-1, -1/4, 14
Let d = 114 + -341/3. Let s = -4 + 4. Solve s - 1/3*m - d*m**4 - m**2 - m**3 = 0 for m.
-1, 0
Let s = 690 - 62099/90. Let x(w) be the second derivative of 8/9*w**2 - 4/27*w**3 - 1/27*w**4 + 0 + s*w**5 + 8*w. Factor x(o).
2*(o - 2)**2*(o + 2)/9
Find s, given that 0 - 4/11*s**3 + 2/11*s**2 - 2/11*s**4 + 4/11*s = 0.
-2, -1, 0, 1
Let p(s) be the second derivative of 2*s**6/75 - 2*s**4/15 + 2*s**2/5 + 65*s - 1. Suppose p(v) = 0. Calculate v.
-1, 1
Let p(z) be the second derivative of -8/5*z**3 - 50*z + 26/5*z**2 + 0 - 1/15*z**4. Factor p(l).
-4*(l - 1)*(l + 13)/5
Let h(u) = u**4 - 2*u**3 - u - 2. Let t(g) = 6*g**4 - 4*g**3 + 12*g**2 + 3*g - 10. Let j(a) = 15*h(a) - 3*t(a). Determine v, given that j(v) = 0.
-2, 0
Let g = -4 + 6. Suppose -6 + 3*u**2 + g - 12*u**3 + 12*u + 1 = 0. Calculate u.
-1, 1/4, 1
Suppose 87*i - 40 = 77*i. Let l(t) be the second derivative of 1/20*t**6 - 1/56*t**7 - 3/80*t**5 + 0*t**i + 0 - 7*t + 0*t**3 + 0*t**2. Let l(n) = 0. What is n?
0, 1
Let j(k) be the first derivative of -k**8/7560 + k**6/540 - k**5/270 + 19*k**3/3 - 17. Let p(h) be the third derivative of j(h). Solve p(z) = 0.
-2, 0, 1
Let v(u) = u**3 + 18*u**2 + u + 21. Let g be v(-18). Factor -2*p**g - 9*p - 2*p**2 + p**3 - p**2 - 3*p**2.
-p*(p + 3)**2
Let f(z) be the third derivative of -z**9/12096 + 5*z**8/4032 - z**7/252 - 3*z**5/5 - 12*z**2. Let b(v) be the third derivative of f(v). What is x in b(x) = 0?
0, 1, 4
Suppose -5*r + 1/2*r**2 + 21/2 = 0. What is r?
3, 7
Let n(d) be the third derivative of -d**5/140 - d**4/28 + 48*d**2. Factor n(w).
-3*w*(w + 2)/7
Let v(j) = 6*j + 32. Let r be v(17). Solve 48*y**2 + 256 + 86*y + 8*y + r*y + 4*y**3 - 36*y = 0.
-4
Let z(n) be the first derivative of 68*n**5/35 + 5*n**4/7 - 197. Factor z(g).
4*g**3*(17*g + 5)/7
Let q(s) be the second derivative of 1/2*s**4 + 0*s**2 + 1/3*s**3 - 47*s - 1/10*s**5 + 0 - 1/5*s**6. Factor q(z).
-2*z*(z - 1)*(z + 1)*(3*z + 1)
Let r(w) = w**4 - w**3 - w**2 - w + 2. Let p(q) = 3*q**5 - 15*q**4 - 57*q**3 + 11*q**2 + 90*q - 32. Let v(s) = p(s) + 2*r(s). Solve v(u) = 0 for u.
-2, 1/3, 1, 7
Let g(k) = -4*k**3 + 2*k + 1. Let v(u) = -70*u**4 + 163*u**3 + 359*u**2 + 124*u + 13. Let q(c) = -10*g(c) + 2*v(c). Find j, given that q(j) = 0.
-1, -2/7, -1/10, 4
Let k be (44/77)/(4/14). Let a be (-11)/(-1) + k/(-1). Find z such that -6*z**4 + 4*z**3 + 6 + 21*z + 9*z**2 - a*z**4 - 25*z**3 = 0.
-1, -2/5, 1
Factor 0*o + 6*o**2 + 64/11*o**3 - 2/11*o**4 + 0.
-2*o**2*(o - 33)*(o + 1)/11
Let x(m) be the third derivative of -m**10/75600 - m**9/30240 + m**5/20 - m**2. Let w(g) be the third derivative of x(g). Solve w(f) = 0 for f.
-1, 0
Let n(j) = j**4 - j - 1. Let u(i) = i**3 + 5*i**2 + 2*i - 1. Let d(b) = -2*n(b) + 2*u(b). Factor d(p).
-2*p*(p - 3)*(p + 1)**2
Let r(d) be the second derivative of -d**5/70 - 5*d**4/6 - 32*d**3/21 + 68*d**2/7 + 615*d. Factor r(q).
-2*(q - 1)*(q + 2)*(q + 34)/7
Let m = 671 + -669. Let p(b) be the third derivative of 1/12*b**4 + 0 + 1/45*b**5 + 1/9*b**3 - 1/105*b**7 - 5*b**m + 0*b - 1/504*b**8 - 1/90*b**6. Factor p(a).
-2*(a - 1)*(a + 1)**4/3
Suppose 3*n + 2*n = 3*k + 143, 2*n + 5*k = 51. Find d such that 12*d + 4*d**2 + 15*d + n*d - 35*d = 0.
-5, 0
Let m(a) be the first derivative of -2*a**5/65 - a**4/13 + 16*a**3/39 - 423. Find u such that m(u) = 0.
-4, 0, 2
Factor 122/13*l**3 - 798/13*l**2 - 6/13*l**4 + 1470/13*l + 1372/13.
-2*(l - 7)**3*(3*l + 2)/13
Let w(v) be the third derivative of -v**9/4536 - v**8/5040 + v**7/2520 - 3*v**3 - 10*v**2. Let p(a) be the first derivative of w(a). Factor p(s).
-s**3*(s + 1)*(2*s - 1)/3
Suppose 2*p - r - 4*r = 1, -2*p = 3*r - 9. Let n(y) be the first derivative of 2/3*y**p + 18*y - 6*y**2 + 2. Factor n(h).
2*(h - 3)**2
Let i(g) be the first derivative of 4*g**5/5 + 7*g**4 + 20*g**3 + 26*g**2 + 16*g + 83. Factor i(x).
4*(x + 1)**3*(x + 4)
Let -5*d**2 - 222 - 13*d + 222 + 73*d = 0. What is d?
0, 12
Let p(w) be the second derivative of -3*w**6/40 + 4*w**5/15 + w**4/6 + 21*w**2/2 + 19*w. Let z(h) be the first derivative of p(h). Factor z(k).
-k*(k - 2)*(9*k + 2)
Let w = 60 + -25. Suppose 75*g**3 - 35*g**5 - 38*g**5 + 78*g**5 + 45*g**4 + w*g**2 = 0. Calculate g.
-7, -1, 0
Let p(g) be the second derivative of -5*g**4/12 - 10*g**3 - 55*g**2/2 + 15*g. Factor p(q).
-5*(q + 1)*(q + 11)
Factor -83/5*r + 0 + 1/5*r**2.
r*(r - 83)/5
Let q(f) = 7*f**4 - 27*f**3 + 45*f**2 - 29*f + 6. Let w(m) = 36*m**4 - 135*m**3 + 225*m**2 - 145*m + 30. Let z(d) = 22*q(d) - 4*w(d). Let z(k) = 0. Calculate k.
2/5, 1, 3
Determine f so that 18*f**3 + 7*f**2 - 942*f**4 + 14*f**2 + 939*f**4 = 0.
-1, 0, 7
Suppose b + 34*b - 105 = 0. Let p(m) be the first derivative of 0*m + 3/7*m**b - 1 + 3/28*m**4 + 3/7*m**2. Factor p(o).
3*o*(o + 1)*(o + 2)/7
Factor 0*a**2 - 4/7*a + 2/7 - 2/7*a**4 + 4/7*a**3.
-2*(a - 1)**3*(a + 1)/7
Let x(l) be the first derivative of -l - 5 + 0*l**2 - 1/5*l**3 - 1/20*l**4. Let n(u) be the first derivative of x(u). Suppose n(q) = 0. Calculate q.
-2, 0
Let v(g) be the third derivative of 1/105*g**7 + 0*g**6 + 0 + 1/3*g**3 + 0*g**4 + 0*g - 23*g**2 - 1/15*g**5. Solve v(y) = 0.
-1, 1
Let c(j) be the first derivative of 0*j**3 + 2/55*j**5 + 0*j + 1/22*j**4 + 12 + 0*j**2. Factor c(k).
2*k**3*(k + 1)/11
Let g(a) be the first derivative of -a**3/9 - 8*a**2/3 - 5*a - 36. Solve g(y) = 0 for y.
-15, -1
Let d = -3/305 - -178/11895. Let q(r) be the second derivative of 10*r + 0*r**3 + 3/130*r**5 + d*r**6 + 0*r**2 + 1/39*r**4 + 0. Factor q(j).
2*j**2*(j + 1)*(j + 2)/13
Let u(s) = s**3 + 2*s**2 - 8*s + 1. Let q be u(-4). Factor -3*n**3 - 12*n**2 - 7 - 15*n + q - 4*n**3 + 4*n**3.
-3*(n + 1)**2*(n + 2)
Determine b, given that 2*b + 11*b + b - 6*b - 4*b**2 = 0.
0, 2
Let g(v) = -2*v**2 + 25*v**3 - 18 - 5*v**3 - 4*v + 19 + 3*v**2. Let c(f) = 21*f**3 - 4*f + 2. Let o(w) = -4*c(w) + 6*g(w). Find u, given that o(u) = 0.
-1/3, 1/2
Let p(n) be the third derivative of n**6/1440 + n**5/240 - n**4/32 + 25*n**3/6 - 2*n**2. Let t(q) be the first derivative of p(q). Factor t(g).
(g - 1)*(g + 3)/4
Let r be -1 - (-3)/6 - 49/(-2). Suppose 0 = -c - 7*c + r. Factor -4/13*v + 10/13*v**4 + 0 - 18/13*v**c - 2/13*v**5 + 14/13*v**2.
-2*v*(v - 2)*(v - 1)**3/13
Let k(j) = 33*j**3 + 1095*j**2 - 734*j + 118. Let r(d) = 98*d**3 + 3286*d**2 - 2200*d + 352. Let o(c) = 10*k(c) - 3*r(c). What is p in o(p) = 0?
-31, 1/3
Let g(z) be the third derivative of -z**8/336 + 3*z**7/14 - 29*z**6/8 - 317*z**5/12 - 70*z**4 - 96*z**3 + 94*z**2. Determine r, given that g(r) = 0.
-1, 24
Suppose -4*v = -5*p - 51, -8*v - 3*p = -10 - 1. Find q such that 0*q**3 + 0 + 2/23*q**2 + 0*q - 2/23*q**v = 0.
-1, 0, 1
Solve -17 + 33*h**2 - 25 + 125*h + 1 + 1 - 20*h**3 + 112*h**2 = 0.
-1, 1/4, 8
Let p(j) be the first derivative of -2/27*j**3 + 1/3*j**2 - 4/9*j + 11. Suppose p(f) = 0. Calculate f.
1, 2
Let w be -5*(1 + 8/(-20)). Let k(x) = -x**2 - x + 1. Let u(c) = c**3 + 21*c**2 + 189*c + 515. Let m(b) = w*k(b) + u(b). Let m(l) = 0. What is l?
-8
Let q(z) be the first derivative of z**4/22 - 92*z**3/33 + 43*z**2/11 + 180*z/11 + 313. Factor q(i).
2*(i - 45)*(i - 2)*(i + 1)/11
Let p be 23 - -2*(2 - 1). Let c = p - 20. Solve j**3 + 99*j**2 - j**4 - 98*j**2 - 3*j**5 + 2*j**c = 0 for j.
-1, 0, 1
Let a be -2 + 25*9/45. Let i(p) be the second derivative of -1/2*p**4 + 3/20*p**5 - 6*p + a*p**2 - 1/2*p**3 + 0. Suppose i(b) = 0. Calculate b.
-1, 1, 2
Suppose 5*y = g - 3*g + 8, 3*g = -y - 1. Factor -20*r + 18*r**2 - 11*r**y - 12*r**2 - 20.
-5*(r + 2)**2
Let y be (4 - (-24)/(-5))*(8 - (-252)/(-27)). What is m in -2/3*m**2 - 4/15*m - 2/15*m**3 + y = 0?
-4, -2, 1
Determine y so that 8*y**3 + 0*y**3 - 4*y**3 - 63*y + 76*y + 184*y**2 + 167*y = 0.
-45, -1, 0
Factor 18*m**2 + 16*m + 21*m + 55*m - 22*m**2.
-4*m*(m - 23)
Factor -11 - 1/2*v**2 - 23/2*v.
-(v + 1)*(v + 22)/2
Let a(n) be the third derivative of -n**5/150 + 11*n**4/10 - 363*n**3/5 + 2*n**2 + 2. Factor a(z).
-2*(z - 33)**2/5
Let a(o) be the first derivative of -o**6/14 - 33*o**5/35 - 69*o**4/14 - 90*o**3/7 - 243*o**2/14 - 81*o/7 + 353. Factor a(r).
-3*(r + 1)**2*(r + 3)**3/7
Let w(y) be the third derivative of 0*y**3 + 1/75*y**5 + 1/1680*y**8 + 2/525*y**7 + 1/120*y**4 + 2*y**2 + 1/100*y**6 + 0*y + 0. Solve w(k) = 0.
-1, 0
Let x(g) be the first derivative of -1/210*g**5 + 0*g + 2*g**2 - 1/420*g**