0*w - w**3 - 3*w**2 - 31*w - z + 0*w**2. Factor d(v).
-3*(v - 1)*(v + 3)
Let d(l) = l**2 + 32*l - 27. Let q be d(-28). Let u = -136 - q. Let w**4 + 2/3*w - w**2 - 1/3*w**5 + 0 - 1/3*w**u = 0. Calculate w.
-1, 0, 1, 2
Let n(c) be the third derivative of -c**5/12 + 125*c**4/24 - 20*c**3 + 65*c**2. Suppose n(y) = 0. What is y?
1, 24
Let f(d) be the first derivative of -d**4/32 - d**3/12 + d**2/4 + d - 50. Let f(i) = 0. What is i?
-2, 2
Let b(p) = 5 - 6 - 12 - 2 - 5*p. Let q be b(-3). Determine a, given that -2/3*a**2 + 2/9 + q*a + 4/9*a**3 = 0.
-1/2, 1
Let k(j) = 2*j**5 + 828*j**2 - 51*j**3 - 3*j**5 - 904*j**2 - 56*j - 17*j**4 - 17. Let m(q) = -q**5 + q**4 + q**3 + 1. Let t(p) = -2*k(p) - 2*m(p). Factor t(o).
4*(o + 1)**2*(o + 2)**3
Let b(y) be the second derivative of -3*y**5/140 - 305*y**4/28 - 1672*y**3 - 34656*y**2/7 - 686*y. Factor b(h).
-3*(h + 1)*(h + 152)**2/7
Let x(l) = 2*l**4 - l**3 - l**2 + l + 2. Let z(q) = 13*q**4 - 8*q**3 - 14*q**2 + 8*q + 16. Let o(g) = -5*x(g) + z(g). Suppose o(s) = 0. Calculate s.
-1, 1, 2
What is h in 398*h**3 - 8*h**2 + 0*h**2 - 42*h**2 - 343*h**3 - 5*h**4 = 0?
0, 1, 10
Suppose 413*x + 14 = -2*a + 411*x, -2*a = 4*x + 32. Factor 0 + 3/5*k**4 + 0*k + 0*k**a + 3/5*k**3.
3*k**3*(k + 1)/5
Let s(k) be the second derivative of -k**7/1120 + k**6/80 - k**5/32 + 13*k**3/3 + 22*k. Let m(d) be the second derivative of s(d). Let m(r) = 0. Calculate r.
0, 1, 5
Let a(u) be the first derivative of -2*u**3/27 - 272*u**2/9 - 36992*u/9 - 100. Factor a(g).
-2*(g + 136)**2/9
Let f = 931/2115 + 1/235. Solve -8/9*l**2 + 4/9 + f*l**4 - 4/9*l**5 + 8/9*l**3 - 4/9*l = 0 for l.
-1, 1
Let j(s) be the third derivative of s**7/210 - s**6/30 - s**5/60 + s**4/6 - s**2 + 3*s. Factor j(a).
a*(a - 4)*(a - 1)*(a + 1)
Let y(l) = 7*l**2 + 409*l - 390. Let c(u) = 8*u**2 + 411*u - 380. Let s(x) = 2*c(x) - 3*y(x). Let s(z) = 0. Calculate z.
-82, 1
Let r(z) = -z**3 - 6*z**2 + 9*z. Let n be r(-8). Suppose 16*w - 2*w - n = 0. Suppose -6/5*x**2 + w*x - 6/5 = 0. What is x?
1/3, 3
Let t = -3 + 6. Factor -428*h**2 + 8*h + 7*h - 8 - t*h + 424*h**2.
-4*(h - 2)*(h - 1)
Let r(h) = h**2 - 2. Let l be r(-2). Let w(c) = -2*c**2 + 10*c + 51. Let m be w(8). Let 2*k**3 - k**m - l*k**3 + 8*k - 7*k - k**4 + k**2 = 0. What is k?
-1, 0, 1
Let z(x) be the third derivative of -x**7/315 - x**6/180 + x**5/90 + x**4/36 - 269*x**2. Determine t, given that z(t) = 0.
-1, 0, 1
Let p(d) be the first derivative of -d**6/14 + 6*d**4/7 - 6*d**3/7 - 3*d**2/2 + 18*d/7 + 513. Let p(a) = 0. Calculate a.
-3, -1, 1, 2
Let r = -3117 + 9358/3. Let i(q) be the second derivative of 2*q**2 + 0 + 3/10*q**5 + r*q**3 + 4/3*q**4 - 12*q. Factor i(t).
2*(t + 1)**2*(3*t + 2)
Let t(q) be the second derivative of q**5/180 - 25*q**4/108 + 4*q**3/9 + q - 193. Solve t(c) = 0 for c.
0, 1, 24
Let g(q) be the first derivative of -1/2*q**2 + 1/6*q**3 + 8 + 0*q + 1/8*q**4. Factor g(x).
x*(x - 1)*(x + 2)/2
Let j(d) be the first derivative of 5*d**9/3024 + d**8/336 - d**7/56 - d**6/72 + d**5/12 - 2*d**3 + 9. Let l(c) be the third derivative of j(c). Factor l(k).
5*k*(k - 1)**2*(k + 1)*(k + 2)
Let k(j) = j**4 - 2*j**3 + 39*j**2 + 150*j + 114. Let r(n) = -n**4 + n - 1. Let m(i) = -k(i) - 2*r(i). Let m(b) = 0. Calculate b.
-4, -1, 7
Let p(u) = -u**2 + 25*u + 87. Let d be p(28). Let g(k) be the second derivative of 0 - 1/2*k**2 + d*k - 1/24*k**4 - 1/4*k**3. Factor g(c).
-(c + 1)*(c + 2)/2
Let p be 2/(-3)*(-84)/(-56). Let h be (-4)/p - 28/8*1. Let -1/10*x**2 + 0 - h*x**3 + 0*x - 2/5*x**4 = 0. What is x?
-1, -1/4, 0
Let w(s) = s**5 + 2*s**2 + s + 1. Let u(n) = 7*n**5 + 3*n**4 - 10*n**3 + 12*n**2 + 6*n + 6. Let x(r) = -u(r) + 6*w(r). Factor x(f).
-f**3*(f - 2)*(f + 5)
Let q(r) be the first derivative of -r**6/420 - r**5/70 - 2*r**2 - 4. Let b(u) be the second derivative of q(u). Find f such that b(f) = 0.
-3, 0
Let a(i) be the first derivative of i**5/4 + 21*i**4/4 + 8*i**3 - i**2 - 4*i - 18. Let w(f) be the second derivative of a(f). Factor w(t).
3*(t + 8)*(5*t + 2)
Let x(s) = -s**3 - 6*s**2 - 2*s - 10. Let h be (-4)/(24/(-9))*-4. Let p be x(h). Factor 4*g**4 - g**5 + 14*g - 2*g**2 - p*g**4 - 13*g.
-g*(g - 1)**3*(g + 1)
Suppose 6*h - 3*h = -2*i + 41, -30 = -2*h - 4*i. Factor 0 + h*l - 16 - 2*l**2 + 5*l.
-2*(l - 8)*(l - 1)
Let s(y) be the second derivative of -29*y + 0*y**2 + 2/27*y**3 + 0 - 1/108*y**4. Find i such that s(i) = 0.
0, 4
Let t be 2/(-8) + 416/128. Let 6*k + k - 4*k**2 + k - 2*k**t + 0*k + k**4 = 0. Calculate k.
-2, 0, 2
Suppose -14 = 2*c - 4*c - 2*r, -r - 25 = -3*c. Let j be (-3)/3*(-3)/(12/c). Factor 1/5*h**j + 3/5*h - 2/5 + 1/5*h**4 - 3/5*h**3.
(h - 2)*(h - 1)**2*(h + 1)/5
Suppose -1 + 25 = 8*d. Let w be 0/(0 + -1 + -1). Factor w*m**3 + 7*m - 7*m + 2*m**d.
2*m**3
Let w = 315 + -313. Let d(y) be the third derivative of -2*y**w - 1/60*y**5 + 1/3*y**3 - 1/210*y**7 + 0*y + 0 - 1/8*y**4 + 1/40*y**6. Factor d(o).
-(o - 2)*(o - 1)**2*(o + 1)
Let q(k) be the second derivative of 2*k**6/15 - 2*k**5/5 + k**4/3 + 119*k. Solve q(h) = 0 for h.
0, 1
Let k(p) = 11*p**2 + 130*p + 109. Let x(a) = 27*a**2 + 324*a + 273. Let n(o) = -12*k(o) + 5*x(o). Factor n(y).
3*(y + 1)*(y + 19)
Let c(p) be the first derivative of -p**7/420 + p**6/15 - 4*p**5/5 + 16*p**4/3 + 12*p**3 - 41. Let q(y) be the third derivative of c(y). Solve q(j) = 0 for j.
4
Suppose -2/15*o**4 - 4/3*o**3 - 10/3*o**2 + 0 + 0*o = 0. What is o?
-5, 0
Let x(c) be the second derivative of 7/12*c**4 + 0 + 1/42*c**7 - 1/10*c**6 - 2*c**2 + 0*c**3 - 1/20*c**5 + 2*c. Solve x(a) = 0.
-1, 1, 2
Let s(k) be the first derivative of 5*k**4/2 - 125*k**3/3 + 85*k**2 - 55*k + 303. Factor s(z).
5*(z - 11)*(z - 1)*(2*z - 1)
Let z be 90/4 - 3/2*-1. Suppose 0 = -w + 2, 8 = -4*i - 4*w + z. What is g in 0 + g**3 + 8/5*g**i + 1/5*g**4 + 4/5*g = 0?
-2, -1, 0
Let o(k) = 3*k**2 + 2*k. Let n be o(-2). Suppose t = 5*r - 21, 0 = 5*r - 2*t - 22 - 0. Solve 6*c**3 + 18*c**2 + n*c - 9*c**r - 4*c - 19*c**4 = 0 for c.
-1/2, -2/7, 0, 1
Let v = 2543 + -2540. Let -1/9*m**v + 0*m + 0 - 1/9*m**2 = 0. What is m?
-1, 0
Let y(n) be the third derivative of n**5/450 - 13*n**4/180 - 14*n**3/45 + 110*n**2. Factor y(h).
2*(h - 14)*(h + 1)/15
Suppose 0 = -6*j + 4*j - 4. Let i(f) = -20*f - 3. Let v be i(j). Factor 12*y**3 + v*y**4 - 8*y**4 + 31*y**4 + 75*y**5.
3*y**3*(5*y + 2)**2
Factor 42/5*v + 3/5*v**3 + 21/5*v**2 + 24/5.
3*(v + 1)*(v + 2)*(v + 4)/5
Let j be (-175)/(-49) - (-1)/(-1 + -2 + 2). Factor -2/7 + 24/7*q**3 - 8/7*q + 4/7*q**2 - j*q**4.
-2*(q - 1)**2*(3*q + 1)**2/7
Let n = 206 + -188. Suppose m - n = -o, 10 = -2*o + 7*o. Find x, given that -m*x - 1/3*x**3 - 4*x**2 - 64/3 = 0.
-4
Suppose -38*x + 114 - 114 = 0. Let d(s) be the second derivative of 0*s**6 + 0*s**3 + 0 + 0*s**4 + x*s**2 + 1/35*s**5 - 3*s - 2/147*s**7. Factor d(c).
-4*c**3*(c - 1)*(c + 1)/7
Let m(r) be the first derivative of -r**4 + 52*r**3/3 + 32*r**2 - 112*r - 381. Solve m(u) = 0.
-2, 1, 14
Let n(y) be the first derivative of -y**4/16 + 7*y**3/12 - 104. Factor n(g).
-g**2*(g - 7)/4
Suppose 1/8*u**5 + 1/8*u**2 - 1/8*u**4 + 0 + 1/4*u - 3/8*u**3 = 0. What is u?
-1, 0, 1, 2
Let m be (13 + 203/(-14))*8/(-3). Suppose -2/3*z**5 - 46/9*z**3 - 28/9*z**m - 8/9*z + 0 - 32/9*z**2 = 0. Calculate z.
-2, -1, -2/3, 0
Let q(i) be the third derivative of i**7/140 - 7*i**5/40 - 3*i**4/8 - 110*i**2. Factor q(b).
3*b*(b - 3)*(b + 1)*(b + 2)/2
Let n(z) be the third derivative of -2 + 0*z**3 + 3*z**2 + 0*z - 1/78*z**4 + 1/390*z**5. Let n(v) = 0. What is v?
0, 2
Factor -64 - 394*j**2 + 560*j - 1106*j**2 + 348*j**2 - 324*j**3.
-4*(j + 4)*(9*j - 2)**2
Let a(t) = t**3 + t + 2. Let j(g) = 16*g**3 - 80*g**2 + 112*g - 32. Let p(m) = -4*a(m) + j(m). Find n, given that p(n) = 0.
2/3, 1, 5
Let i(m) be the first derivative of -m**4/2 + 4*m**2 - 154. Factor i(y).
-2*y*(y - 2)*(y + 2)
Let d(g) = 3*g - 2. Let l(z) = 3*z**2 - 33*z + 30. Let s(m) = -6*d(m) - l(m). Factor s(w).
-3*(w - 3)*(w - 2)
Suppose 0 = -4*s + 40 - 8. Suppose t + t = s. Factor q**3 - 3*q**4 + 2*q**4 + 0*q**t + 0*q**3.
-q**3*(q - 1)
Let j(l) be the third derivative of -l**7/735 + 3*l**6/140 - 4*l**5/35 + 4*l**4/21 - 102*l**2. Factor j(b).
-2*b*(b - 4)**2*(b - 1)/7
Let y(p) be the third derivative of p**8/392 + p**7/245 - 3*p**6/140 - p**5/70 + p**4/14 - 2*p**2 + 3*p. Let y(t) = 0. What is t?
-2, -1, 0