
Let p(i) be the third derivative of 5*i**4/24 + 5*i**3 - 14*i**2. Let j be p(0). Suppose -60*d**3 - j*d**2 + 32*d - 40*d**4 - 78*d + 41*d = 0. What is d?
-1/2, 0
Find g, given that 0 + 1/6*g**2 + 17/2*g = 0.
-51, 0
Let y be 10 + 102/(-5) - (-2)/5. Let a be ((-14)/y - 2)*1060/(-477). Let -2/3*u + 2/3*u**2 - a = 0. What is u?
-1, 2
Let i = 57/3473 - 67501741/31257. Let s = 2160 + i. Find k such that s*k**3 - 16/9*k**2 - 44/9*k - 8/3 = 0.
-1, 6
Let w(k) be the second derivative of -k**7/2520 - 29*k**6/360 - 841*k**5/120 + 115*k**4/12 + 2*k - 30. Let l(g) be the third derivative of w(g). Factor l(u).
-(u + 29)**2
Let z = -98725 - -394927/4. Solve z*a - 6 - 3/4*a**2 = 0.
1, 8
Let g(p) be the first derivative of -1/30*p**5 + 0*p**3 - 16 - 1/12*p**4 - 3*p**2 + 0*p. Let b(z) be the second derivative of g(z). Factor b(s).
-2*s*(s + 1)
Factor -10*z + 8732 + 10*z**2 - 15*z - z**3 - 3*z - 8708.
-(z - 6)*(z - 2)**2
Let m = 456326 + -456322. Let 0 + 21/2*t + 3/8*t**5 + 261/8*t**3 + 255/8*t**2 + 93/8*t**m = 0. Calculate t.
-28, -1, 0
Suppose -3*n = -5*n + 8. Let w(x) = -x**2 - 26*x - 57. Let z(t) = 3*t**2 + 53*t + 111. Let i(y) = n*z(y) + 7*w(y). Suppose i(q) = 0. Calculate q.
-3
Let b(y) = -y**2 + y + 4. Let h(w) = -4*w**2 - 93*w + 2421. Let c(m) = 5*b(m) - h(m). Let c(s) = 0. What is s?
49
Suppose 0 = 5*v + 6*v + 66. Let a be ((-20)/v)/(220/88). Factor 10/3*o**3 + 8/3*o**2 + 2/3*o + 0 + a*o**4.
2*o*(o + 1)**2*(2*o + 1)/3
Let g(k) = -1 + 3483*k**3 - 18*k + 1 + 48*k**2 - 8*k**4 - 3423*k**3. Let t(n) = 17*n**4 - 119*n**3 - 97*n**2 + 34*n. Let m(y) = -5*g(y) - 2*t(y). Factor m(p).
2*p*(p - 11)*(p + 1)*(3*p - 1)
Suppose -3*x - 88 = -4*o, 5*x + 3*o + 74 + 63 = 0. Let u = 284/9 + x. Find f, given that 16/9*f + 2/9*f**3 - u + 14/9*f**2 = 0.
-4, 1
Let v be ((5*40/(-32) + 4)/(-6))/3. Find a such that -v*a**3 + 1/2*a**2 - 1/2*a + 0 = 0.
0, 2
Let f be -11 - (7400 + -10)/(-10)*(-6)/(-78). Let -40/13 - 530/13*p**2 + f*p**3 - 330/13*p**4 + 72/13*p**5 + 232/13*p = 0. Calculate p.
2/3, 1, 5/4
Suppose 5*i - 36 - 34 = 5*j, 5*i + j - 58 = 0. What is h in 3*h**5 + i*h**2 + 45*h**3 + 4*h - 11*h - 49*h - 8*h**4 - 4*h - 16*h**4 = 0?
-1, 0, 2, 5
Let v(j) be the second derivative of 7*j**4/6 + 5*j**3 - 18*j**2 + 489*j - 1. Suppose v(s) = 0. Calculate s.
-3, 6/7
Let o(p) = -p - 4. Let j be o(2). Let u = j + 8. Factor -3*m**u + 11*m**2 - 8*m**2 + 2*m**3.
2*m**3
Let z = -218766 - -218768. Factor -2/3*l - z + 1/6*l**2.
(l - 6)*(l + 2)/6
Let g(w) = w**3 - 15*w**2 + 4*w + 27. Let r be g(15). Let k = r - 75. Factor 48*y - k*y**3 - 4*y**4 + 4*y**2 + 32 + y**2 + 3*y**2.
-4*(y - 2)*(y + 1)*(y + 2)**2
Let y(r) be the third derivative of -r**5/40 + 21*r**4/16 + 14*r**2 - 17*r. Factor y(o).
-3*o*(o - 21)/2
Let 235/8*i**3 + 13689/8*i + 1/8*i**4 + 13923/8*i**2 + 0 = 0. Calculate i.
-117, -1, 0
Suppose 269*h = 311*h - 210. Let w(r) be the second derivative of -1/9*r**3 + 0 - 1/18*r**4 - 14*r + 1/30*r**h + 1/3*r**2. Find b, given that w(b) = 0.
-1, 1
Let -m**3 - 1042*m**4 + 481*m**4 + 45*m**2 + 536*m**4 - 20 + 5*m - 4*m**3 = 0. Calculate m.
-1, 4/5, 1
What is a in -187*a**3 + 663 - 663 + 192*a**3 + 165*a**2 + 310*a = 0?
-31, -2, 0
What is z in -64*z**3 + 15*z**2 - 12 - 3*z**4 + 199*z**3 - 74*z**3 - 61*z**3 = 0?
-2, -1, 1, 2
Let q(r) = -31*r**2 + 287*r - 1192. Let t(j) = -90*j**2 + 860*j - 3575. Let l(a) = 35*q(a) - 12*t(a). Factor l(c).
-5*(c - 4)*(c + 59)
Let l = -80408 + 241226/3. Solve 1/6*q**2 - 5/6*q + l = 0 for q.
1, 4
Let q(o) be the second derivative of 59*o + 2 + 1/40*o**6 - 1/56*o**7 - 1/8*o**3 + 3/8*o**2 + 3/40*o**5 - 1/8*o**4. Factor q(g).
-3*(g - 1)**3*(g + 1)**2/4
Let x(i) be the second derivative of -i**5/4 + 965*i**4/4 - 1925*i**3/2 + 2885*i**2/2 + 8*i - 75. Factor x(p).
-5*(p - 577)*(p - 1)**2
Let s(u) be the first derivative of -u**5/20 - 107*u**4/16 + 109*u**3/12 + 107*u**2/8 - 27*u - 368. Determine a so that s(a) = 0.
-108, -1, 1
Let r(f) be the third derivative of f**6/600 - 7*f**5/300 - f**4/2 - 534*f**2. Factor r(d).
d*(d - 12)*(d + 5)/5
Let r(f) = -5*f**2 + 6*f + 44. Let i(t) = -84*t**2 + 100*t + 744. Let m(y) = -6*i(y) + 100*r(y). What is j in m(j) = 0?
-4, 4
Suppose 720*t**3 - 64*t**2 - 1436*t**3 + 717*t**3 + 95220 + 345*t**2 + 20424*t = 0. Calculate t.
-138, -5
Suppose -26*u = 37*u + 216*u + 17*u + 124*u. Determine t so that 1/5*t**4 + u + 7/5*t**2 + t**3 + 3/5*t = 0.
-3, -1, 0
Solve 74/5*o**2 - 70 - 3/5*o**3 + 39/5*o = 0.
-7/3, 2, 25
Let l = 320 - 206. Suppose 31*u - 10 = l. Let -4/7*q**u + 16/7*q**3 - 4/7 - 24/7*q**2 + 16/7*q = 0. Calculate q.
1
Factor -13/2*t**2 - 15/2 + 98*t.
-(t - 15)*(13*t - 1)/2
Let c(p) be the first derivative of -p**5 + 25*p**4/4 + 1055*p**3/3 + 2015*p**2/2 + 990*p + 3414. Suppose c(b) = 0. Calculate b.
-11, -1, 18
Let r(o) be the third derivative of o**7/1050 - o**6/100 + 11*o**5/300 - o**4/20 - 3779*o**2. Factor r(x).
x*(x - 3)*(x - 2)*(x - 1)/5
Suppose -1011*k + 515*k = -530*k. Factor 0*m + k*m**2 - 36/23*m**3 + 0 + 2/23*m**4.
2*m**3*(m - 18)/23
Let s(u) = -28*u**4 + 388*u**3 - 2696*u**2 - 5408*u + 18432. Let y(r) = -9*r**4 + 129*r**3 - 897*r**2 - 1802*r + 6144. Let t(d) = 5*s(d) - 16*y(d). Factor t(c).
4*(c - 16)**2*(c - 2)*(c + 3)
Let u = -255 - -331. Suppose -15*j = -34*j + u. Factor 1/5*d**j + 0 + 0*d + 1/5*d**3 - 1/5*d**5 - 1/5*d**2.
-d**2*(d - 1)**2*(d + 1)/5
Let w = -29/6965 + 1024/6965. Find y such that -5/7*y - w*y**2 - 4/7 = 0.
-4, -1
Let x be (-1)/(-360)*-4319 + (16 - 4). Let c(y) be the third derivative of -17*y**2 + x*y**6 + 0 - 1/9*y**3 - 1/72*y**4 + 1/90*y**5 + 0*y. Factor c(t).
(t - 1)*(t + 1)*(t + 2)/3
Let y be -4*12/8 - 3. Let p be 340/90 - 2/y. Solve 6*o - 9*o**2 - 3*o**p + 7*o**4 - o**4 = 0.
-2, 0, 1
Suppose -6*d - 7 = -3*d + j, -24 = 4*d + 5*j. Let q(h) = -h**2 - 1. Let k(a) = 4*a**2 - 15*a + 19. Let w(i) = d*k(i) - q(i). Determine n, given that w(n) = 0.
2, 3
Let d be (3 - ((-4)/(-1))/1) + 0. Let h be d - (2/2*-1 + -1). Factor 6*r + 2 - h - 4 + 57*r**2 - 60*r**2.
-3*(r - 1)**2
Let y(n) be the second derivative of n**4/48 + 107*n**3/24 + 53*n**2/4 - 3*n - 78. What is x in y(x) = 0?
-106, -1
Determine o, given that -840*o**2 - 3*o**4 + 11260*o**3 - 11035*o**3 - 2*o**4 + 820*o = 0.
0, 2, 41
Let 10/7*p**2 + 18/7 - 36/7*p = 0. Calculate p.
3/5, 3
What is h in -576 + 2/5*h**4 + 124/5*h**2 - 42/5*h**3 + 1344/5*h = 0?
-5, 2, 12
What is t in -4372847132672/5 - 14384365568/5*t - 9728/5*t**3 - 17743872/5*t**2 - 2/5*t**4 = 0?
-1216
Determine k, given that -327 - 315 - 406*k - 3*k**2 + 48 + 103*k = 0.
-99, -2
Let v(b) be the first derivative of -9/20*b**4 - 24/5*b + 18/5*b**2 + 66 - 2/5*b**3 + 3/25*b**5. What is t in v(t) = 0?
-2, 1, 2
Suppose 0 - 8/7*q**3 - 2/7*q**4 + 230/7*q**2 - 100*q = 0. Calculate q.
-14, 0, 5
Let u be 217/(-42) + 2900/435. Determine b so that 5/4 + 1/4*b**2 - u*b = 0.
1, 5
Suppose -85 = -2*v + 4*h + h, 95 = 2*v - 3*h. Suppose 2*u - v = -5. Factor 20*j**4 - 4 - 11 - 45*j**3 + u*j + 13*j**2 + 2*j**2.
5*(j - 1)**3*(4*j + 3)
Let b(l) be the third derivative of -l**5/40 - 5*l**4/2 - 39*l**3/4 + 377*l**2. Suppose b(h) = 0. What is h?
-39, -1
What is o in 1109/10*o**2 - 7/10*o**4 + 14 - 237/5*o**3 - 384/5*o = 0?
-70, 2/7, 1
Let u(n) be the third derivative of n**11/83160 - n**9/5040 - n**8/2520 + 29*n**5/30 - 2*n**2 + 2. Let j(s) be the third derivative of u(s). Solve j(c) = 0.
-1, 0, 2
Let d = 86309/5 + -17261. Let s(h) be the first derivative of -d*h**2 - 7/5*h - 2 - 1/15*h**3. Find v such that s(v) = 0.
-7, -1
Let l(p) be the first derivative of -3*p**5/40 + 3*p**3/4 - 3*p**2/2 + 7*p - 56. Let x(w) be the first derivative of l(w). Find o, given that x(o) = 0.
-2, 1
Let t be (-35 + 29)*(-150)/315. Factor -t*g**3 - 8/7*g**2 + 0*g - 16/7*g**4 + 0 - 4/7*g**5.
-4*g**2*(g + 1)**2*(g + 2)/7
What is z in -428868/7*z + 1111158/7 + 2/7*z**4 + 20520/7*z**2 - 348/7*z**3 = 0?
3, 57
Suppose 2*a = -3*d + 6922, -d = a - 5*a - 2326. Let f = d - 2310. Solve f*y**2 + 2/5*y**3 - 6/5*y - 4/5 = 0.
-1, 2
Let w(h) = -48*h**2 + 700*h - 2128. Let y(q) = -109*q**2 + 1401*q - 4257. Let k(v) = -9*w(v) + 4*y(v). Factor k(s).
-4*(s - 3)*(s + 177)
Suppose 207 = x + 247. Let p be x/(-72) - (-1)/(-3). Factor 1/9*z**2 + 1/9*z - p.
(z - 1)*(z + 2)/9
Let c(i) be the third derivative of -i**5/40 + 1375*i**4/8 - 1890625*i**3/4 + i**2 - 8. Let c(s) 