**2 - 1368/5*j = 0.
342
Let k = 49412 + -49410. Determine b so that -k*b - 2/5*b**2 + 0 = 0.
-5, 0
Let i(g) be the first derivative of -3 - 26*g - g**3 + 2*g**2 + 1/6*g**4. Let b(o) be the first derivative of i(o). Suppose b(k) = 0. What is k?
1, 2
Let g(f) be the third derivative of 0*f - 3/4*f**4 + 0 - 1/10*f**7 - 5/672*f**8 + 0*f**3 - 121/240*f**6 - 11/10*f**5 + 11*f**2. Let g(u) = 0. What is u?
-3, -2, -2/5, 0
Let l(s) be the first derivative of s**6/30 - 4*s**5 + 200*s**4 - 16000*s**3/3 - 49*s**2/2 + 2*s + 57. Let o(k) be the second derivative of l(k). Factor o(f).
4*(f - 20)**3
Let i = 587228/5 + -117445. Factor i*z**3 - 18/5 - 18/5*z**2 + 33/5*z.
3*(z - 3)*(z - 2)*(z - 1)/5
Let l(v) be the second derivative of -6*v**5 - v**4/4 + 20*v**3 + 3*v**2/2 + 47*v - 2. Factor l(i).
-3*(i - 1)*(i + 1)*(40*i + 1)
Let h(x) = -x**3 - 10*x**2 + 10*x + 25. Let d be h(-11). Suppose 3*o - d = -2*b, -4 + 2 = -o. Factor u**3 + 8*u**3 - 23 + 20 + b*u - 21*u**2.
3*(u - 1)**2*(3*u - 1)
Let g = 749 + -751. Let u(m) = -m**2 + m. Let i(x) = 4*x**2 - 18*x + 8. Suppose -l - r - 20 = 0, 5*l + 4*r = 3*l - 40. Let q(a) = g*i(a) + l*u(a). Factor q(y).
4*(y + 2)*(3*y - 2)
Let l(h) = 19*h**2 + 412*h - 91. Let z(q) = 9*q**2 + 202*q - 47. Let x(c) = -3*l(c) + 5*z(c). Factor x(f).
-2*(f + 19)*(6*f - 1)
Suppose 9*f + 3/8*f**2 - 39/2 = 0. Calculate f.
-26, 2
Let a(x) = -x - 7. Let w be a(-5). Let y be (w - 22)*(-29)/3. Factor -d**5 - 230*d**2 + 3*d**3 + y*d**2 + 0*d**5.
-d**2*(d - 2)*(d + 1)**2
Suppose -12 = -s + 5*k, -8 + 13 = -5*k. Factor -5*m**2 + 5 + 17*m**2 + s + 13*m - 11*m**2.
(m + 1)*(m + 12)
Let s(m) be the first derivative of 0*m + 1/120*m**5 + 5/12*m**4 + 14*m**2 + 25 + 25/3*m**3. Let v(c) be the second derivative of s(c). Solve v(y) = 0.
-10
Let v(b) be the first derivative of b**5/5 + 5*b**4/3 + 2*b**3 - 18*b**2 - 43*b - 21. Let p(g) be the first derivative of v(g). Factor p(y).
4*(y - 1)*(y + 3)**2
Suppose 10*j = 5*j - u + 45, 5*u = -3*j + 27. Suppose -2*k = 5*c - 0*k, 0 = -3*c + 3*k + 21. Factor 7*m**c - 52*m - j*m**2 + 6*m**2.
4*m*(m - 13)
Suppose -31*r + 591 = -2571. Factor -32 + 20 - 33*k - 32*k + 60 + r + 5*k**2.
5*(k - 10)*(k - 3)
Suppose 0 = 294*l + 89*l - 766. Factor 242 + 1/2*k**l + 22*k.
(k + 22)**2/2
Suppose -4*o + 90 = 58. Suppose g + 4*g = 2*b + 14, g - 3*b - o = 0. Solve 8*u**4 - 6/5 - 1/5*u - 7/5*u**5 - 72/5*u**3 + 46/5*u**g = 0.
-2/7, 1, 3
Let w(r) be the first derivative of -4*r**5/5 + 320*r**4 + 4663. Factor w(t).
-4*t**3*(t - 320)
Let t(j) be the first derivative of -4*j**5/5 - 14*j**4 + 548*j**3/3 - 420*j**2 - 1853. What is s in t(s) = 0?
-21, 0, 2, 5
Let n(m) be the first derivative of -m**6/120 - m**5/20 + m**4/48 + m**3/6 - 10*m - 5. Let i(z) be the first derivative of n(z). Solve i(t) = 0.
-4, -1, 0, 1
Let c = 925 - 230. Suppose u - 2*q = -6*q + 237, 4*q - c = -3*u. Let u*g**2 - 10 + 224*g**2 + 18*g - 5 - 456*g**2 = 0. What is g?
1, 5
Let r(a) = 2*a**2 - 4*a. Let q(c) = 5*c**2 + 158*c - 95*c - 71*c. Let u = -1 + -5. Let k(b) = u*q(b) + 14*r(b). Factor k(x).
-2*x*(x + 4)
Let 15 + 4318*n**4 + 57 - 22*n**2 - 29*n**3 - 2152*n**4 - 2161*n**4 + 84*n = 0. What is n?
-6/5, -1, 2, 6
Let q(x) be the first derivative of -39*x**4/16 + 11*x**3/4 + 3*x**2/4 - 998. Let q(g) = 0. What is g?
-2/13, 0, 1
Let x(y) = -29*y + 551. Let n be x(19). Let p(m) be the first derivative of 3/5*m**5 + 0*m**2 + n*m + 3/4*m**4 + 0*m**3 - 8. Solve p(k) = 0.
-1, 0
Suppose -8 = 19*l - 103. Let s be (l + (-32)/6)*-9. Factor 1/5*p**2 + 0 - 3/5*p + 3/5*p**s - 1/5*p**4.
-p*(p - 3)*(p - 1)*(p + 1)/5
Let y = -2065/12 + 1033/6. Let c(r) be the third derivative of 0 - 2/105*r**7 - 1/15*r**5 + 0*r + 0*r**3 - y*r**6 + 12*r**2 + 0*r**4. Solve c(m) = 0 for m.
-2, -1/2, 0
Let r(o) be the third derivative of -1/210*o**5 + 0 + 0*o + 1/21*o**3 + 52*o**2 + 0*o**4. Suppose r(v) = 0. What is v?
-1, 1
Let h(g) = -27*g**3 + 18*g**2 + 19*g. Let w(b) = -11*b**3 + 8*b**2 + 10*b. Let r(k) = 6*h(k) - 15*w(k). Factor r(s).
3*s*(s - 6)*(s + 2)
Let d(v) be the third derivative of -1/420*v**7 + 9 - 1/4032*v**8 + 9*v**2 + 0*v - 1/96*v**4 - 1/120*v**6 + 0*v**3 - 1/72*v**5. Solve d(w) = 0 for w.
-3, -1, 0
Suppose -f + 5*g + 9 = 4, -2*f - 3 = 3*g. Let s(k) be the second derivative of 0*k**2 + f*k**3 + 1/40*k**5 + 1/12*k**4 - 16*k + 0. Factor s(u).
u**2*(u + 2)/2
Let t be 8/32*4*5. Determine a so that t*a**2 + 6 + 345*a - 320*a + 24 = 0.
-3, -2
Let a be 9 - 7*24/28. Let d(f) be the first derivative of -a - 117/8*f**4 + 5/2*f**3 + 0*f + 4*f**6 + 108/5*f**5 + 0*f**2. Factor d(n).
3*n**2*(n + 5)*(4*n - 1)**2/2
Let s = -1 - -3. Let i = -320 - -324. Factor s*o**i + 53 + o - 3*o**3 - 53.
o*(o - 1)**2*(2*o + 1)
Let p(x) be the first derivative of x**5/4 + 25*x**4/12 + 20*x**3/3 + 10*x**2 + 102*x + 80. Let i(k) be the first derivative of p(k). Find d such that i(d) = 0.
-2, -1
Let r(k) = -1 - 77 + 7 - 3*k + 32. Let b be r(-13). Let -8 - 8/3*i + b*i**3 - 2/3*i**4 + 6*i**2 = 0. What is i?
-3, -1, 2
Let p be ((-238)/77 + 3)/(((-112)/(-22))/(-14)). Factor 1/4 + p*q**3 - 3/8*q**2 - 3/8*q.
(q - 2)*(q + 1)*(2*q - 1)/8
Suppose 0 = -3*m + 2*c + 15, c = -5*m + 3*c + 21. Suppose -5*j + 25 = 5*o, -o + m*j - 3 = -0*o. Factor -7*g + o*g**2 + g**2 - 3*g - 2*g**2.
2*g*(g - 5)
Suppose -55 = -7*k - 55. Let w(v) be the second derivative of 0*v**3 - 1/7*v**4 - 9/35*v**5 - 27*v - 1/14*v**6 + 0 + k*v**2. Determine l so that w(l) = 0.
-2, -2/5, 0
Suppose -5*b + 14 = f - 10*b, -4*f = -5*b - 41. Let u = 13 - f. Find z such that 4*z**5 - 305*z**u - 2*z**2 - 4*z**3 + 309*z**4 - 2*z**2 = 0.
-1, 0, 1
Solve -3*h - 276 + 45*h**3 - 4*h**4 - 2*h**4 + 294 - 54*h**2 = 0.
-1/2, 1, 6
Let q be 6*-4*55/(-40). Let a = q + -27. Factor 3 - a - 222*z - 300*z**2 + 282*z.
-3*(10*z - 1)**2
Let o be 3 - (-403 - -2 - 72/24). Suppose 411*g = o*g + 8. Factor -4/7*h + 2/7*h**g + 0.
2*h*(h - 2)/7
Let s(z) be the third derivative of z**5/60 + 1553*z**4/12 + 2411809*z**3/6 + 26*z**2 - z + 1. What is n in s(n) = 0?
-1553
Let v(f) be the second derivative of f**5/300 - f**4/20 + 3*f**3/10 + 139*f**2/2 - 32*f - 1. Let n(m) be the first derivative of v(m). Factor n(z).
(z - 3)**2/5
Suppose 41904/13*h**2 - 4038/13*h**3 + 152/13*h**4 - 120960/13*h + 82944/13 - 2/13*h**5 = 0. Calculate h.
1, 3, 24
Let l be (((-8)/3)/((-2)/9))/(-12 + 18). Factor 3*w + 0 + 6/7*w**l.
3*w*(2*w + 7)/7
Let y(m) be the third derivative of 0*m**5 + 0*m + m**2 + 1/1344*m**8 + 0*m**4 + 1/240*m**6 + 0*m**3 + 24 - 1/280*m**7. Find r such that y(r) = 0.
0, 1, 2
Factor -5*x**2 + 470*x + 6493*x - 6658580 + 2075*x + 935*x + 1567*x.
-5*(x - 1154)**2
Let f(l) be the first derivative of 1/6*l**5 + 1/45*l**6 - 8/3*l**2 + 1/3*l**4 - 2 - 4/9*l**3 - l. Let q(s) be the first derivative of f(s). Factor q(n).
2*(n - 1)*(n + 2)**3/3
Let 57/5*x**2 + 6*x + 0 - 3/5*x**4 + 24/5*x**3 = 0. Calculate x.
-1, 0, 10
Let i(a) be the first derivative of 15*a**4/8 - 43*a**3/2 + 78*a**2 - 72*a + 4424. Factor i(b).
3*(b - 4)**2*(5*b - 3)/2
Factor 5*n**4 + 107 - 68*n**2 - 3*n**4 + 2*n**4 + 133 + 26*n**3 - 2*n**4 - 104*n.
2*(n - 2)**2*(n + 2)*(n + 15)
Let x(j) be the third derivative of j**6/480 - 31*j**5/240 - 65*j**4/96 - 11*j**3/8 + 28*j**2 - 3*j + 3. Factor x(p).
(p - 33)*(p + 1)**2/4
Let p be 90/675 - -1*5758/15. Factor -18700 + 12288*n - 29273 - 83099 + 4*n**3 - p*n**2.
4*(n - 32)**3
Let v = 197512 + -987527/5. What is l in 3/5*l**2 + v*l + 6 = 0?
-10, -1
Let z(o) be the first derivative of -4/3*o**3 + 70 + 0*o + o**4 + 2/3*o**2 - 4/15*o**5. Factor z(h).
-4*h*(h - 1)**3/3
Suppose 0 = -x + 5 - 2. Let d be (-17 - -4)*(-536)/19162. Let 10/11*q**2 - 8/11*q**x + 0 - d*q + 2/11*q**4 = 0. Calculate q.
0, 1, 2
Let z(s) be the first derivative of -s**6/45 + 4*s**5/75 + 8*s**4/5 + 64*s**3/45 - 256*s**2/15 - 10563. Let z(f) = 0. Calculate f.
-4, 0, 2, 8
Let n(k) be the second derivative of -2*k**7/105 - k**6/5 + 3*k**5/5 + 7*k**4/3 + 52*k**2 - 77*k + 2. Let i(v) be the first derivative of n(v). Factor i(y).
-4*y*(y - 2)*(y + 1)*(y + 7)
Suppose 0 - 5/4*s**4 + 0*s - 1/4*s**3 + 5/4*s**2 + 1/4*s**5 = 0. What is s?
-1, 0, 1, 5
Let d(k) = 9*k - 24. Let c be d(3). Suppose 32 = 4*b - c*n, -3*n + 32 = 38*b - 34*b. Factor -b + 8/3*v - 2/9*v**2.
-2*(v - 6)**2/9
Let g(v) be the third derivative of v**8/84 - 23*v**7/105 + 9*v**6/10 + 29*v**5/30 -