80 + s**3/6 - 2*s**2. Let q(p) be the first derivative of f(p). Factor q(n).
n**2*(n - 1)**3/3
Let k(v) be the third derivative of -1/160*v**6 + 0*v**5 + 0*v + 0*v**3 + 0*v**4 + 0 + v**2 - 1/448*v**8 - 1/140*v**7. Factor k(n).
-3*n**3*(n + 1)**2/4
Let b(d) = d**2 - 1. Let k(l) = -2*l**2 - l + 3. Let r(f) = -3*b(f) - 3*k(f). Factor r(y).
3*(y - 1)*(y + 2)
Let n = 2073/7 - 296. Factor 0 + 0*v**3 + 0*v**2 + 1/7*v**4 - n*v**5 + 0*v.
-v**4*(v - 1)/7
Factor -2*c**5 + 6*c**4 + c**5 - 4*c**3 + 3*c**5 + 8*c**3.
2*c**3*(c + 1)*(c + 2)
Let s(l) be the second derivative of -l**6/270 - 7*l**5/180 - l**4/12 + l**3/2 + 3*l**2 - 11*l - 1. Find o, given that s(o) = 0.
-3, 2
Factor 9*j**3 - 5*j**3 - 18*j**4 + 16*j**4.
-2*j**3*(j - 2)
Let n(u) be the third derivative of u**5/15 - u**4/6 + u**3/3 + u**2. Let d(c) = 15*c**2 - 16*c + 9. Let j(b) = -2*d(b) + 9*n(b). Let j(p) = 0. Calculate p.
0, 2/3
Let t(n) = -3*n**2 + 2*n. Let y(g) = -16*g**2 + 10*g. Let z(o) = -o**2 + 7*o + 10. Let m be z(8). Let d(u) = m*y(u) - 11*t(u). What is b in d(b) = 0?
0, 2
Suppose 3*o + 9*y = 4*y + 30, 30 = 3*o - 5*y. Factor 2*m**2 + m**2 - o + 4*m + 4 - m.
3*(m - 1)*(m + 2)
Solve 42/5*m**3 + 0 - 34/5*m**4 - 22/5*m**2 + 4/5*m + 2*m**5 = 0.
0, 2/5, 1
What is y in 16/11*y + 24/11 - 2/11*y**3 - 2/11*y**2 = 0?
-2, 3
Find z such that 2*z**5 + 8*z + 2*z**5 - 8*z**3 - 3*z - z = 0.
-1, 0, 1
Let d(b) = b**2. Let c = 21 + -24. Let j(f) = 6*f**2 + 3*f. Let g(y) = c*d(y) + j(y). Suppose g(h) = 0. Calculate h.
-1, 0
Let z(w) be the first derivative of -49*w**5/20 - 133*w**4/48 - 10*w**3/9 - w**2/6 + 1. Solve z(j) = 0.
-1/3, -2/7, 0
Let k be (2/8)/(1/(-49)). Let g = k + 547/44. Determine b so that g*b**3 + 6/11*b - 6/11*b**2 - 2/11 = 0.
1
Let k be -3*77/(-396) - (-2)/(-6). Let 0*i + 1/4*i**2 - k = 0. What is i?
-1, 1
Let o be 1/((-2)/24*-3). Let j = o + 1. What is t in 2*t**2 - t**5 + 2*t**3 - t**j + 0*t**3 - 2*t**4 = 0?
-1, 0, 1
Let k(j) be the third derivative of j**5/60 - j**4/24 + 17*j**2. What is z in k(z) = 0?
0, 1
Let x(g) be the third derivative of g**6/120 + 7*g**5/60 + g**4/4 + g**3/2 + 5*g**2. Let k be x(-6). Solve f**2 + 0*f + 0*f**k - 1/2*f**4 - 1/2 = 0 for f.
-1, 1
Let u(i) be the second derivative of -1/10*i**6 + 0 + 9/20*i**5 + 3*i**2 - 3/2*i**3 - 2*i - 1/4*i**4. Find y such that u(y) = 0.
-1, 1, 2
Suppose 1 - 5 = -r. Let n(d) be the second derivative of 0*d**6 - d - 1/9*d**3 + 0*d**r - 1/63*d**7 + 0 + 1/15*d**5 + 0*d**2. Factor n(i).
-2*i*(i - 1)**2*(i + 1)**2/3
Let y(x) = 2*x**2. Let h(u) = u**2 + 5*u - 5. Let n(s) = -2*s**2 - 8*s + 8. Let c(o) = -8*h(o) - 5*n(o). Let w(d) = -3*c(d) + 2*y(d). Factor w(j).
-2*j**2
Let f(r) = 6*r**3 + 2*r**2 + 4*r. Suppose 3 = -2*d - 11. Let p(w) = 11*w**3 + 3*w**2 + 7*w. Let t(k) = d*f(k) + 4*p(k). Factor t(y).
2*y**2*(y - 1)
Let -14/9*k + 10/9*k**2 - 2/9*k**3 + 2/3 = 0. Calculate k.
1, 3
Let r be 1/(4 - 1)*0. Factor 4*v**2 - 4 - v**3 + 3*v**3 + 10*v - 12*v**2 + r*v**3.
2*(v - 2)*(v - 1)**2
Let h = -1298 - -3860/3. Let p = 38/3 + h. Factor 4*f**3 + 2/3*f**2 + 0 - p*f.
2*f*(2*f - 1)*(3*f + 2)/3
Let i = 32/1007 + 128958/61427. Let j = i + 1896/427. Factor -8/7 + 40/7*d - j*d**2 + 2*d**3.
2*(d - 2)*(d - 1)*(7*d - 2)/7
Let l be (-363)/(-9) + (-4)/(-6). Let y = 124/3 - l. What is c in 4/3 + 4/3*c + y*c**2 = 0?
-2
Let n = 146 + -1018/7. Let h = -1286/7 + 184. Let -h - 8/7*u**3 + 4/7*u**2 + 4/7*u**5 - 2/7*u**4 + n*u = 0. What is u?
-1, 1/2, 1
Let v be (22/6)/(-1) + (1 - -3). Factor -1/3*y**2 - v*y + 1/3 + 1/3*y**3.
(y - 1)**2*(y + 1)/3
Let q(r) be the third derivative of 1/1512*r**8 - 5*r**2 + 0*r**5 + 0*r**4 + 0*r + 0 + 0*r**6 - 1/945*r**7 + 0*r**3. Let q(g) = 0. Calculate g.
0, 1
Let v be 4/(-26) + 63/156. Factor 1/4*i**2 - 1/2 - v*i.
(i - 2)*(i + 1)/4
Let y(k) = 0*k**4 + 7*k + 16*k**2 + 5*k**3 - 1 - 4*k**2 - 2*k**4. Let s(j) = 7*j**4 - 20*j**3 - 47*j**2 - 28*j + 3. Let p(d) = -6*s(d) - 22*y(d). Factor p(f).
2*(f + 1)**3*(f + 2)
Let c be (-6)/(-7)*(-28)/(-6). Solve -4 + 20*f**2 + 21*f**3 - 29*f**2 + 9*f**4 - 6*f + c - 15*f**5 = 0.
-1, -2/5, 0, 1
Let c(i) be the third derivative of -1/300*i**6 + 1/12*i**4 - 2/15*i**3 + 2*i**2 + 0*i + 1/525*i**7 - 1/50*i**5 + 0. Find f such that c(f) = 0.
-2, 1
Let q(k) = -5*k**3 - 35*k**2 - 35*k + 5. Let t(a) = a**2 - a - 1. Let g(w) = -q(w) - 5*t(w). What is m in g(m) = 0?
-4, -2, 0
Let p(f) be the second derivative of -1/30*f**3 + 1/30*f**4 + 0 - 1/210*f**7 + 1/50*f**5 - 1/10*f**2 - f - 1/150*f**6. What is w in p(w) = 0?
-1, 1
Let l(q) = -q**3 - 5*q**2 - 5*q. Let x be l(-4). Factor 4*g**3 - x*g**3 + 3*g**3 - 3*g.
3*g*(g - 1)*(g + 1)
Let g(z) be the second derivative of -z**7/840 + 3*z**6/320 - z**5/80 + 5*z**4/12 + z. Let v(j) be the third derivative of g(j). Factor v(i).
-3*(i - 2)*(4*i - 1)/4
Let u(c) = 6*c**3 - 23*c**2 + 13*c - 1. Let g(i) = 21*i**3 - 81*i**2 + 45*i - 3. Let w(y) = 5*g(y) - 18*u(y). Factor w(j).
-3*(j - 1)**3
Suppose 3*g - 6 = g + 2*f, -f = 3*g - 21. Let p be g/28 + 10/35. Suppose -m - 1/2 - p*m**2 = 0. Calculate m.
-1
Let d(x) be the first derivative of -1/60*x**4 - x**3 + 4 + 0*x**2 - 1/100*x**5 - 1/450*x**6 + 0*x. Let b(v) be the third derivative of d(v). Factor b(j).
-2*(j + 1)*(2*j + 1)/5
Let w(u) = 2*u**4 - 4*u**3 - 6*u**2 - 8*u - 2. Let x(k) = 4*k**4 - 9*k**3 - 12*k**2 - 17*k - 5. Let s(d) = 13*w(d) - 6*x(d). Solve s(j) = 0.
-2, -1, 1
Let l(z) be the first derivative of -1/10*z**4 + 4/15*z**3 - 1/5*z**2 + 0*z - 1. Factor l(f).
-2*f*(f - 1)**2/5
Let v(q) = 7*q**3 - 17*q**2 - q + 23. Let s(d) = 64*d**3 - 152*d**2 - 8*d + 208. Let k(b) = 3*s(b) - 28*v(b). Factor k(f).
-4*(f - 5)*(f - 1)*(f + 1)
Let x = -8 + 13. Suppose l + 2 = -4*h + 3, h = -5*l + x. Determine z so that -2/7*z**5 - 2/7*z**2 + 0 + 2/7*z**4 + 2/7*z**3 + h*z = 0.
-1, 0, 1
Let y(c) = 3*c**2 + 6*c - 3. Let x(f) = -6*f**2 - 12*f + 5. Let s(r) = -r**2 + 8*r + 6. Let n be s(8). Let b(p) = n*x(p) + 11*y(p). Factor b(q).
-3*(q + 1)**2
Let z = -3 + 3. Suppose 10*r = 39 + 11. Suppose 1/4*o**r + z + 9/4*o**3 + 1/2*o - 5/4*o**4 - 7/4*o**2 = 0. Calculate o.
0, 1, 2
Suppose -3*i + 0 = -6. Factor -i*q**3 + 2*q**4 - 4*q - 2 - 3*q**3 + 9*q**3.
2*(q - 1)*(q + 1)**3
Let m(a) be the first derivative of 1/5*a**2 + 2 - 2/15*a**3 + 0*a. Determine q, given that m(q) = 0.
0, 1
Let v(t) be the second derivative of -t**6/90 - t**5/20 - t**4/12 - t**3/18 - 6*t. Solve v(m) = 0.
-1, 0
Let s(g) be the second derivative of -27*g**5/20 + 11*g**4/4 - g**3 - 47*g. Factor s(w).
-3*w*(w - 1)*(9*w - 2)
Suppose 2*l + 3*l = 3*l. Factor 28/5*b**5 - 8/5*b**3 + l*b**2 - 4*b**4 + 0*b + 0.
4*b**3*(b - 1)*(7*b + 2)/5
Suppose 686/9 + 14/3*p**2 + 98/3*p + 2/9*p**3 = 0. What is p?
-7
Let c(t) be the second derivative of -4*t + 0 + 1/9*t**3 + 1/18*t**4 - 2/3*t**2. Suppose c(d) = 0. What is d?
-2, 1
Let l(v) be the second derivative of v**7/357 + v**6/85 + 3*v**5/170 + v**4/102 - 8*v. Solve l(n) = 0.
-1, 0
Let 51*k**3 + 28*k + 4*k**4 - 12*k - 63*k**3 = 0. What is k?
-1, 0, 2
Let k(j) be the third derivative of j**8/448 - j**7/280 - j**6/160 + j**5/80 + 8*j**2. Suppose k(u) = 0. What is u?
-1, 0, 1
Find o such that -40*o**2 - 25*o**3 - 21*o - 5*o - 30*o**2 - 8 - 18*o = 0.
-2, -2/5
Let c(g) = -3*g**3 + 3*g**2 + 9*g + 9. Let t(o) = 6*o**3 - 5*o**2 - 17*o - 17. Let s(b) = 11*c(b) + 6*t(b). Let s(a) = 0. Calculate a.
-1, 1
Let u(l) be the third derivative of l**8/6720 - l**7/1680 + l**5/30 + 5*l**2. Let t(v) be the third derivative of u(v). Let t(x) = 0. What is x?
0, 1
Let q = 14 + -8. Suppose -2 - 4*h**2 + 2*h**3 - h + q*h**2 - h = 0. Calculate h.
-1, 1
Let b(y) be the second derivative of -9*y**5/20 - 7*y**4/4 - y**3 - 11*y. Solve b(n) = 0.
-2, -1/3, 0
Let w(j) be the first derivative of 2*j**3/15 + j**2/5 - 2. Factor w(t).
2*t*(t + 1)/5
Suppose -m + 3*c + 0 = 7, -3*m = -5*c + 9. Factor -2/5*f**4 + 0 + 0*f - 4/5*f**m - 6/5*f**3.
-2*f**2*(f + 1)*(f + 2)/5
Let l = 184/249 + -6/83. Factor -l*v**2 - 4/3 - 2*v.
-2*(v + 1)*(v + 2)/3
Let x = 47 + -46. Suppose -x - g**4 - 1/2*g**5 + g**3 - 1/2*g + 2*g**2 = 0. Calculate g.
-2, -1, 1
Let p = 71/150 + 2/75. Suppose -3/2*u - 1 - p*u**2 = 0. What is u?
-2, -1
Let t(n) be the first derivative of n**5/5 + n**4/3 - n + 7. Let r(z) be the first derivative of t(z). Determine y, given that r(y) = 0.
-1, 0
Let i(u) be the first derivative of -3*u**5/