first derivative of a(q). Factor l(d).
d**2*(d - 1)*(d + 1)/4
Determine y, given that 196*y - 3*y**2 - 202*y - 18*y**2 + 0*y**2 = 0.
-2/7, 0
Let t(h) be the first derivative of 52/15*h**5 + 1/3*h**2 - 12 - 7/9*h**6 - 17/3*h**4 + 32/9*h**3 - 4/3*h. Factor t(g).
-2*(g - 1)**4*(7*g + 2)/3
Let h be 3 + -2 + (-3 - 9)/(-4). Factor 34*f**5 + 32*f**5 - 62*f**5 - h*f**4.
4*f**4*(f - 1)
Factor -7/2 - 1/2*u**3 - 5/2*u**2 + 13/2*u.
-(u - 1)**2*(u + 7)/2
Let g be (2*3/30)/(27/270). What is n in 2/11*n**3 - 2/11*n**5 - 4/11*n**4 + 0*n + 4/11*n**g + 0 = 0?
-2, -1, 0, 1
Let p(z) be the third derivative of 2/105*z**5 + 1/84*z**4 + 4/735*z**7 + 0 + 1/70*z**6 + 0*z + 1/1176*z**8 - 9*z**2 + 0*z**3. Let p(d) = 0. What is d?
-1, 0
Find t, given that 50/3 - 5/3*t**3 - 50/3*t**2 + 5/3*t = 0.
-10, -1, 1
Suppose 26*f**5 + 0 + 61/3*f**4 + 31/3*f**2 + 2*f - 176/3*f**3 = 0. Calculate f.
-2, -3/26, 0, 1/3, 1
Let y(i) be the second derivative of 16/5*i**2 + 0 + 9*i - 8/15*i**3 + 1/30*i**4. Factor y(h).
2*(h - 4)**2/5
Let b(i) be the second derivative of i**4/12 + 5*i**3/3 + 21*i**2/2 - 143*i. Suppose b(t) = 0. What is t?
-7, -3
Let f(c) be the second derivative of -1/6*c**3 - 1/14*c**7 - 1/15*c**5 - 1/3*c**6 + 7/18*c**4 + 0*c**2 + 0 + 37*c. Let f(o) = 0. Calculate o.
-3, -1, 0, 1/3
Suppose 1/3*i**3 - 2 - 5/3*i + 2/3*i**2 = 0. Calculate i.
-3, -1, 2
Let n be (-98)/(-30) - (-588)/(-56)*4/14. Find q such that 0*q + 0 - n*q**2 + 2/5*q**3 - 2/15*q**4 = 0.
0, 1, 2
Factor -1/3*d**4 - 2/9*d**3 - 8/9*d + 0 + 4/3*d**2 + 1/9*d**5.
d*(d - 2)**2*(d - 1)*(d + 2)/9
Let g = -13 + 13. Suppose g*a = -4*a. Factor 6 + 3*l**2 - 9 + a*l**2.
3*(l - 1)*(l + 1)
Factor -4 - 10/3*i + 2/3*i**2.
2*(i - 6)*(i + 1)/3
Solve -9/2 + 0*k**2 + 21/4*k - 3/4*k**3 = 0 for k.
-3, 1, 2
Let c(b) be the second derivative of b**7/105 - b**6/75 - 3*b**5/50 + b**4/30 + 2*b**3/15 - 38*b - 2. Let c(r) = 0. What is r?
-1, 0, 1, 2
Let k(y) be the third derivative of y**5/50 - y**4/30 - y**3/15 - 26*y**2 - y. Let k(f) = 0. Calculate f.
-1/3, 1
Let a = -69 + 70. Let x be a*((-45)/25 + 2). Factor -x*p**2 - 2/5 + 3/5*p.
-(p - 2)*(p - 1)/5
Let k(l) be the second derivative of -27*l + 0 - 1/110*l**5 + 0*l**2 - 1/33*l**4 - 1/33*l**3. Let k(q) = 0. What is q?
-1, 0
Let d(i) = -6*i**4 - 26*i**3 - 28*i**2 + 8*i. Let x(w) = 2*w**4 + 9*w**3 + 10*w**2 - 3*w. Let o(r) = -3*d(r) - 8*x(r). Factor o(y).
2*y**2*(y + 1)*(y + 2)
Let b(m) be the first derivative of 22/3*m**3 - 7/2*m**4 - 6*m - 28 - m**2. Let b(h) = 0. Calculate h.
-3/7, 1
Suppose -96/5*r + 96/5*r**3 - 16/5 + 44/5*r**4 - 28/5*r**2 = 0. Calculate r.
-2, -1, -2/11, 1
Let k(q) be the first derivative of 1/12*q**3 + 36 - 3/2*q + 5/8*q**2. Factor k(d).
(d - 1)*(d + 6)/4
Let m be (-3 - -18)/5 + 55. Suppose -2 + m*q**2 - 29*q**2 - 27*q**2 - 2*q**3 + 2*q = 0. Calculate q.
-1, 1
Let x(l) = 2*l**2 - 3*l + 1. Let a(g) = -9*g**2 + 13*g - 4 - 1 + 2*g**2 - g**2. Let t(d) = -6*a(d) - 22*x(d). Factor t(n).
4*(n - 2)*(n - 1)
Let r(u) be the second derivative of u**4/30 - 2*u**3/5 - 7*u**2/5 - 18*u - 10. Factor r(w).
2*(w - 7)*(w + 1)/5
Factor -12*q**2 - q + 4 + q**3 - 9*q**2 + 17*q**2 + 0*q.
(q - 4)*(q - 1)*(q + 1)
Let f = -139 + 141. Factor -f*i**3 - i**2 + 28*i + 9*i**2 - 1 + 17 - 2*i**3.
-4*(i - 4)*(i + 1)**2
Let w(d) = -3*d**2 - 2*d + 7. Let i(c) = -19*c**2 - 11*c + 43. Let m(s) = -6*i(s) + 39*w(s). Factor m(l).
-3*(l - 1)*(l + 5)
Let m(a) = -20*a**3 - 5*a**2 - 5*a - 225. Let o(i) = -i**3 + i - 9. Let l(b) = m(b) - 25*o(b). Factor l(u).
5*u*(u - 3)*(u + 2)
Let h(c) = -c**3 + 5*c**2 + 8*c - 13. Let t be h(6). Let w be t*(-6)/90*(-3)/(-1). Factor -w + 2/5*j - 1/5*j**2.
-(j - 1)**2/5
Factor -11/3*j**3 - 1/3*j**4 + 10/3 + 11/3*j - 3*j**2.
-(j - 1)*(j + 1)**2*(j + 10)/3
Factor -376*p**3 - 9*p + 377*p**3 + 31*p + 13*p**2.
p*(p + 2)*(p + 11)
Let s(d) be the second derivative of -d**5/40 + d**4/16 + 3*d**3/4 + d**2 - 5*d - 16. Factor s(b).
-(b - 4)*(b + 2)*(2*b + 1)/4
Factor 10461 + 2*k**2 - 1745 - 204 + 5938 - 340*k.
2*(k - 85)**2
Let g(y) = 2*y**3 - y - 1. Let i(b) = 17*b**3 + 6*b**2 - 15*b - 8. Let t(j) = 6*g(j) - i(j). Factor t(f).
-(f - 1)*(f + 2)*(5*f + 1)
Let k(f) = 2*f - 9. Let q(n) = -n + 5. Let h(p) = -4*k(p) - 7*q(p). Let u(c) = 3*c**2 - 15*c + 12. Let g(j) = -3*h(j) + u(j). Determine x, given that g(x) = 0.
1, 3
Let c(o) be the first derivative of 7*o**6/30 - 58*o**5/25 + 149*o**4/20 - 122*o**3/15 + 12*o**2/5 - 96. Solve c(x) = 0 for x.
0, 2/7, 1, 3, 4
Suppose -735/2*k**2 + 30 - 410*k + 145/2*k**3 = 0. What is k?
-1, 2/29, 6
Let u(j) be the second derivative of -5*j**7/42 + j**5/4 - 91*j. Factor u(z).
-5*z**3*(z - 1)*(z + 1)
Let l = -31/8 - -33/8. Factor l*u + 1/4*u**2 - 1/2.
(u - 1)*(u + 2)/4
Let k be -7*(2 - 160/56). Let c(l) be the third derivative of -4/21*l**3 - 4/105*l**5 + 5/42*l**4 + 1/210*l**k + 10*l**2 + 0*l + 0. Factor c(v).
4*(v - 2)*(v - 1)**2/7
Let g be (10/(-3))/(-6 + (-48)/(-9)). What is z in 2*z**2 + 49*z + 2*z**4 - 4*z**2 + 2*z**g - 49*z - 2*z**3 = 0?
-1, 0, 1
Let a = 8/107 - -11/1284. Let x(f) be the second derivative of 1/20*f**5 - 1/6*f**3 - 1/2*f**2 + 0 - 3*f + a*f**4. Find w such that x(w) = 0.
-1, 1
Suppose -5*b + 8 = -12. Let 3*d**2 - 2*d + 7*d - 5*d**5 - 10*d**b + 7*d**2 = 0. What is d?
-1, 0, 1
Suppose -39 + 62 = -9*s + 41. Suppose 0 + 1/2*d + 1/2*d**s = 0. What is d?
-1, 0
Suppose -78*d**2 - 76*d**2 + 3 + 15 + 57*d + 163*d**2 = 0. Calculate d.
-6, -1/3
Suppose -p - 6 = -5*y, 0 = 2*p - p + 4*y - 12. Let f(v