2
Let 8/7 - 58/7*w**2 + 16*w = 0. What is w?
-2/29, 2
Let j(f) = -f**2 + 13*f + 4. Let y be j(0). Let m(s) be the third derivative of 1/30*s**6 - 1/6*s**y + 0*s + 4*s**2 + 4/15*s**3 - 2/75*s**5 + 0. Factor m(u).
4*(u - 1)*(u + 1)*(5*u - 2)/5
Let f(s) be the first derivative of -s**5/10 - 21*s**4/8 - 33*s**3/2 + 121*s**2/4 + 120. Factor f(h).
-h*(h - 1)*(h + 11)**2/2
Let -2/3*i**2 - 12 - 38/3*i = 0. Calculate i.
-18, -1
Factor -32/9*v**2 - 2 + 26/3*v - 128/9*v**3.
-2*(v + 1)*(8*v - 3)**2/9
Let j(o) be the second derivative of o**8/10080 + o**7/5040 - o**6/4320 + 7*o**4/12 + 11*o. Let d(i) be the third derivative of j(i). Let d(n) = 0. Calculate n.
-1, 0, 1/4
Let r = 19738 + -19736. What is n in -3/2*n**4 - 2 + 0*n - 1/2*n**3 + 1/2*n**5 + 7/2*n**r = 0?
-1, 1, 2
Let u(l) be the second derivative of -l**4/24 - 4*l**3/3 - 16*l**2 - 60*l + 1. Factor u(k).
-(k + 8)**2/2
Let c(l) be the third derivative of l**7/70 - l**6/8 + 7*l**5/20 - 3*l**4/8 - 2*l**2. Let c(f) = 0. What is f?
0, 1, 3
Let f(j) = j**2 - 7*j + 11. Let c be f(9). Let w = c - 29. Find z such that -1/3*z**3 + 0*z**2 - 1/3*z**5 + 2/3*z**4 + w + 0*z = 0.
0, 1
Find d such that -990*d**4 - 20*d + 10 + 180*d**2 + 56 - 66 - 605*d**5 - 185*d**3 = 0.
-1, 0, 2/11
Let c(f) be the first derivative of -f**5/30 + f**4/6 + 2*f**3/3 - 22. Factor c(h).
-h**2*(h - 6)*(h + 2)/6
Suppose o + 3*o - 4*c = 32, 3*o - c - 14 = 0. Let g(u) be the first derivative of 1/3*u**o + 0*u + 1/2*u**2 + 3. Suppose g(y) = 0. Calculate y.
-1, 0
Let n be 6/33 + (2 + -2)/(-119 - -121). Suppose -16/11*g - 32/11 - n*g**2 = 0. What is g?
-4
Let y(o) be the second derivative of o**7/1260 + o**6/180 + o**5/90 + o**3/6 - 32*o. Let t(x) be the second derivative of y(x). Find v, given that t(v) = 0.
-2, -1, 0
Let k be 2/3*(-36)/(-8). Suppose 0 = 2*l - 3*l + k. Factor -9*j + 0*j**3 - 7 + 10 - 3*j**l + 9*j**2.
-3*(j - 1)**3
Solve 8/3*s**2 - 4 + 2/3*s + 2/3*s**3 = 0 for s.
-3, -2, 1
Let t = -277 + 833/3. Factor t + 1/6*w**2 - 2/3*w.
(w - 2)**2/6
Let k = 92/905 - -798/9955. Factor -k*p**2 + 52/11*p - 338/11.
-2*(p - 13)**2/11
Let b(u) = u**3 + 3*u**2 + 2*u - 3. Let a be b(-3). Let c = a + 21. What is q in c*q**2 - 4*q**3 - 8*q - 72 + 72 = 0?
0, 1, 2
Let t(d) be the first derivative of 4*d**3/27 + 11*d**2/6 + 8*d/9 - 445. Suppose t(s) = 0. What is s?
-8, -1/4
Suppose 17 = 2*c - c. Let u = c + -15. Factor -16*g + 16*g + u*g**2 - 2.
2*(g - 1)*(g + 1)
Solve -46*l**2 - 7257*l + 2*l**4 - 7240*l - 20*l**3 + 14473*l = 0 for l.
-1, 0, 12
Let u be (-670)/1474*(-36)/20. Factor -u*b**2 - 2/11*b + 0.
-b*(9*b + 2)/11
Let n(l) be the first derivative of l**4/2 - 6*l**3/7 - 12*l**2/7 + 8*l/7 - 66. Determine w, given that n(w) = 0.
-1, 2/7, 2
Let p(d) be the second derivative of d**9/52920 - d**7/2205 + d**4 - d. Let k(c) be the third derivative of p(c). Factor k(y).
2*y**2*(y - 2)*(y + 2)/7
Factor -4/9*i**4 + 4/9*i**2 - 4/3*i**3 + 4/3*i + 0.
-4*i*(i - 1)*(i + 1)*(i + 3)/9
Let d = -84 - -87. Factor 8*z**2 - 20*z - 28*z**2 + 3*z**d - 4*z**3 - 4*z**3.
-5*z*(z + 2)**2
Solve 6*d**2 + 3*d**3 + d**2 + 12*d - 16 - d**2 - 12*d**3 + 7*d**3 = 0 for d.
-2, 1, 4
Let z(i) = i. Let m be z(3). Factor -2 - 27*f - 18*f**2 - 5*f**3 + 2*f**m - 4 - 6.
-3*(f + 1)**2*(f + 4)
Let g be (6799/(-14644))/((-1)/24). Suppose 9*v + 15/7 + 27/7*v**4 + g*v**3 + 102/7*v**2 + 3/7*v**5 = 0. Calculate v.
-5, -1
Let t(z) be the third derivative of 2*z**7/105 - z**6/15 - 13*z**5/15 - 5*z**4/3 - 2*z**2 - 36. Suppose t(l) = 0. What is l?
-2, -1, 0, 5
Factor -15/2*b + 3/4*b**3 - 9/4*b**2 + 0.
3*b*(b - 5)*(b + 2)/4
Find r such that 1/5*r**5 - 25*r**4 + 3967/5*r**3 - 3968/5*r - 3719/5*r**2 + 3844/5 = 0.
-1, 1, 62
Let l = 19411/3 - 147652/21. Let f = l - -563. Factor 10/7*j**2 + f + 44/7*j.
2*(j + 4)*(5*j + 2)/7
Let w be 2277/184*2/3*-2. Let r = 101/6 + w. Solve -1/3*v**3 + 0 - r*v - 2/3*v**2 = 0 for v.
-1, 0
Solve 200/19*j + 0 - 398/19*j**2 + 2/19*j**4 + 196/19*j**3 = 0.
-100, 0, 1
Let n(t) = 3*t**3 + 140*t**2 - 7*t - 144. Let k(r) = r**3 + r + 2. Let j(c) = -2*k(c) - n(c). Factor j(d).
-5*(d - 1)*(d + 1)*(d + 28)
Suppose 34*h + 10541*h**2 - 2*h - 10509*h**2 - 5*h**4 - 6*h**3 + h**5 = 0. Calculate h.
-2, -1, 0, 4
What is j in 4/9*j**2 + 8/9 - 2/9*j**3 + 14/9*j = 0?
-1, 4
Suppose -5*a + 3*i = -90, -4*a - 2*i = -89 - 5. Let s = 23 - a. Factor -f + 2*f - 3*f - 2*f + 2*f**s.
2*f*(f - 2)
Let -17*p**2 + 2*p**2 + 15*p**2 - 5*p**3 = 0. Calculate p.
0
Let x(n) be the first derivative of 1/2*n**2 - 1/4*n**5 + 10/3*n**3 - 3 + 0*n - 1/24*n**6 + 0*n**4. Let g(j) be the second derivative of x(j). Factor g(l).
-5*(l - 1)*(l + 2)**2
Let q(f) = -2*f + 28. Let s be q(13). Suppose s*m**5 + 0*m**3 - m**5 - 2*m**3 + m = 0. What is m?
-1, 0, 1
Let q be ((-51)/(-68)*1)/((-27)/(-12)). Factor 1/3 - q*o**2 - 1/3*o + 1/3*o**3.
(o - 1)**2*(o + 1)/3
Factor -12*g**3 + 50*g**2 + 19*g**3 - 68*g + 23*g - 12*g**3.
-5*g*(g - 9)*(g - 1)
Let a(q) be the second derivative of q**7/21 - 6*q**6/5 + 16*q**5/5 - 121*q. Solve a(b) = 0 for b.
0, 2, 16
Let u(h) be the first derivative of h**2/2 + 7*h - 39. Let o be u(-4). Let 0*l + 0*l**2 + 0 + 4/7*l**o + 4/7*l**4 = 0. Calculate l.
-1, 0
Let i(w) be the first derivative of -5*w**4 + 44*w**3/3 + 10*w**2 - 44*w + 93. Let i(q) = 0. Calculate q.
-1, 1, 11/5
Suppose -1 + 64 = 21*n. Let s(c) be the third derivative of 0*c - 1/30*c**4 + 0*c**n + 1/50*c**5 + 8*c**2 + 0 - 1/300*c**6. Solve s(m) = 0 for m.
0, 1, 2
Factor 2/13*o**3 - 44/13*o**2 + 44/13 - 2/13*o.
2*(o - 22)*(o - 1)*(o + 1)/13
Let y(c) be the second derivative of c**4/20 + 8*c**3/5 + 42*c**2/5 - 78*c. Suppose y(k) = 0. Calculate k.
-14, -2
Let q be (-2444)/(-572) - (12/22)/2. Factor -1/3*z**q + 0*z - 2/3*z**3 + 0 - 1/3*z**2.
-z**2*(z + 1)**2/3
Let k(q) be the first derivative of q**6/1080 - q**5/120 + q**4/36 - 49*q**3/3 - 36. Let b(h) be the third derivative of k(h). Suppose b(r) = 0. Calculate r.
1, 2
Let t(n) be the second derivative of -n**8/448 + n**6/32 - n**4/8 - 17*n**2/2 - 29*n. Let j(s) be the first derivative of t(s). Let j(m) = 0. Calculate m.
-2, -1, 0, 1, 2
Let o(f) = 31*f**4 + 84*f**3 + 63*f**2 + 6*f - 4. Let p(d) = -30*d**4 - 85*d**3 - 65*d**2 - 5*d + 5. Let j(i) = -5*o(i) - 4*p(i). Factor j(s).
-5*s*(s + 1)**2*(7*s + 2)
Let 726/17*i**2 + 2/17*i**4 + 240/17 + 246/17*i**3 + 722/17*i = 0. Calculate i.
-120, -1
Let u(o) = o**3 - 8*o**2 - 5*o + 2. Let b be u(8). Let h = b - -305/8. Find l, given that h*l**2 + 0 + 1/4*l - 1/8*l**3 = 0.
-1, 0, 2
Let u(v) be the first derivative of 4*v**5/15 - 10*v**4/3 + 44*v**3/3 - 80*v**2/3 + 64*v/3 - 30. Factor u(z).
4*(z - 4)**2*(z - 1)**2/3
Let t = -50 + 53. Suppose 0 = u + 3*v - 2, -2*u - v = t*v - 4. Factor -2/5*q**u - 18/5 + 12/5*q.
-2*(q - 3)**2/5
Let r = -61/30 + 11/5. Let i(z) be the first derivative of -r*z**2 + 0*z - 1/18*z**3 + 1/8*z**4 - 2. Suppose i(g) = 0. What is g?
-2/3, 0, 1
Let i = -14 - -15. Suppose 2*s - 3 = i. Let 56*f**s - 27 - 10*f**3 + 9 - 18 - 66*f = 0. Calculate f.
-2/5, 3
Let d(y) = -187*y + 9913. Let w be d(53). What is b in 9/8*b + 3/4 - 3/8*b**3 + 0*b**w = 0?
-1, 2
Let u = -1/664 + 1997/3320. Let 14/5*n**4 + 13/5*n**3 + u*n**5 - 4*n + 8/5 - 18/5*n**2 = 0. Calculate n.
-2, 1/3, 1
Let z = -86 - -433/5. Factor z*p + 1/5*p**3 - 4/5*p**2 + 0.
p*(p - 3)*(p - 1)/5
Let h(d) be the first derivative of -4*d**5/5 + 580*d**4 - 168200*d**3 + 24389000*d**2 - 1768202500*d + 184. Suppose h(v) = 0. Calculate v.
145
Let v(w) be the first derivative of 5*w**3/3 + 65*w**2/2 - 150*w + 339. Factor v(a).
5*(a - 2)*(a + 15)
Let f = 67 - 64. Factor 69*o - 44*o + 11*o**2 - 20*o**4 - 36*o**2 + 55*o**f - 35*o.
-5*o*(o - 2)*(o - 1)*(4*o + 1)
Let l(d) be the second derivative of 0 + 0*d**2 - 10/3*d**3 - 14*d - 5/12*d**4. Determine j, given that l(j) = 0.
-4, 0
Let p = 12262 + -12258. Find d such that -3/4*d**p + 0*d**2 + 9/4*d**3 - 3*d + 0 = 0.
-1, 0, 2
Determine z, given that 54675/8 + 3/8*z**2 - 405/4*z = 0.
135
Let r(t) = t**3 + t**2. Let z be r(1). Let b be z/(-4)*-4*(-1 - -2). Determine f so that 36/5*f**5 - 4/5*f + 64/5*f**3 + 87/5*f**4 + 2*f**b - 1/5 = 0.
-1, -1/3, 1/4
Let n(w) be the second derivative of -w**6/240 + w**5/120 + w**4/24 + 23*w**2/2 + 18*w. Let a(f) be the first derivative of n(f). Factor a(g).
-g*(g - 2)*(g + 1)/2
Let 0 + 0*d + 2/3*d**2 - 2*d**4 + 4/3*d**3 = 0. Ca