
3*m*(m + 1)/2
Let s(y) = 2*y + 19. Let w be s(-8). Find r, given that -5*r**2 + 5*r - 15 - 5*r**w + 4 + 4 + 12 = 0.
-1, 1
Let b(x) be the first derivative of -x**5/15 + x**4/3 - 2*x**3/3 - 2*x**2 + 9*x - 77. Let r(t) be the second derivative of b(t). Factor r(k).
-4*(k - 1)**2
Suppose 2*g + 4*x + 12 = 6*g, 3*g - 2*x = 12. Let t(h) be the second derivative of -3/2*h**3 + 14*h + 0 + 1/4*h**4 - g*h**2. Solve t(p) = 0 for p.
-1, 4
Let v(t) be the second derivative of -4*t**2 + 234*t + 4/3*t**3 + 1/6*t**4 - 1/10*t**5 + 0. Factor v(z).
-2*(z - 2)*(z - 1)*(z + 2)
Determine r, given that -64082 + 358*r - 1/2*r**2 = 0.
358
Solve 2/3*w**2 - 140/3 + 6*w = 0 for w.
-14, 5
Find d, given that -3/7*d**2 - 120/7*d + 528/7 = 0.
-44, 4
Let c(r) = -25*r**3 + 84*r**2 + 73*r - 490. Let f(z) = -238*z**3 + 757*z**2 + 656*z - 4412. Let d(i) = 19*c(i) - 2*f(i). Factor d(m).
(m - 2)*(m + 3)*(m + 81)
Let x(z) be the second derivative of -8/17*z**2 + 20*z + 0 + 20/17*z**3 - 9/17*z**4 + 13/170*z**5. Solve x(p) = 0.
2/13, 2
Let i(x) be the second derivative of -x**6/90 - 163*x**5/30 - 161*x**4/3 - 1924*x**3/9 - 1280*x**2/3 + 7*x + 6. Factor i(a).
-(a + 2)**3*(a + 320)/3
Factor -1059968*x - 1456*x**2 - 2/3*x**3 - 771656704/3.
-2*(x + 728)**3/3
Let q(u) = 22*u**2 - 1370*u - 1440. Let p(w) = 13*w**2 - 823*w - 864. Let y(j) = -12*p(j) + 7*q(j). Let y(a) = 0. Calculate a.
-1, 144
Let g(o) = 8*o - 95. Let u be g(13). What is a in 4*a + a - 2*a**2 - 7*a**3 + a**5 + 3*a**4 - u*a**2 + a + 8 = 0?
-4, -1, 1, 2
Let n = 834431 + -9178739/11. Let n*v**2 - 180/11*v + 4050/11 = 0. What is v?
45
Let w(c) be the first derivative of c**4/12 + c**3/3 - 4*c**2 - 173*c + 185. Let l(m) be the first derivative of w(m). Factor l(s).
(s - 2)*(s + 4)
Let a = -35 + -31. Let x = a + 68. Find b, given that -5*b**4 - 5*b**2 - 2*b**2 + 15*b**3 + 0*b + 5*b - 8*b**x = 0.
0, 1
Let c be 14/(-21) - (2218/(-960) + 1). Let p = c - -37/32. Solve p*t**2 - 6/5*t**3 - 4/5*t + 0 + 1/5*t**4 = 0.
0, 1, 4
Find s, given that 5/4*s**2 - 505/4*s + 0 = 0.
0, 101
Factor 31/2*g**3 - 517/4*g**2 - 1/4*g**4 - 12321 - 3441*g.
-(g - 37)**2*(g + 6)**2/4
Let v(o) = -10*o**2 - 72*o - 14. Suppose 2*r - 5*z = -34, z = 2*r + 19 - 1. Let a be v(r). Factor 0 - 2/7*u**3 - 2/7*u**4 + a*u + 4/7*u**2.
-2*u**2*(u - 1)*(u + 2)/7
Suppose 0 = -21*p - 15 + 57. Factor -v**2 - 6 + 6*v**2 - 2*v**p + 5*v**2 + 4*v - 6*v**2.
2*(v - 1)*(v + 3)
Let z = -3170498/11 + 288228. Factor -6/11*p**3 - 4/11*p - 2/11*p**4 + 2/11*p**5 + z*p**2 + 0.
2*p*(p - 1)**3*(p + 2)/11
Suppose 246 = 180144*d - 180062*d. Suppose -2/9*g**4 + 0 - 2/3*g**2 - 2/9*g - 2/3*g**d = 0. What is g?
-1, 0
Let p(x) = x**4 + x**3 + x**2 - x + 2. Let u(y) = -8*y**4 - 4*y**3 - 5*y**2 + 9*y - 18. Let v = -755 + 791. Let b(w) = v*p(w) + 4*u(w). Solve b(o) = 0.
-4, -1, 0
Suppose 4*i - 4*a + 8 + 4 = 0, i + 5*a - 15 = 0. Suppose j - 4*j + 9 = i. Factor 10 + 16*z**4 - 11*z**4 - 18*z + 45*z**2 - 25*z**j - 17*z.
5*(z - 2)*(z - 1)**3
Solve 4*l**2 + 8*l**2 - 143*l**5 - 480*l**3 + 142*l**5 + 640*l + 163*l**4 - 16*l**2 = 0 for l.
-1, 0, 2, 160
Let c be -5*12/165 + (-963)/(-198). Solve 15/4*g + 3/4*g**2 - c = 0 for g.
-6, 1
Factor -68/9*p**4 - 4400/9*p**2 + 0 - 2/9*p**5 - 8000/9*p - 280/3*p**3.
-2*p*(p + 4)*(p + 10)**3/9
Let w(a) be the second derivative of 1/2*a**3 + 1/84*a**7 - 127*a - 7/40*a**5 - 1/12*a**6 + 5/24*a**4 + 0 + 0*a**2. Let w(j) = 0. Calculate j.
-1, 0, 1, 6
Let f(j) be the first derivative of -j**8/3360 + j**7/240 + 28*j**3 - 89. Let m(k) be the third derivative of f(k). Factor m(x).
-x**3*(x - 7)/2
Let w(v) = -v**3 + 15*v**2 + 6*v - 28. Let g(q) = -q**3 + 16*q**2 + 4*q - 29. Let p(c) = 4*g(c) - 5*w(c). Find h such that p(h) = 0.
-2, 1, 12
Let g be ((-17446)/1001 + 18)*((-6)/21 + (-122)/(-84)). Solve g*w + 4/3 - 2/3*w**3 + 2/3*w**4 - 2*w**2 = 0.
-1, 1, 2
Suppose c + 21 = 25. Let r be 4/(-4)*c - -6. Factor -15/4*v - 5/2*v**r - 5/4.
-5*(v + 1)*(2*v + 1)/4
Let s(b) be the second derivative of b**7/3780 - b**6/360 - b**5/10 + 15*b**4/4 + b**3/6 + 14*b - 4. Let h(w) be the third derivative of s(w). Factor h(x).
2*(x - 6)*(x + 3)/3
Suppose 53*g + 332 + 77 = 325*g - 135. Find s, given that 16/21*s**g - 2/21*s**3 + 6/7*s + 0 = 0.
-1, 0, 9
Let o(i) be the second derivative of -i**6/40 - 9*i**5/16 - 39*i**4/16 - 37*i**3/8 - 9*i**2/2 + 3*i + 15. Factor o(p).
-3*(p + 1)**3*(p + 12)/4
Let o be 1938/(-12597) + (-145)/(-13). Factor -7/3*i**3 + 10/3*i + 0 - o*i**2.
-i*(i + 5)*(7*i - 2)/3
Let z(l) = 7*l**3 + 78*l**2 - 288*l + 280. Let g(q) = -18*q**3 - 234*q**2 + 864*q - 840. Let v(j) = 3*g(j) + 8*z(j). Suppose v(o) = 0. What is o?
2, 35
Let z = 250/71 + -9040/2769. Let f(y) be the first derivative of 0*y**2 - z*y**3 - 17 - 11/26*y**4 + 0*y - 4/65*y**5. Solve f(a) = 0 for a.
-5, -1/2, 0
Let j(l) be the first derivative of -3 - 17*l + 10/7*l**3 - 1/28*l**4 - 150/7*l**2. Let d(k) be the first derivative of j(k). Suppose d(m) = 0. Calculate m.
10
Let v = 336 + -334. Factor -53*p + p**v + 1089 - 11*p - 2*p.
(p - 33)**2
Suppose 363 = -294*a + 415*a. Determine b so that 2/7*b**a - 36/7 - 40/7*b**2 + 74/7*b = 0.
1, 18
Let t(l) be the third derivative of -l**7/280 - l**6/4 + 63*l**5/40 - 4*l**4 + 43*l**3/8 + 217*l**2 + 2*l + 3. Factor t(v).
-3*(v - 1)**3*(v + 43)/4
Let z(f) be the first derivative of 16/3*f + 32/3*f**2 - 4*f**3 - 29. Factor z(g).
-4*(g - 2)*(9*g + 2)/3
Suppose -6*d - 351 + 171 = 0. Let z be ((-96)/(-18))/(3 + 76/d). Suppose 46/7*q**4 - 6/7*q**5 + 0*q - z*q**3 + 0 - 32/7*q**2 = 0. What is q?
-1/3, 0, 4
Let l(k) = 2*k**3 - 21*k**2 + 51*k + 33. Let j be l(26). Solve 1 - 16*d**4 - 404*d**2 - j*d**3 + 21975*d**3 - 80*d - 1 = 0 for d.
-20, -1, -1/4, 0
Let t(o) be the third derivative of -20/33*o**3 + 30*o - 2*o**2 - 4/11*o**4 + 0 + 1/66*o**5. Let t(l) = 0. Calculate l.
-2/5, 10
Let s(j) be the second derivative of 0*j**2 - 3/20*j**5 + 0*j**6 + 0*j**4 - 1 + 1/4*j**3 + 1/28*j**7 + 67*j. Suppose s(v) = 0. Calculate v.
-1, 0, 1
Let t(a) = 51*a + 3. Let c be t(0). Find l, given that 5*l**5 + 42*l**4 + 30*l**c - 51*l**4 + 25*l**5 + 10*l**4 + 54*l**4 + 5*l**2 = 0.
-1, -1/2, -1/3, 0
Suppose -715 = -p + 3*u + 474, -1189 = -p + 4*u. Let z = -1184 + p. What is o in -19/2*o**2 + 7*o + 25/4*o**3 - 2 - 2*o**4 + 1/4*o**z = 0?
1, 2
Find q, given that -123/4*q**2 + 45/2*q + 33/4 = 0.
-11/41, 1
Let x(n) = -n**3 - n**2 - 62*n - 62. Let a be x(-1). Factor -6/5*i**3 + 0 + a*i**4 + 0*i + 2/5*i**5 - 4/5*i**2.
2*i**2*(i - 2)*(i + 1)**2/5
Factor 2/3*k**2 + 137/6*k + 403/6.
(k + 31)*(4*k + 13)/6
Let w(t) be the second derivative of t**7/105 + 37*t**6/75 + 197*t**5/25 + 97*t**4/3 + 901*t**3/15 + 289*t**2/5 - 525*t - 2. Determine y, given that w(y) = 0.
-17, -1
Factor -61*t**2 - 55*t**2 - 60*t**2 + 229*t**2 - 656*t - 57*t**2 - 26896.
-4*(t + 82)**2
Let 1/8*m**2 + 85/2 - 341/8*m = 0. What is m?
1, 340
Let g(k) be the first derivative of 2*k**5/35 - 3*k**4/7 + 16*k**3/21 + 468. Let g(j) = 0. Calculate j.
0, 2, 4
Let a(d) = d**2 - 3*d + 2. Let q(n) = -3*n**3 - 1835*n**2 - 282756*n - 280900. Let x(w) = 4*a(w) - q(w). Find z, given that x(z) = 0.
-306, -1
Find y such that 328971 + 132*y + 129*y**2 - 3*y**3 - 328971 = 0.
-1, 0, 44
Let s(g) be the first derivative of 2/33*g**3 + 4 + 0*g - 10/11*g**2. Determine k, given that s(k) = 0.
0, 10
Let -568/9*m**2 - 14/9*m**4 + 0 - 2/9*m**5 + 200/9*m**3 + 160/3*m = 0. What is m?
-15, 0, 2, 4
Let m = -122 - -125. Suppose -4*x = -m*x + h - 5, 5*h - 25 = -4*x. Factor 2*w + 8 + 2*w**2 + 4*w - 4 + x*w**2.
2*(w + 1)*(w + 2)
Factor -5*i**2 + 2067*i - 4019*i + 2047*i + 1650.
-5*(i - 30)*(i + 11)
Suppose b - 224 = -212. Suppose 0 = -14*q - b*q + 104. Factor 0 + 3/4*w**5 - 3/4*w**3 + 3/4*w**2 - 3/4*w**q + 0*w.
3*w**2*(w - 1)**2*(w + 1)/4
Let w(v) be the third derivative of -10*v**2 + 1/16*v**4 + 0 + 1/1344*v**8 + 0*v**3 + v - 17/240*v**5 + 17/480*v**6 - 1/120*v**7. Suppose w(a) = 0. Calculate a.
0, 1, 2, 3
Let m(g) be the first derivative of 23*g**6/420 + g**5/10 - g**4/42 - g**2 - 59*g + 68. Let z(i) be the second derivative of m(i). Factor z(r).
2*r*(r + 1)*(23*r - 2)/7
Let a = 597 + -595. Suppose 0 = -i + 4*t - 5*t - 1, a*i = 4*t + 28. Factor 2/5 - 2/5*h**2 + 0*h**i + 3/5*h - 4/5*h**3 + 1/5*h**5.
(h - 2)*(h - 1)*(h + 1)**3/5
Let n(b) be the first derivative of 7/15*b**5 + 1/18*b**6 - 5/2*b**2 + 7/6