t i(u) = 5*u**3 + 8*u**2 + 9*u - 4. Suppose -k = 3, -7*k + 5*k = -3*p + 9. Let n(l) = p*i(l) + 2*w(l). Factor n(r).
5*r*(r + 1)**2
Let f = 40 - 36. Solve 16*j - 27*j**3 + 2*j**5 - 14*j**2 - 57*j**3 + 66*j**3 + 14*j**f = 0 for j.
-8, -1, 0, 1
Let u be 47/(-30) + 1704/710. Let t(z) be the second derivative of -z**2 + 0 + 1/30*z**6 - u*z**3 + 1/20*z**5 - 22*z - 1/4*z**4. Let t(p) = 0. What is p?
-1, 2
Let w = -7967 - -199177/25. Let v(q) be the first derivative of 0*q**2 + 19 - 1/30*q**6 + 2/15*q**3 + 1/20*q**4 - w*q**5 + 0*q. Suppose v(t) = 0. What is t?
-2, -1, 0, 1
Let o = 3131 - 3129. Let k(c) be the first derivative of 0*c + 1/3*c**6 + 0*c**3 + 8/5*c**5 + 0*c**2 - 7 + o*c**4. Suppose k(t) = 0. What is t?
-2, 0
Suppose 202/3*z**3 - 1088/3*z - 14/3*z**5 - 16*z**4 + 192 + 124*z**2 = 0. Calculate z.
-4, 1, 18/7
Let g = 366 + -363. Suppose 4*f - 37 = -5*w, g*f - 16 = -4*w + 13. Solve -1/6*q**f - 1/3*q**2 - 1/6*q + 0 = 0 for q.
-1, 0
Suppose -21*n + 1028 = -547. Factor 2*l**5 - 24*l**4 + 4*l**4 + n*l**3 - 72*l**2 - 9*l**3.
2*l**2*(l - 4)*(l - 3)**2
Let n be (-15)/18 + 1 - 289/(-102). Solve -3*t**n + 10*t + 5*t**3 - 548*t**2 + 536*t**2 = 0 for t.
0, 1, 5
Let f(k) be the third derivative of -k**7/420 + 11*k**6/80 - 109*k**5/60 - 75*k**4/4 - 54*k**3 - 576*k**2 + 1. Determine l, given that f(l) = 0.
-2, -1, 18
Find f, given that -57/4*f + 51/4*f**2 - 27/2 + 3/4*f**4 + 57/4*f**3 = 0.
-18, -1, 1
Suppose -5*c + 37057*o = 37054*o - 40, 4*o + 48 = 4*c. What is k in 10/3*k**c - 10/3*k**4 + 0*k - 5/3*k**3 + 5/3*k**5 + 0 = 0?
-1, 0, 1, 2
Let m(z) be the third derivative of -z**6/120 - z**5/4 - 19*z**4/12 - 4*z**3 + 481*z**2 - z + 2. Let m(u) = 0. What is u?
-12, -2, -1
Let -105/2*f**2 + 47/8*f**3 - 1/8*f**4 - 338 - 793/2*f = 0. What is f?
-4, -1, 26
Suppose 13465*o**3 - 25782*o**3 + 5*o**5 - 10935*o + 13127*o**3 + 120*o**4 = 0. What is o?
-9, 0, 3
Suppose -4*v - 5*z = 5, 0 = -3*v - z + 10680 - 10670. What is s in 0*s**2 + 1/2*s**v + 0 - s**3 + 0*s + 1/2*s**4 = 0?
-2, 0, 1
Let s be ((-3)/(-6))/(4 - 924/232). Factor -s*m**2 - 10*m + 5 + 21*m**2 + 13*m**2.
5*(m - 1)**2
Let q(f) be the second derivative of f**4/30 - 79*f**3/15 + 7*f + 27. Factor q(v).
2*v*(v - 79)/5
Factor 0*u - 2147*u**2 - 1359*u**2 + 5*u**3 + 0*u - 2764*u**2.
5*u**2*(u - 1254)
Let j be 2/4 - 2/8. Let n = -1461 + 1461. Suppose 1/4*v**2 - 1/4*v**4 - 1/4*v + n + j*v**3 = 0. What is v?
-1, 0, 1
Suppose -3*i - 21 = -5*r, -3*r - 441*i + 437*i = -1. Find z, given that -3*z + 0 - 1/4*z**r + 7/4*z**2 = 0.
0, 3, 4
Let a(g) = -41*g**2 - 6220*g - 18498. Let c(r) = -92*r**2 - 13996*r - 41620. Let d(n) = -20*a(n) + 9*c(n). Factor d(w).
-4*(w + 3)*(2*w + 385)
Let s(u) be the third derivative of u**6/60 - 113*u**5/30 - u**4/3 + 452*u**3/3 + 30*u**2 + 4*u. Factor s(w).
2*(w - 113)*(w - 2)*(w + 2)
Let v = 12 - 9. Let x be (93/(-5) - (-15)/25)/(17 + -25). Factor -x*w + v*w**2 - 3/4*w**3 + 0.
-3*w*(w - 3)*(w - 1)/4
Suppose -46 + 142 + 66 = 54*n. Determine l, given that -28/11*l**n - 14/11*l**4 + 18/11 - 2/11*l**5 - 4/11*l**2 + 30/11*l = 0.
-3, -1, 1
Let d(f) = 10*f**3 - 4*f**2 - 17. Let j(o) = -o**3 + o + 1. Let u be ((-11)/2)/((24/8)/12). Let z(a) = u*j(a) - 2*d(a). Factor z(h).
2*(h - 1)**2*(h + 6)
What is p in 4*p**2 - 2743*p + 4*p**3 + 2799*p - 40*p**2 = 0?
0, 2, 7
Let k be (4 - (-8 - 4)) + 6. Factor -3*x**2 + k - 4 + 15 + 4*x**2 - 3 - 13*x.
(x - 10)*(x - 3)
Let v(u) be the third derivative of -18*u**2 + 0*u + 5/48*u**4 - 1/60*u**5 + 0 + 1/4*u**3. Let v(r) = 0. What is r?
-1/2, 3
Suppose 2*m + 417 = 29*r, 5*m - 147 = 5*r + 228. Suppose -40/11 + 22*t**4 - 850/11*t**2 + m*t**3 - 408/11*t = 0. Calculate t.
-5, -2/11, 1
Let r(a) be the third derivative of -a**6/30 - 169*a**5/15 - 83*a**4/3 + 224*a**3 + 46*a**2. Factor r(t).
-4*(t - 1)*(t + 2)*(t + 168)
Let l(v) be the second derivative of -2 + 1/3*v**4 - 48*v**2 - 10*v - 10/3*v**3. Solve l(y) = 0 for y.
-3, 8
Let y = -142 + 138. Let m(s) = 10*s**2 + 465*s + 10590. Let q(l) = -9*l**2 - 464*l - 10588. Let v(c) = y*m(c) - 5*q(c). Factor v(t).
5*(t + 46)**2
Let s(a) be the second derivative of a**6/5 - 113*a**5/40 + 7*a**4/8 + 209*a**3/12 + 63*a**2/4 - 9*a + 248. Suppose s(c) = 0. What is c?
-1, -1/3, 7/4, 9
Let k(t) be the first derivative of t**5/45 - t**4/18 - 35*t**3/27 - 758. Factor k(n).
n**2*(n - 7)*(n + 5)/9
Find w such that -6760/3 - 26365/3*w**2 - 35/3*w**5 - 1295/3*w**3 - 31070/3*w + 725/3*w**4 = 0.
-4, -1, -2/7, 13
Let j = -4/415 - -87/415. Let x(u) be the first derivative of 7/3*u**3 + 17 - 1/2*u**2 - 4/3*u - 17/12*u**4 + j*u**5. Find i, given that x(i) = 0.
-1/3, 1, 4
Let v(y) be the first derivative of 450/7*y - 30/7*y**2 + 2/21*y**3 - 98. Suppose v(g) = 0. What is g?
15
Let v be 24/288 - (-6)/36. Suppose 0*q + q**3 + 0*q**2 + v*q**4 + 0 = 0. Calculate q.
-4, 0
Let m be (-8)/3*(-30)/40. Factor 3072 + 38*p - 24*p**3 + 2*p**4 + 154*p + 116*p - 144*p**m + 460*p + p**4.
3*(p - 8)**2*(p + 4)**2
Let s(h) = -h**3 + 20*h**2 - 21*h + 68. Let k be s(19). Factor 88*v**2 - 167*v**2 - k + 9*v + 82*v**2.
3*(v - 2)*(v + 5)
Factor 3*c**5 - 212*c**2 + 677*c - 126 + 342*c**3 + 34*c**2 - 170*c**2 - 230*c - 240*c**2 - 78*c**4.
3*(c - 21)*(c - 2)*(c - 1)**3
Let h = -4 + 5. Let a(n) = 0*n**2 + n + 14*n**2 - 31*n**2 + 16*n**2. Let g(u) = -20*u. Let o(s) = h*g(s) + 15*a(s). Find i such that o(i) = 0.
-1/3, 0
Let p(n) be the third derivative of -n**9/68040 - n**8/10080 + n**6/810 - 89*n**4/24 - 8*n**2 + 7*n. Let w(o) be the second derivative of p(o). Factor w(c).
-2*c*(c - 1)*(c + 2)**2/9
Let x(y) be the third derivative of 0*y + 0 - 268*y**2 - 1/900*y**6 + 1/45*y**4 + 1/450*y**5 - 4/45*y**3. Determine u so that x(u) = 0.
-2, 1, 2
Let x(g) be the first derivative of -g**6/405 + g**5/36 - g**4/12 + 2*g**3/3 + 50*g + 13. Let o(m) be the third derivative of x(m). Factor o(y).
-2*(y - 3)*(4*y - 3)/9
Find u such that 39*u**3 + 38*u**2 + 0 - 4/3*u + 59/6*u**4 = 0.
-2, 0, 2/59
Suppose -10682307/2*w - 5661/2*w**2 - 6719171103/2 - 1/2*w**3 = 0. Calculate w.
-1887
Let m = 8848862/7 - 1264118. Let 4/7*k**5 + 108/7*k**3 + 0*k - 108/7*k**2 + 0 - m*k**4 = 0. What is k?
0, 3
Suppose 54 = 28*a - 2. Factor -9*q**2 + 10*q**2 + 35 + 40*q - 3*q**a + 7.
-2*(q - 21)*(q + 1)
Let v be (-2 + 86/40)*(-19 + 7981/414). Let a(x) be the first derivative of 1/6*x**3 + 0*x + 0*x**2 - v*x**6 - 5/16*x**4 + 1/5*x**5 - 11. Factor a(r).
-r**2*(r - 2)*(r - 1)**2/4
Suppose 18 = n - 3*s, -3*s + 0 = -12. Factor n + 27 - 90 - 9*i + 30 - 6*i**2.
-3*(i + 1)*(2*i + 1)
Let o(t) = 3*t**2 - t - 1. Let s be (-1)/(1/(3/3 + 0)). Let r be o(s). Find c, given that -5*c**2 - r*c**4 + 7*c**4 + c**4 = 0.
-1, 0, 1
Solve 78*o - 28*o + 145*o + 293810*o**3 - 293811*o**3 + 756 + 16*o**2 + 74*o = 0.
-7, -4, 27
Let 1170*b**4 + 959*b**3 + 1676*b - 4865*b**3 - 4067*b + 450 + 4652*b**2 + 16*b**5 - 14*b**5 + 23*b**5 = 0. Calculate b.
-50, 3/5, 1
Let w(j) be the first derivative of 9*j**5/5 - 597*j**4/2 + 793*j**3/3 - 66*j**2 + 1454. Find r, given that w(r) = 0.
0, 1/3, 132
Let n = 47 + -38. Suppose 0 = 5*m - t - n, -t - 2*t = m - 5. Solve -2*k - 5*k - k**2 + 4*k**m + 4*k - 3*k**4 + 3*k**3 = 0 for k.
-1, 0, 1
Suppose -192 = -54*v - 54*v + 12*v. Let -10/3*j + 1/6*j**v - 7/2 = 0. Calculate j.
-1, 21
Let n be (-2 + 1)/((-1)/(-18)). Let k = 164/9 + n. Let 0 - 8/9*q - k*q**2 = 0. Calculate q.
-4, 0
Let d(o) be the first derivative of -o**3/3 - 103*o**2 - 408*o + 2478. Factor d(n).
-(n + 2)*(n + 204)
Let t(x) be the first derivative of 5*x**7/42 + x**6/6 - 5*x**5/4 + 5*x**4/4 - 58*x + 112. Let r(v) be the first derivative of t(v). Factor r(y).
5*y**2*(y - 1)**2*(y + 3)
Let i(q) be the first derivative of -q**4/6 + 107*q**3/21 - 30*q**2/7 + 194*q + 35. Let g(h) be the first derivative of i(h). Factor g(k).
-2*(k - 15)*(7*k - 2)/7
Suppose -q - 4*j + 53 = -7*j, -q + 2*j = -49. Find r, given that 67*r**3 - 24 + 0*r**4 - 20*r**4 + 58*r**2 + 116*r - 238*r**2 + q*r**3 = 0.
2/5, 1, 3
Suppose 25*z - 132840 = -3240. Factor -z*b**3 + 156*b + 38*b**2 + 15 - 326*b**2 - 35 + 12.
-4*(9*b + 2)*(12*b - 1)**2
Factor -849/7*v**2 - 121*v + 2/7.
-(v + 1)*(849*v - 2)/7
Factor 52/5*x**2 + 107/5*x + 3/5*x**3 + 6.
(x + 2)*(x + 15)*(3*x + 1)/5
Let f = -175/3 + 59. Let r = -10809 - -10811. Solve r*p - 2*p**3 - 4/3 + 2/3*p**2 + f*p**4 = 0.
-1, 1, 2
Suppose 33*d - 392 = 25*