**2*(v + 2)**2/3
Factor -3 + 6*u**2 + 3 + 493*u**3 - 495*u**3.
-2*u**2*(u - 3)
Let d(k) be the third derivative of k**7/210 + k**6/20 + 13*k**5/60 + k**4/2 + 2*k**3/3 - k**2. Let d(o) = 0. Calculate o.
-2, -1
Let s(h) be the third derivative of h**7/2520 - h**6/180 + h**5/30 - h**4/6 + h**2. Let n(i) be the second derivative of s(i). Let n(b) = 0. Calculate b.
2
Let n(o) be the second derivative of 0*o**5 + 0*o**2 + 1/66*o**4 + 2/231*o**7 - 5*o + 0*o**3 + 0 - 1/55*o**6. Find j such that n(j) = 0.
-1/2, 0, 1
Let c(r) = -3*r**3 + 9*r**2 - 6*r + 3. Let u(m) = 3*m**3 - 8*m**2 + 5*m - 2. Let x(f) = -2*c(f) - 3*u(f). Factor x(n).
-3*n*(n - 1)**2
Let y be (-8)/(-28) - (-132)/(-266). Let o = -1/95 - y. Factor -o - 3/5*g + 4/5*g**2.
(g - 1)*(4*g + 1)/5
Factor -2/15*i**2 - 4/15*i - 2/15.
-2*(i + 1)**2/15
Factor -1 - 4*n - 2*n**2 - 2 + 3.
-2*n*(n + 2)
Let -4*t**5 + 2*t**4 + 3*t**5 + 3*t**5 - t**3 - 3*t**5 = 0. What is t?
0, 1
Let x(j) be the second derivative of -j**6/30 + j**4/4 - j**3/3 - 12*j. Suppose x(d) = 0. Calculate d.
-2, 0, 1
Let q(u) be the second derivative of u**4/54 - u**2/9 - 8*u. Find r, given that q(r) = 0.
-1, 1
Suppose b + 3*b - 32 = 0. Suppose z + 3*g = 7*g + b, 0 = -5*g - 10. Factor 1/2*m - 1/2*m**5 + z + m**4 - m**2 + 0*m**3.
-m*(m - 1)**3*(m + 1)/2
Let t = -9 - -14. Solve -2*s - 2*s**2 - 1 + 2*s**4 - 2*s**t + 3*s**3 + s**3 + 3 - 2*s**2 = 0.
-1, 1
Let p(q) be the second derivative of q**6/6 - 5*q**4/12 - 2*q. Factor p(d).
5*d**2*(d - 1)*(d + 1)
Suppose -2*i - 1 = -5*m - 0, 2*m - 2 = 0. Solve -2*k**4 - k**3 + 0*k**2 + i*k**2 - k**3 - k + 3*k = 0 for k.
-1, 0, 1
Suppose -32 = -5*g - 3*k, -24 = -2*g - 4*k - 0*k. Suppose 0 = -g*l - l + a + 12, 5*a = 2*l - 14. Factor 0*d - 10/3*d**4 + 4/3*d**3 + l*d**5 + 0*d**2 + 0.
2*d**3*(d - 1)*(3*d - 2)/3
Let k(z) be the third derivative of 0*z + 0 - 9*z**2 - 1/40*z**4 + 1/100*z**5 + 1/200*z**6 - 1/350*z**7 + 0*z**3. What is y in k(y) = 0?
-1, 0, 1
Let q(h) = -h**3 + h**2 + 1. Let z be q(0). Let s be z/2*2 - 1. Find a such that s + 0*a**2 - 1/5*a + 1/5*a**3 = 0.
-1, 0, 1
Let o = -15 - -27. Factor 3*r - 12 - 2*r**2 + o - r**2.
-3*r*(r - 1)
Let c(i) = -6*i**2 - 4*i + 1. Let h(w) = -w**2 + 1. Let d(g) = c(g) - 5*h(g). Suppose d(a) = 0. Calculate a.
-2
Let a(w) be the third derivative of -w**6/540 + 2*w**5/45 + w**4/108 - 4*w**3/9 - 43*w**2. Factor a(i).
-2*(i - 12)*(i - 1)*(i + 1)/9
Let f(g) = g + 5. Let y = -2 - 3. Let i be f(y). Suppose 0 - 2/3*j**5 + 0*j + i*j**4 + 2/3*j**3 + 0*j**2 = 0. What is j?
-1, 0, 1
Let o(s) = -s**3 - 2*s**2 + 12*s - 13. Let d be o(-5). Factor -2/9*t**3 + 4/3*t**d - 8/3*t + 16/9.
-2*(t - 2)**3/9
Suppose -4*r + 4 = x, -4 = 3*r - x - 0*x. Suppose 5*b - 2*h - 19 = r, -2*b + 5*h + 13 = -b. Factor -2*w + 10*w**5 + 20*w**2 - 4 + 0*w**b - 16*w**4 - 8*w**3 + 0.
2*(w - 1)**3*(w + 1)*(5*w + 2)
Let l(f) be the first derivative of -f**6/15 - 18*f**5/25 - 13*f**4/5 - 68*f**3/15 - 21*f**2/5 - 2*f - 19. Factor l(o).
-2*(o + 1)**4*(o + 5)/5
Let d = 88/7 - 9437/63. Let n = -137 - d. Determine v, given that -n + 2/9*v**3 + 2/9*v**2 - 2/9*v = 0.
-1, 1
Let t(d) be the first derivative of -d**3/18 + 4*d**2/3 - 5*d/2 + 56. Let t(m) = 0. Calculate m.
1, 15
Let c = 37 + -35. Let m(p) be the second derivative of 0 - c*p**2 + 1/5*p**5 - p**3 + 1/2*p**4 + p. Solve m(t) = 0.
-2, -1/2, 1
Let f(d) = 2*d**2 - 12*d - 14. Suppose -z + 14 + 11 = -5*w, 0 = 4*z. Let q(n) = 3*n**2 - 12*n - 13. Let o(s) = w*f(s) + 4*q(s). Factor o(l).
2*(l + 3)**2
Suppose -4 = 4*a + y - 21, 5*a - 3*y = 0. Let t be 1/7*-26 + (10 - 6). Factor -t*i**a + 2/7*i**2 + 2/7*i - 2/7.
-2*(i - 1)**2*(i + 1)/7
Suppose 2*l = 4*a + 18, -5*l - a + 6 = -2*l. Let i(k) be the first derivative of 0*k**2 - 2/9*k - l + 0*k**4 + 4/27*k**3 - 2/45*k**5. Factor i(m).
-2*(m - 1)**2*(m + 1)**2/9
Let l be (-6)/(-2)*(-2)/(-8). Let c be (1 - 0) + 24/(-32). Factor 0 - l*r**2 - c*r.
-r*(3*r + 1)/4
Let c(k) be the first derivative of -k**6/3 + k**5 - 3*k**4/4 - k**3/3 + k**2/2 - 17. Factor c(v).
-v*(v - 1)**3*(2*v + 1)
Let a(q) = -2*q**3 + 9*q**2 - 5*q. Let w(g) = 3*g**3 - 13*g**2 + 7*g. Let p(x) = -7*a(x) - 5*w(x). Find d, given that p(d) = 0.
0, 2
Let c = -19 - -19. Let b(d) be the third derivative of 0*d - 5/44*d**4 + 2*d**2 - 1/33*d**6 - 2/33*d**3 + c - 1/10*d**5. Solve b(m) = 0 for m.
-1, -2/5, -1/4
Factor -2/5*y**3 - 2*y**2 - 16/5*y - 8/5.
-2*(y + 1)*(y + 2)**2/5
Let r(a) be the second derivative of -a**9/3024 + a**7/840 - a**3/2 - 2*a. Let o(j) be the second derivative of r(j). Let o(m) = 0. What is m?
-1, 0, 1
Determine s, given that -2*s**4 - 2*s**3 - 3*s**3 - s**3 = 0.
-3, 0
Let d(q) be the first derivative of -q**3/3 - q**2 - q - 7. Factor d(n).
-(n + 1)**2
Let u(m) be the first derivative of m**8/1260 - m**6/270 + 4*m**3/3 - 5. Let p(s) be the third derivative of u(s). Find i such that p(i) = 0.
-1, 0, 1
Let l(v) = 2*v + 13. Let f be l(-5). Solve 6*j + 12*j**2 + 2*j**f - 5*j**3 - 4*j**2 - 5*j**2 = 0 for j.
-1, 0, 2
Let j(m) = 4*m**3 - 18*m**2 - 12*m. Suppose 2*i + 11 = 3*z + 4, 0 = 4*z + 4*i - 16. Let a(o) = o**3 - 6*o**2 - 4*o. Let x(h) = z*j(h) - 10*a(h). Factor x(b).
2*b*(b + 1)*(b + 2)
Suppose 27 = g + 7. Let b = -16 + g. Factor -2/5 - 8/5*q**3 - 8/5*q - 2/5*q**b - 12/5*q**2.
-2*(q + 1)**4/5
Factor 2/5*p + 4/5 - 2/5*p**2.
-2*(p - 2)*(p + 1)/5
Let b = 49 - 146/3. Factor 1/3*i + 0 + b*i**2.
i*(i + 1)/3
Suppose -10*p**4 - 1183*p**5 + 5*p**3 + 0*p**4 + 1188*p**5 = 0. Calculate p.
0, 1
Let v(h) = h**3 + 8*h**2 - h - 5. Let p be v(-8). Let c be (2/p)/(5/6). Factor 2/5*d - 2/5*d**5 + 0*d**3 - 4/5*d**4 + c*d**2 + 0.
-2*d*(d - 1)*(d + 1)**3/5
Let k be (8/12)/(2/9). Solve 11*w + w**k - 12*w - 2*w**2 + w**2 + 1 = 0.
-1, 1
Let g(j) be the second derivative of 0 - 5*j - 1/33*j**3 + 0*j**2 + 1/11*j**4 - 9/110*j**5. Factor g(r).
-2*r*(3*r - 1)**2/11
Let r(n) be the third derivative of -n**7/1365 + n**6/260 - n**5/130 + n**4/156 - 35*n**2. Factor r(v).
-2*v*(v - 1)**3/13
Let f = -851456/35 - -24329. Let l = -9/7 + f. Factor 4/5*j + 0 - l*j**2 - 2/5*j**3.
-2*j*(j - 1)*(j + 2)/5
Let u = -109/2 - -55. Suppose -1/2*n**3 - 3/2*n**2 + 3/2*n**4 + u*n + 0 = 0. What is n?
-1, 0, 1/3, 1
Let d(m) be the first derivative of m**3/3 - m**2/2 - 6*m - 7. Find i, given that d(i) = 0.
-2, 3
Let i = 1/99 + 889/198. Suppose i*x**4 + 1/2*x**2 + 0 + 0*x + 2*x**5 + 3*x**3 = 0. Calculate x.
-1, -1/4, 0
Solve -1/3 + 0*q + 1/3*q**2 = 0.
-1, 1
Let t(c) be the second derivative of -c**6/10 - 9*c**5/20 + 2*c**3 - 4*c. Factor t(n).
-3*n*(n - 1)*(n + 2)**2
Factor 8/7*k**3 + 4/7*k - 2/7*k**4 + 0 - 10/7*k**2.
-2*k*(k - 2)*(k - 1)**2/7
Let b = 1/62 - -241/434. Let q be (-36)/60 - (-102)/70. Determine v so that -b*v**3 + 0 + 0*v**2 - 2/7*v**5 + 0*v - q*v**4 = 0.
-2, -1, 0
Let k be -2 + ((-30)/(-16) - 4/(-32)). Let d(i) be the first derivative of k*i - 3/2*i**2 + 0*i**4 + 3 - 3*i**3 + 12/5*i**5. Solve d(z) = 0.
-1/2, 0, 1
Let i be ((-14)/12)/(4/3). Let o = i - -11/8. Find s such that -s**2 + o*s**5 + 1/2 + 1/2*s**4 - s**3 + 1/2*s = 0.
-1, 1
Let f = -48 + 195/4. Factor 0*v + 0 - 1/4*v**2 - f*v**4 + 1/4*v**5 + 3/4*v**3.
v**2*(v - 1)**3/4
Let n(h) be the second derivative of h**7/21 + 4*h**6/15 + 3*h**5/5 + 2*h**4/3 + h**3/3 - 5*h. Solve n(a) = 0.
-1, 0
Suppose 6 = k - 6. Let g be (-4)/1*(-6)/k. Factor -4*c**g - 1/2*c - 9*c**3 + 27/2*c**5 + 0 + 0*c**4.
c*(c - 1)*(3*c + 1)**3/2
Factor 2/3*s**3 + 1024/3 + 128*s + 16*s**2.
2*(s + 8)**3/3
Let c be 0*((-9)/36)/((-1)/(-2)). Determine k, given that -k**3 + 0*k - k**4 + c - 1/3*k**5 - 1/3*k**2 = 0.
-1, 0
Let i be (-2)/40*((-22)/8 - 1). Let u(l) be the second derivative of 1/4*l**2 - l - 7/24*l**3 + 1/120*l**6 + 0 - 1/16*l**5 + i*l**4. Factor u(m).
(m - 2)*(m - 1)**3/4
Factor 1 + 1/4*r**2 - r.
(r - 2)**2/4
Let o(c) = -c**2 - c + 1. Let m(s) = -2*s**3 - 6*s**2 - 6*s + 6. Let f(q) = -m(q) + 8*o(q). Factor f(u).
2*(u - 1)**2*(u + 1)
Let k(h) = -3*h - 18. Let n be k(-8). Factor 4 + 10 + 4*v - n - 4*v**2.
-4*(v - 2)*(v + 1)
Let g = 64/35 + -8/35. Let j(h) be the first derivative of 1/2*h**4 - 8/3*h**3 + g*h**5 + 1 - h**2 + 0*h. Factor j(q).
2*q*(q - 1)*(q + 1)*(4*q + 1)
Let d(t) be the third derivative of -1/24*t**3 + 1/210*t**7 + 11/480*t**6 + 0*t + t**2 + 0 + 1/96*t**4 + 3/80*t**5. Factor d(a).
(a + 1)**3*(4*a - 1)/4
Let d(j) be the first derivative of 2/25*