(k + 1)*(k + 3)/2
Let y(u) be the third derivative of -u**5/12 + 625*u**4/24 + 1625*u**3/3 - 7042*u**2. Factor y(z).
-5*(z - 130)*(z + 5)
Let h(a) be the third derivative of a**5/60 - a**4 + 21*a**3/2 - 20*a**2. Suppose h(n) = 0. Calculate n.
3, 21
Let s = -1297 + 1291. Let v be (-10)/(-2) + (s - (13 + -14)). Suppose -1/8*x - 1/8*x**3 + v - 1/4*x**2 = 0. Calculate x.
-1, 0
Let x(f) be the second derivative of f**8/1008 - f**6/120 - f**5/90 - 79*f**2/2 + 14*f + 2. Let r(b) be the first derivative of x(b). Factor r(g).
g**2*(g - 2)*(g + 1)**2/3
Let c(w) be the first derivative of w**7/540 + w**6/810 + 5*w**3 - 46. Let z(q) be the third derivative of c(q). What is b in z(b) = 0?
-2/7, 0
Determine x, given that -348/19*x**2 + 90/19*x**3 - 144/19 - 4/19*x**4 + 440/19*x = 0.
1/2, 2, 18
Suppose -z + 103 = 91. Let p be 8/(-70) + 1/30*z. Factor 0 - 8/7*n**3 - 10/7*n**2 - 4/7*n - p*n**4.
-2*n*(n + 1)**2*(n + 2)/7
Let d(h) = -5*h**4 - 46*h**3 + 46*h**2 + 44*h - 37. Let c(l) = -8*l**4 - 47*l**3 + 48*l**2 + 44*l - 34. Let t(f) = 4*c(f) - 6*d(f). Factor t(z).
-2*(z - 43)*(z - 1)**2*(z + 1)
Let x(h) = h**3 - h**2. Let l(f) = 22*f**3 + 210*f**2 - 1656*f - 576. Let s(a) = l(a) - 10*x(a). Factor s(z).
4*(z - 6)*(z + 24)*(3*z + 1)
Let z(n) be the second derivative of -n**6/30 - 13*n**5/15 - 8*n**4 - 24*n**3 + 51*n**2 + 2*n - 62. Let c(p) be the first derivative of z(p). Factor c(x).
-4*(x + 1)*(x + 6)**2
Let d = 23896/59 - 405. Let k = d - -56/177. Factor 1/2*n**2 + 7/6*n + k.
(n + 2)*(3*n + 1)/6
Let -658/17*q**4 - 10272/17 - 2/17*q**5 - 5184/17*q**3 - 15472/17*q**2 - 20576/17*q = 0. Calculate q.
-321, -2
Factor 1296*s + 1440*s**2 - 23*s**3 + 4*s**4 + 65*s**3 + 106*s**3.
4*s*(s + 1)*(s + 18)**2
Let l be (3 + -3)/(7 + -5 + 2). Let u(s) be the third derivative of 1/24*s**4 + 0 + 1/3*s**3 - 1/60*s**5 + l*s - 30*s**2. What is c in u(c) = 0?
-1, 2
Let h be (-17)/(-60) - (-586)/11720. Factor 5/3*x - h*x**2 - 4/3.
-(x - 4)*(x - 1)/3
Factor 2/9*s**2 + 40/3 + 32/9*s.
2*(s + 6)*(s + 10)/9
Let m(l) be the first derivative of 2*l**5/55 + 9*l**4/22 - 20*l**3/33 - 461. Factor m(i).
2*i**2*(i - 1)*(i + 10)/11
Let v(w) = -23*w**2 + 342*w + 1133. Let o(z) = 4*z**2 + 3*z - 7. Let t(g) = -5*o(g) - v(g). Factor t(l).
3*(l - 122)*(l + 3)
Let w(h) be the third derivative of -5*h**6/84 + 151*h**5/42 + 22*h**4/3 + 124*h**3/21 + 1510*h**2. Factor w(k).
-2*(k - 31)*(5*k + 2)**2/7
Let w(k) = k**2 + 4*k + 1. Let h(q) = -q**3 + 38*q**2 + 126*q + 77. Let p(i) = -h(i) + 5*w(i). Let p(l) = 0. What is l?
-2, -1, 36
Let x(y) be the first derivative of -5*y**4/3 - 928*y**3/9 - 206*y**2 + 360*y + 5173. Determine v, given that x(v) = 0.
-45, -2, 3/5
Determine b, given that -55/3*b + 5/3*b**2 + 140/3 = 0.
4, 7
Let i(r) be the third derivative of -r**6/30 + 8*r**5 - 118*r**4/3 + 5502*r**2. Find y, given that i(y) = 0.
0, 2, 118
Let q(v) be the second derivative of v**6/120 - 19*v**5/60 + 205*v**2/2 + 22*v + 5. Let o(b) be the first derivative of q(b). Determine m so that o(m) = 0.
0, 19
Let x(n) be the first derivative of -11*n**4 - 12/5*n**5 + 44 - 8*n**3 + 0*n + 0*n**2. Determine y so that x(y) = 0.
-3, -2/3, 0
Let t = 101 + -354. Let d = t + 255. Factor -162*y**d - 729/5 - 243*y - 3/5*y**5 - 9*y**4 - 54*y**3.
-3*(y + 3)**5/5
Let j(i) be the second derivative of i**7/126 - 11*i**6/90 + 11*i**5/30 + 5*i**4/3 - 4*i**3 + 993*i. Factor j(g).
g*(g - 6)**2*(g - 1)*(g + 2)/3
Let k be (-1 - (-2)/(-4))*(-72)/27. Let j(f) = f**3 + f**2 - 1. Let d(a) = 5*a**4 - 24*a**3 - 29*a**2 + 4. Let g(z) = k*j(z) + d(z). Factor g(i).
5*i**2*(i - 5)*(i + 1)
Let a(l) be the first derivative of l**5/7 - 52*l**4/7 - 2084*l**3/21 - 400*l**2/7 - 9148. Suppose a(q) = 0. What is q?
-8, -2/5, 0, 50
Let t = 9709 + -9709. Let x(v) be the third derivative of 0 + 1/2*v**4 + 1/15*v**5 + t*v**3 - 27*v**2 + 0*v. Determine o, given that x(o) = 0.
-3, 0
Let w be ((-700284)/858)/(-3 + 29/11). Factor w + 1/2*t**2 + 67*t.
(t + 67)**2/2
Let h(m) = -6*m**2 + 212*m - 255. Let c be h(34). Let y(z) be the first derivative of -c - 1/3*z + 5/18*z**3 - 1/4*z**2. Determine q, given that y(q) = 0.
-2/5, 1
Let s(u) be the third derivative of u**7/105 + 218*u**6/15 + 31972*u**5/5 + 189224*u**4/3 + 753424*u**3/3 - 63*u**2 + 10. Factor s(f).
2*(f + 2)**2*(f + 434)**2
Suppose 0 = 3*m + 5*q - 933, 0 = m - 0*q - 5*q - 311. Let i(f) = 39*f + 11. Let z be i(8). Let -64 + z*d**2 - d**3 - m*d**2 - d**3 = 0. What is d?
-2, 4
Let x(u) be the first derivative of 17/13*u**2 - 1/26*u**4 - 18/13*u + 48 - 14/39*u**3. What is t in x(t) = 0?
-9, 1
Let x(l) be the third derivative of -l**5/180 + 37*l**4/24 - 55*l**3/9 + 2339*l**2. Factor x(n).
-(n - 110)*(n - 1)/3
Factor 1256641/3 + 1/3*n**2 - 2242/3*n.
(n - 1121)**2/3
Let d(p) = -p**4 - p**3 + 2*p**2 - p - 3. Let s(i) = 22*i**3 + 2*i**2 - 26*i - 6. Let y(r) = 4*d(r) - 2*s(r). Solve y(c) = 0.
-12, -1, 0, 1
Suppose -43*w - 1460 = -165*w - 170*w. Let p(q) be the third derivative of 0*q - 9/80*q**6 - 1/2*q**3 - 17*q**2 + 0 - 13/16*q**4 - 3/5*q**w. Factor p(r).
-3*(r + 2)*(3*r + 1)**2/2
Suppose 78*s = 60*s + 54. Let u(x) be the first derivative of -18 - 5/4*x**4 - 5/2*x + 5/2*x**2 + 1/2*x**5 + 0*x**s. Let u(b) = 0. Calculate b.
-1, 1
Suppose 6*r + 47 = 5*r + n, 0 = 4*n - 16. Let p be r/(-72) - 12/54. Solve -3/4*t - 3/8*t**5 + p*t**4 + 9/8*t**3 + 0 - 3/8*t**2 = 0.
-1, 0, 1, 2
Let -404*h**2 + 50*h**3 - 93*h**4 + 34*h**2 + 32*h**4 + 59*h**4 + 70*h**2 = 0. What is h?
0, 10, 15
Let d(a) = 165*a**3 - 4635*a**2 - 104725*a - 502645. Let z(b) = -29*b**3 + 818*b**2 + 18481*b + 88702. Let p(x) = 7*d(x) + 40*z(x). Factor p(f).
-5*(f - 73)*(f + 9)**2
Let f = -21/122 + 41/61. Let d(p) be the second derivative of -22*p + 0 - f*p**3 - 9/4*p**2 - 1/24*p**4. Factor d(i).
-(i + 3)**2/2
Factor 7*n**2 + 5*n**4 - 142*n**2 - 20*n**3 - 125*n + 5 - 85 - 65*n.
5*(n - 8)*(n + 1)**2*(n + 2)
Factor -888*x + 1773/2 + 3/2*x**2.
3*(x - 591)*(x - 1)/2
Let l(m) = -2*m**2. Let n(p) = 7*p**2 - 11*p - 24. Let q(y) = 8*l(y) + 2*n(y). Factor q(g).
-2*(g + 3)*(g + 8)
Let u(y) be the first derivative of 2*y**3/45 + 441*y**2/5 - 2648*y/15 + 2101. Find j such that u(j) = 0.
-1324, 1
Suppose -8*w - 33 = -65. Solve -500*m**4 + w*m**2 - 4*m**2 - 6*m**3 + 503*m**4 = 0.
0, 2
Let k(s) be the first derivative of 343*s**6/45 - 3136*s**5/25 + 3584*s**4/5 - 65536*s**3/45 - 814. Factor k(f).
2*f**2*(7*f - 32)**3/15
Let c(s) = s**2 - 13*s + 1. Let o be c(15). Suppose p + 15 = 4*a, -2*a + 3*p + o = 16. What is f in -14/5*f**2 + 8/5 - 4*f**a + 8/5*f - 6/5*f**4 = 0?
-2, -1, 2/3
Suppose 14 = o + 2. Suppose 0 = 5*p + 4*t - 20, 12*t + 12 = 3*p + 13*t. Solve -4*k**3 + 3 - p - 12*k - 1 - o*k**2 - 2 = 0.
-1
Suppose -197*a - 440*a + 2522 = 624*a. Let 504 + 24*y + 2/7*y**a = 0. What is y?
-42
Let m(z) = -2*z**2 + 25. Let i(t) = 9*t**2 - 1230*t + 75595. Let f(k) = -i(k) - 2*m(k). Factor f(g).
-5*(g - 123)**2
Let k = 57 + -37. Suppose 19*g + k = 24*g. Let -5*p**2 - 3*p**3 + 5*p**4 - 5*p**4 - 5*p + 5*p**g + 8*p**3 = 0. What is p?
-1, 0, 1
Let b(i) be the first derivative of i**3/15 - 392*i**2/5 + 153664*i/5 - 2581. Determine u so that b(u) = 0.
392
Let h = 527836/77 + -6855. Let a(j) be the second derivative of 1/55*j**6 + 3/110*j**5 + 0 + 0*j**3 - 7*j + 0*j**2 - h*j**7 - 1/22*j**4. Factor a(w).
-6*w**2*(w - 1)**2*(w + 1)/11
Factor 4*a + 88/9 + 4/3*a**3 - 136/9*a**2.
4*(a - 11)*(a - 1)*(3*a + 2)/9
Let -725 - 50*o**3 - 3*o**3 + 5*o**4 - 960*o**2 - o**3 - 56*o**3 - 1570*o = 0. What is o?
-5, -1, 29
Let c(o) be the first derivative of -200 + 16*o + 0*o**2 - 4/3*o**3. Solve c(n) = 0 for n.
-2, 2
Let y(j) be the third derivative of 0*j + 0*j**5 + 0 + 1/525*j**7 - 12*j**2 + 0*j**4 + 0*j**3 - 1/300*j**6. Let y(v) = 0. Calculate v.
0, 1
Let m(l) be the first derivative of 2*l**3/3 - 43*l**2 + 1907. Solve m(q) = 0.
0, 43
Let u be 14 - (3 - (-2 + 7)). Factor -275 + u*c**2 + 88*c - 2*c**3 - 309 + 680.
-2*(c - 12)*(c + 2)**2
Let b(a) be the third derivative of a**6/420 + 569*a**5/210 + 26885*a**4/28 - 27075*a**3/7 + 2780*a**2. Let b(d) = 0. Calculate d.
-285, 1
Let k(x) be the third derivative of x**2 - 35/24*x**4 + 0*x**3 - 55 + 0*x - 5/6*x**5 - 1/8*x**6. Find n, given that k(n) = 0.
-7/3, -1, 0
Suppose -108 = -17*o - 10*o. Let 3 - 2*u**4 + 6*u**o - u**4 + 48*u**2 - 54*u**2 = 0. What is u?
-1, 1
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