3
Suppose -16/5*z**2 - 2 + 26/5*z = 0. Calculate z.
5/8, 1
Suppose -4*v + a + 15 = 0, -4*a = 5*v - 0*a - 3. Factor -g**5 - g**v + 0*g**5 - 7*g**4 + 9*g**4.
-g**3*(g - 1)**2
Suppose -23*j + 54 = 4*j. Find i, given that -1/3*i**j - 2/3*i - 1/3 = 0.
-1
Let i = -201 + 1411/7. Let w = 2159 - 2157. Factor 2/7*h + 0 + 2/7*h**3 - i*h**w.
2*h*(h - 1)**2/7
Suppose 0 = -5*r - 10, 22 + 30 = 2*u + r. Suppose -2*q + j + 64 = 11, 0 = -4*j + 4. Solve u*w + 2*w**2 - q*w = 0.
0
Suppose 149*l - 2*x = 153*l, 3*x = -5*l - 2. Factor 2/25*r**3 - 4/25*r + 0 - 2/25*r**l.
2*r*(r - 2)*(r + 1)/25
Let x be (46/((-4784)/130))/((-10)/(-16)*-3). Factor 62/3*o - 34/3*o**2 - 10 + x*o**3.
2*(o - 15)*(o - 1)**2/3
Suppose 363*z - 30 = 353*z. Let -2/5*n**4 - 2/5 + 0*n + 0*n**z + 4/5*n**2 = 0. Calculate n.
-1, 1
Factor -266*y + 50*y**3 - 35*y**2 + 5*y**4 + 46*y - 760*y + 0*y**4.
5*y*(y - 4)*(y + 7)**2
Suppose 16/5*a**4 - 8/5 + 32/5*a**5 - 52/5*a - 88/5*a**3 - 116/5*a**2 = 0. What is a?
-1, -1/2, 2
Let y be 37/3 + 58 + -70. Let 0*x + 7/6*x**5 + 0*x**3 - y*x**4 + 0 + 0*x**2 = 0. What is x?
0, 2/7
Let a(x) be the second derivative of -x**6/30 - x**5/5 + 8*x**3/3 - 11*x**2/2 + 10*x. Let s(d) be the first derivative of a(d). Factor s(g).
-4*(g - 1)*(g + 2)**2
Let y(f) = 7*f**2 - 91*f + 28. Let k(j) = -j**2 + j - 1. Let c(r) = 2*k(r) - y(r). Factor c(n).
-3*(n - 10)*(3*n - 1)
Let p(w) be the first derivative of -3*w**2 - 1/4*w**4 + 5/3*w**3 + 12 + 0*w. Factor p(o).
-o*(o - 3)*(o - 2)
Let l(p) be the second derivative of 0 + 9*p - 1/60*p**5 + 0*p**4 + 1/270*p**6 + 2/27*p**3 + 0*p**2. Let l(z) = 0. What is z?
-1, 0, 2
Let d(h) be the third derivative of 1/2*h**4 + 0 + 8*h**2 + 0*h**3 - 1/20*h**5 + 0*h. Determine b, given that d(b) = 0.
0, 4
Let o(r) be the first derivative of 2*r**5/25 + r**4/5 - 2*r**3/15 - 2*r**2/5 - 70. Solve o(n) = 0 for n.
-2, -1, 0, 1
Let p(w) be the third derivative of w**7/350 + 9*w**6/200 + 7*w**5/100 - 9*w**4/40 - 4*w**3/5 - 86*w**2. Factor p(t).
3*(t - 1)*(t + 1)**2*(t + 8)/5
Suppose -2*l = 3*a + 1 - 2, 4*a + 5*l = -8. Let n be -1 - (a - -3)/(-2). Factor 4/9 + 2/9*b**n - 2/3*b.
2*(b - 2)*(b - 1)/9
Suppose 6 = 2*p, 4*o + 25*p = 28*p - 5. Factor 0*f + 1/4*f**3 - 3/4*f**2 + o.
(f - 2)**2*(f + 1)/4
What is x in -20/13 - 88/13*x**2 - 118/13*x + 10/13*x**3 = 0?
-1, -1/5, 10
Let q be 640/(-525) - (0 + -2). Let n = -8/21 + q. Factor -2/5*i + 0 + n*i**4 - 2/5*i**2 + 2/5*i**3.
2*i*(i - 1)*(i + 1)**2/5
Let d be 2/(-14)*((-504)/45 - -7). Suppose 0 + 0*i - d*i**5 - 3/5*i**2 + 3/5*i**3 + 3/5*i**4 = 0. Calculate i.
-1, 0, 1
Let j(d) = d**3 - 14*d**2 + 15. Let x(f) = f**2 - 1. Let n(h) = -4*j(h) - 44*x(h). Determine l, given that n(l) = 0.
-1, 2
Let z(d) be the second derivative of -2*d**4/39 + 7*d**3/39 + 2*d**2/13 - 47*d - 5. Solve z(c) = 0 for c.
-1/4, 2
Let -2*h**5 - 4*h**2 + 1228*h**4 - 1226*h**4 - 4*h + 2 + 2*h + 4*h**3 = 0. Calculate h.
-1, 1
Factor -2*n**3 + n**3 - 33*n**2 - 72 - 476*n + 582*n.
-(n - 2)*(n - 1)*(n + 36)
Let r(f) = f**3 + 6*f**2 + 4*f + 79. Let a be r(-7). Solve 13/3*m + 28/3*m**a - 2 = 0 for m.
-3/4, 2/7
What is t in 1/4*t**2 + 69/2*t + 4761/4 = 0?
-69
Suppose 0 = 5*i - 10*i + 35. Find q, given that 0*q**2 + 3*q**2 + 6*q**3 + 10*q**4 - i*q**4 = 0.
-1, 0
Let y = -403/12 + 135/4. Let n(z) be the second derivative of 3*z - 8/3*z**3 - 16*z**2 - y*z**4 + 0. Factor n(r).
-2*(r + 4)**2
Let z(w) = 155*w**3 - 595*w**2 + 985*w - 35. Let f(v) = 9*v**3 - 35*v**2 + 58*v - 2. Let q(g) = -35*f(g) + 2*z(g). Suppose q(h) = 0. Calculate h.
0, 3, 4
Let q be ((-132)/121)/((-16)/((-128)/(-24))). Factor 3/11*m**2 + 1/11*m**4 + 4/11*m**3 - q*m - 4/11.
(m - 1)*(m + 1)*(m + 2)**2/11
Let i(l) = -l**2 + 6*l + 1. Let s be i(5). Let b = -4 + s. Solve 2 + 3*f**2 + f - 8*f + 0*f**b = 0 for f.
1/3, 2
Let l(f) be the first derivative of -f**3 + 27*f**2 - 243*f - 35. Factor l(b).
-3*(b - 9)**2
Let r(t) be the second derivative of t**5/180 - t**4/72 + 3*t**2/2 + 6*t. Let c(a) be the first derivative of r(a). Find u such that c(u) = 0.
0, 1
Let w(o) = 14*o**3 - 35*o**2 - 17*o + 17. Let p(d) = -5*d**3 + 12*d**2 + 6*d - 6. Let x(a) = -17*p(a) - 6*w(a). Find n, given that x(n) = 0.
-6, 0
Let a(y) be the first derivative of -2*y**6/27 - 2*y**5/5 - 5*y**4/9 + 10*y**3/27 + 4*y**2/3 + 8*y/9 - 16. Let a(k) = 0. What is k?
-2, -1, -1/2, 1
Let g = 40984 - 532790/13. Find y such that 32/13 - g*y**5 - 14/13*y**4 - 32/13*y**3 - 16/13*y**2 + 32/13*y = 0.
-2, 1
Let s = -179 - -119. Let q be 12/s + 54/70. Find j, given that q - 2*j**3 - 22/7*j + 32/7*j**2 = 0.
2/7, 1
Let s(u) = 24393*u**3 + 10088*u**2 + 1388*u + 56. Let j(i) = -i**3 + i**2 + i + 2. Let y(g) = 4*j(g) + s(g). Determine f so that y(f) = 0.
-4/29
Let y(l) be the second derivative of 15*l + 2/15*l**5 + 0*l**2 + 7/180*l**6 + 1/18*l**4 + 0 + 0*l**3. Suppose y(i) = 0. What is i?
-2, -2/7, 0
Let f be 3822/1540 + 2/(-11) - 57/190. Let q be (-8)/(-2)*(-1)/(-10). Suppose -q*r**f + 6/5*r - 4/5 = 0. What is r?
1, 2
Suppose m - 63 = -6*m. Let x(h) = -h**3 + 10*h**2 - 10*h + 13. Let r be x(m). Factor -r - 4*g + 6*g**3 + 2*g**3 + 4*g**2 - 4*g**3.
4*(g - 1)*(g + 1)**2
Let q(j) be the third derivative of j**7/525 + j**6/300 - 4*j**5/75 - j**4/5 + 36*j**2 - 2*j. Factor q(i).
2*i*(i - 3)*(i + 2)**2/5
Let w be (-196)/(-105) - (-3)/((-450)/(-20)). Suppose 9/4*s**w + 7/4*s - 1/2 = 0. Calculate s.
-1, 2/9
Let y(i) = -3*i**3 - 4*i**2 - 3*i - 2. Let f be y(-2). Suppose -3*p + 3*m + 21 = 0, p + 5*m + 5 = -f. Factor -4*l - 9*l**3 + 4*l + 11*l**p.
2*l**3
Let l(q) = 17*q + 9. Let h(b) = -2*b. Let i(z) = -2*h(z) - l(z). Let d be i(-1). Factor -12/5*u**d + 32/5*u**2 + 64/5 - 2/5*u**5 - 16/5*u**3 + 96/5*u.
-2*(u - 2)*(u + 2)**4/5
Let d(b) be the second derivative of -1/15*b**3 + 12*b + 0*b**2 - 1/50*b**5 + 1/15*b**4 + 0. Solve d(s) = 0 for s.
0, 1
Let c(q) = q - 1. Let t = 46 - 50. Let h(f) = 2*f**2 + 10*f - 12. Let s(n) = t*c(n) + h(n). Suppose s(u) = 0. Calculate u.
-4, 1
Let j = 12 + -10. Let g be (42/7)/(3/j). Factor 7*l**5 - 2*l**5 - 6*l**g - 2*l**5.
3*l**4*(l - 2)
Suppose 63 = -9*v + 2*v. Let f be (-2)/(-5) - v*(-7)/420. Solve 0*c**2 + 0 + f*c**4 + 1/4*c**3 + 0*c = 0 for c.
-1, 0
Let h(s) be the first derivative of 3*s + 48/5*s**5 - 5 + 3/2*s**2 - 51/4*s**4 + 8*s**6 - 17*s**3. Suppose h(z) = 0. Calculate z.
-1, -1/4, 1/4, 1
Let n(i) be the second derivative of -4*i**6/45 + 13*i**5/30 + 97*i**4/18 + 59*i**3/9 - 7*i**2 - 341*i. Find q, given that n(q) = 0.
-3, -1, 1/4, 7
Let u(d) = d**4 + 21*d**3 + 8*d**2 - 3*d - 9. Let y(s) = -6*s**2 - s + 18*s**2 - 10*s**2 - 2 + 5*s**3. Let z(k) = -2*u(k) + 9*y(k). Factor z(l).
-l*(l - 1)*(l + 1)*(2*l - 3)
Let h = 43 + -40. Let x = 13/4 - h. Factor -1/4 - 1/2*y**3 - 1/4*y**4 + 1/4*y**5 + x*y + 1/2*y**2.
(y - 1)**3*(y + 1)**2/4
Suppose 4*d = -5*l + 9 - 1, 2*l - 5*d = 23. Let v(r) be the second derivative of 4/21*r**3 + 0 - 1/21*r**l - 6*r + 6/7*r**2. Suppose v(f) = 0. What is f?
-1, 3
Let q(u) = 3*u. Let y be q(1). Let l be (4/4 + (-1)/(-2))*578/1156. Solve 3/4*g**2 + 3/4*g**5 - 3/4*g**y + 0*g + 0 - l*g**4 = 0.
-1, 0, 1
Factor 35867*z - 272*z**2 + 12998 - 2747*z + 4*z**3 - 452*z**2 - 19247 - 26151.
4*(z - 90)**2*(z - 1)
What is y in 42*y**3 + 49*y**3 + 54*y**3 - 5*y**4 + 812*y**2 - 952*y**2 = 0?
0, 1, 28
Suppose 25 = 23*c - 18*c. Suppose c*j - 12 = -j. What is w in 1/6*w + 0 + 1/6*w**3 + 1/3*w**j = 0?
-1, 0
Let r be (-48)/(-240) + 34/30. Factor 0 - 8/3*h + 8/3*h**3 - 4/3*h**2 + r*h**4.
4*h*(h - 1)*(h + 1)*(h + 2)/3
Let a = 33 - 31. Find j, given that 154*j - 158*j - 4*j**a - 2 + 2 = 0.
-1, 0
Let p(j) = -j**3 + 2*j**2 + 4*j + 6. Let o be p(-2). Let x = o - 12. Let 2/3*b**x + 0*b - 2/3 = 0. Calculate b.
-1, 1
Let z = -54911/11 - -19551297/3916. Let p = z - 1/89. Let -1/4*c - 1/4*c**4 + 0 - 3/4*c**2 - p*c**3 = 0. What is c?
-1, 0
Let g(i) be the first derivative of -3*i**5/5 + 9*i**4/4 - 3*i**3 + 3*i**2/2 - 19*i - 7. Let d(n) be the first derivative of g(n). Factor d(j).
-3*(j - 1)**2*(4*j - 1)
Suppose -12*w = -17*w - 5. Let m be 56/(-72) - (w + 1 + -1). Find i such that 0*i + 2/9 - m*i**2 = 0.
-1, 1
Let t be -3 + 690/171 - 1. Let w = t + 12/19. Factor 2/3*q**2 + 0 + w*q**3 + 0*q.
2*q**2*(q + 1)/3
Let d(z) = 4*z**3 + 4*z**2. Let j(c) = -c**3 + c. Let v(u) = d(u) + 3*j(u). Find o such that v(o) = 0.
-3, -1, 0
Let j = 107 + -102. Le