 be the first derivative of -2/9*s**3 - 1/3*s**2 - 16 - 2/9*s - 1/18*s**4. Suppose j(v) = 0. What is v?
-1
Suppose -85 = -20*o - 45. What is k in 2/3*k**o + 1/3*k**3 + 0*k + 0 - 1/3*k**4 = 0?
-1, 0, 2
Let d(w) be the first derivative of 6*w**2 + 4*w**3 + 4*w + 7 - 5/4*w**4. Let t(s) be the first derivative of d(s). Factor t(v).
-3*(v - 2)*(5*v + 2)
Let v be (-15)/(-30)*1/15*8. Suppose 4/15 - v*a**2 + 2/15*a - 2/15*a**3 = 0. What is a?
-2, -1, 1
Let u be 4/(-10) - (-4886)/(-35). Let g be (2/(-8))/(7/u). Determine o, given that 3*o**5 + 2*o**4 - 2*o**g - o**4 = 0.
-1, 0
Let l(w) be the first derivative of w**2/2 - w + 17. Let d(x) = x**2 - 2*x + 3. Let u(s) = 4*d(s) + 12*l(s). Factor u(r).
4*r*(r + 1)
Suppose 5*b = 5*a - 5, -49*a = -52*a - 3*b - 3. Factor 0*t + 16/5*t**2 + 28/5*t**4 + a + 8*t**3 + 6/5*t**5.
2*t**2*(t + 2)**2*(3*t + 2)/5
Let o = -4 - -6. Let p = -34 + 34. Let -o*c + 0*c**2 + p*c**2 + 2*c**2 = 0. Calculate c.
0, 1
Let p(w) be the second derivative of w**8/10080 + w**7/945 + w**6/360 - 5*w**4/4 - 6*w. Let n(x) be the third derivative of p(x). Find f such that n(f) = 0.
-3, -1, 0
Let g(d) be the second derivative of -d**6/90 + d**5/10 - d**4/4 + 2*d**3/9 + 2*d + 57. Factor g(h).
-h*(h - 4)*(h - 1)**2/3
Let r = 36986/21 - 1761. Let o(p) be the second derivative of -9/10*p**5 + 2/3*p**3 + 0*p**2 + 0 + 13/15*p**6 - r*p**7 - 1/6*p**4 + 9*p. Factor o(g).
-2*g*(g - 1)**3*(5*g + 2)
Suppose h + 1 = -5*p - 22, 3*h - 1 = -p. Let r be (-9)/6 - h/20*-21. Solve -r*o + 0*o**2 + 1/5*o**3 - 2/5 = 0.
-1, 2
Factor 18*q + 243 + 1/3*q**2.
(q + 27)**2/3
Let w = -12845/198 + 584/9. Let r(t) be the third derivative of -3*t**2 + 0*t**3 + w*t**4 + 0*t - 1/110*t**5 + 0. Factor r(c).
-2*c*(3*c - 2)/11
Let j = 38/3 + -61/6. Let b(s) = s**3 - 25*s**2 + 3*s - 73. Let c be b(25). Let 1 + 1/2*r + j*r**3 - 4*r**c = 0. Calculate r.
-2/5, 1
Let h(v) be the first derivative of 3*v**5/5 - 3*v**4/2 - 3*v**3 - 54. Factor h(n).
3*n**2*(n - 3)*(n + 1)
Factor 9 + 2388*l**3 - 4*l**5 - 30*l - 2417*l**3 + 43*l**2 + 3*l**5 - 1 + 9*l**4.
-(l - 4)*(l - 2)*(l - 1)**3
Let k(n) be the first derivative of n**4/48 + n**3/4 + 9*n**2/8 - 7*n - 2. Let h(u) be the first derivative of k(u). Suppose h(a) = 0. Calculate a.
-3
Let v(z) be the third derivative of -z**7/420 + 11*z**6/80 - 317*z**5/120 + 245*z**4/16 - 75*z**3/2 - 4*z**2 - 85. Find d such that v(d) = 0.
1, 2, 15
Let s be 5 - (-702)/171 - (-4)/(-38). Let c be s/(-9) - (-1 + -2 + 2). Determine d, given that -9/4*d**2 - 3/4*d - 3/2*d**3 + c = 0.
-1, -1/2, 0
Let g = 37 + -30. Suppose 10*i - g*i = 6. Factor 1/5 + 3/5*a**4 - 2/5*a - 4/5*a**i + 2/5*a**3.
(a - 1)*(a + 1)**2*(3*a - 1)/5
Let i(u) be the third derivative of -u**6/240 + 7*u**5/120 - 11*u**4/48 + 5*u**3/12 - 2*u**2 + 50*u. Suppose i(j) = 0. Calculate j.
1, 5
Let w(k) be the second derivative of -k**7/840 + k**6/480 + k**5/48 + k**4/32 - 3*k**2/2 - k. Let v(h) be the first derivative of w(h). Factor v(c).
-c*(c - 3)*(c + 1)**2/4
Let n(m) = -m**3 - 11*m**2 + 2*m + 24. Let j be n(-11). Factor 3/4*o**j - 7/4*o - 3/2.
(o - 3)*(3*o + 2)/4
Let o be (((-273)/1820)/(11/(-16)))/((-4)/(-10)). Factor 6/11*h**2 - o*h - 12/11.
6*(h - 2)*(h + 1)/11
Let b = 4873 + -413522/85. Let s = b - -149/17. Find p such that 81/5*p**3 + 54/5*p**2 - 81/5*p**4 - s*p + 24/5 = 0.
-1, 2/3
Let h(z) be the third derivative of -z**6/24 + 37*z**5/6 - 6845*z**4/24 + 631*z**2. Let h(l) = 0. Calculate l.
0, 37
Let i be (-4465)/(-45) + 4/(-54)*3. Find q such that -2*q**2 - 93 + 2*q + i + 2*q = 0.
-1, 3
Suppose 30/13*m**4 - 112/13*m**2 - 32/13 + 288/13*m - 16*m**3 + 34/13*m**5 = 0. What is m?
-2, 2/17, 1, 2
Suppose -w = -2*w. Let q = 6 - w. What is h in 7*h**2 + 3 - q*h**2 + 4*h + 0 = 0?
-3, -1
Suppose -512*r + 2*r**4 + 176 + 160*r + 72*r + 156*r**2 - 34*r**3 = 0. What is r?
2, 11
Let g = 4141/3 - 65657/33. Let b = g - -610. Find y such that b - 6/11*y**2 + 0*y + 2/11*y**3 = 0.
-1, 2
Find a such that 15 + 13/6*a**3 - 34/3*a**2 + 19/2*a = 0.
-10/13, 3
Let r = 30647 - 153231/5. Factor 4/5*t - r*t**2 + 4/5 - 4/5*t**3.
-4*(t - 1)*(t + 1)**2/5
Suppose -6*x + 11*x - 320 = 0. Let k = x - 191/3. Factor 2/3*r**2 + 1/3*r - 2/3*r**3 - 1/3*r**4 + 1/3*r**5 - k.
(r - 1)**3*(r + 1)**2/3
Suppose t - 4 = -2*v, 5*t + 4*v + 8 = 46. Suppose o - 20 = 6*w - t*w, -2*o = -3*w + 15. Let -3/4*f**3 - 3/2*f**4 + 0*f + o + 0*f**2 = 0. Calculate f.
-1/2, 0
Let g(w) = 3*w**2 - 60*w + 165. Let t(z) = z - 1. Let m be -2 - (-4 - (-11)/3)*3. Let i(k) = m*g(k) - 18*t(k). Determine l so that i(l) = 0.
7
Let 1/7 + 0*p - 1/7*p**2 = 0. What is p?
-1, 1
Let i(r) = r**2 + r - 1. Let o(s) = -2*s + 33. Let w be o(16). Let y(g) = 8*g + 12. Let b(m) = w*y(m) + 4*i(m). Determine a so that b(a) = 0.
-2, -1
Let w be (-3 - 375/9)*(-36)/8. Factor 203*t**5 + t**4 - 4*t**3 - w*t**5 + t**4.
2*t**3*(t - 1)*(t + 2)
Find o, given that -7 - 5/2*o + 1/2*o**2 = 0.
-2, 7
Determine o so that 2/11*o**3 + 12/11*o + 14/11*o**2 + 0 = 0.
-6, -1, 0
Let s be ((-13)/3)/(1040/(-720)). Determine q so that 4/5 - 4*q - s*q**3 + 31/5*q**2 = 0.
2/5, 2/3, 1
Suppose 0 + 0*q**3 - 2/9*q**4 + 0*q**2 + 0*q + 2/9*q**5 = 0. Calculate q.
0, 1
Let j be (10/55)/((-2)/(-8)). Let m = -2061 - -22679/11. What is c in -j - m*c - 2/11*c**2 = 0?
-2
Factor -5*j + 9/2 + 1/2*j**2.
(j - 9)*(j - 1)/2
Suppose 3*m - 4 = -1. Let q(n) be the first derivative of -m + 0*n**2 - 2 + n**3 + 3*n**2. Suppose q(u) = 0. What is u?
-2, 0
Let i = -95 - -100. Let m be 35/245 - 4/(-7)*i. Suppose 0 + 2/9*p**m + 4/9*p**2 + 0*p = 0. Calculate p.
-2, 0
Suppose 468*j**2 - 1352*j + 2*j**5 + 2*j**5 + 474*j**3 + 108*j**4 + 298*j**3 = 0. What is j?
-13, -2, 0, 1
Suppose 6*p - 25 = p, t + 5*p - 29 = 0. Let g(h) = -h**2 + 5*h + 2. Let v be g(t). Factor -7 - v - q**2 + 1 + 4*q**2.
3*(q - 2)*(q + 2)
Let m be 12/10*40/24. Suppose 34*q + 5*q**2 - q**m - 18*q = 0. What is q?
-4, 0
Let l = -99 - -225. Let v be (-24)/110 + 4 + l/(-35). Factor 2/11*y**2 + v + 4/11*y.
2*(y + 1)**2/11
Let i(w) = w**2 + 870*w + 37845. Let k(f) = -15*f**2 - 14790*f - 643365. Let s(b) = -35*i(b) - 2*k(b). What is d in s(d) = 0?
-87
Let f(w) = 0*w + 0 - 1 - w. Let l(q) be the first derivative of -q**3/3 + q**2/2 + 2*q + 28. Let b(n) = -2*f(n) - l(n). Solve b(z) = 0.
-1, 0
Factor -6798 - 4*f**2 + 13*f + f**3 + 6804 + 12*f**2.
(f + 1)**2*(f + 6)
Let p(x) be the first derivative of x**6/24 + x**5/10 - x**4/16 - x**3/6 - 39. Let p(h) = 0. Calculate h.
-2, -1, 0, 1
Let k(n) = 15*n**2 - 6*n + 15. Let p(m) = -m**2 + m. Suppose 5 = 3*o + h, -3*o + h - 1 = -h. Let f(c) = o*k(c) + 18*p(c). Let f(v) = 0. Calculate v.
-1, 5
Let u(b) be the third derivative of b**7/490 + b**6/40 + 11*b**5/140 + 5*b**4/56 - 58*b**2. Find x, given that u(x) = 0.
-5, -1, 0
Let k(t) = -2*t**2 + 22*t - 26. Let v be k(9). Find m such that -127*m - 5*m**3 + 10*m**2 + 10 + v*m**2 + 102*m = 0.
1, 2
Let d(x) = 14*x. Let n be d(-1). Let u = -12 - n. Let -7 - 19*q**u - 2 + q**2 - 24*q + 3*q**4 = 0. What is q?
-1, 3
Suppose -43 = -254*l + 541 - 76. Let -2*f + l*f**2 + 0 - 1/2*f**3 = 0. What is f?
0, 2
Let c(t) = 65*t + 45. Let v be c(-3). Let x = 153 + v. Factor 3/4*l**x + 0 + 0*l + 1/4*l**2.
l**2*(3*l + 1)/4
Suppose 5*y - 16*y = 0. Let g(r) be the first derivative of 9/2*r**2 - 3/4*r**4 + 6*r + y*r**3 - 4. What is d in g(d) = 0?
-1, 2
Suppose -6*o**2 - 2*o**4 + 3*o - 37 + 45 - 8*o**3 + 5*o = 0. Calculate o.
-2, -1, 1
Suppose -4*f - 2 = r, -f + 6 = r + 5. Let u(a) be the first derivative of -a - 3/4*a**r + 7 - 1/6*a**3. Factor u(j).
-(j + 1)*(j + 2)/2
Let q(f) be the third derivative of -f**7/5040 + f**6/360 - f**5/80 - f**4/8 + 27*f**2. Let z(y) be the second derivative of q(y). Factor z(i).
-(i - 3)*(i - 1)/2
Let 4/7 + 50/7*f**3 - 60/7*f**2 + 6/7*f = 0. Calculate f.
-1/5, 2/5, 1
Let a = 4 + -2. Let f = -40909/4 + 10228. Factor -1/4*k**3 + 5/4*k - 1/2 + 1/4*k**4 - f*k**a.
(k - 1)**3*(k + 2)/4
Factor 5*t**3 + 1 - 24 + 3*t**3 - 20*t - 2*t**4 + 23 + 14*t**2.
-2*t*(t - 5)*(t - 1)*(t + 2)
Let h(p) be the second derivative of 4*p**5/5 - 17*p**4/3 + 40*p**3/3 - 8*p**2 + 36*p + 1. Let h(n) = 0. What is n?
1/4, 2
Let g(k) be the third derivative of -k**9/10584 - k**8/1960 + k**6/315 - 9*k**3/2 + 31*k**2. Let o(b) be the first derivative of g(b). Factor o(v).
-2*v**2*(v - 1)*(v + 2)**2/7
Suppose 0 = 3*b - 2*h - 0*h - 