
Suppose -18*n = -y - 17*n + 31, 4*y + 5*n = 160. Let s(l) be the first derivative of 2*l**3 - 33*l**2 + 242*l - 1/22*l**4 + y. Factor s(w).
-2*(w - 11)**3/11
Find z, given that 1495/4*z + 529/2 + 1/4*z**4 + 393/4*z**2 - 43/4*z**3 = 0.
-2, -1, 23
Suppose 0 = 13*r - 112 + 73. What is b in 249*b**2 + 19*b**3 + 24 + 3*b**4 - 276*b**2 - 13*b**r - 6*b = 0?
-4, -1, 1, 2
Let g be (-18 - 1344/(-63)) + (-8)/(-60) + 224/(-105). Factor 8/3 - g*a - 1/6*a**3 - 7/6*a**2.
-(a - 1)*(a + 4)**2/6
Let w be -26 + (-492)/(-12) + -13. Determine a so that 0 - 2/5*a**4 - 4/5*a**w + 0*a + 7/5*a**3 - 1/5*a**5 = 0.
-4, 0, 1
Suppose -26071 - 10363 = -866*i + 11858 - 6724. Factor i*l - 288/7 - 50/7*l**2 + 2/7*l**3.
2*(l - 12)**2*(l - 1)/7
Suppose -58/3*k**2 - 32/9*k**3 - 2/9*k**4 - 224/9 - 368/9*k = 0. Calculate k.
-7, -4, -1
Suppose -231*o + 986 = 306 - 475. Find z, given that -3*z + 6*z**3 - 2/3*z**4 + 4/3*z**2 - 3*z**o - 2/3 = 0.
-1, -2/9, 1
Factor 4/9*z**2 + 38/9 - 26/3*z.
2*(z - 19)*(2*z - 1)/9
Let x be (-2)/(-30)*(-24 + 1898/78). Let k(w) be the third derivative of 0*w + 0*w**4 + 0 + x*w**5 + 0*w**3 - 1/90*w**6 + 15*w**2. Determine r so that k(r) = 0.
0, 1
Let k(p) be the first derivative of 7/3*p**3 - 1/12*p**6 + 41 + 3/4*p**4 + 11/4*p**2 - 1/10*p**5 + 3/2*p. Factor k(m).
-(m - 3)*(m + 1)**4/2
Suppose 0 = -3*d + 5 - 8. Let o be -7 + 7 - (8 - d)/(-3). Factor 16*c**2 + 4*c**4 + c**4 - 4*c**4 + o*c**4 - 16*c**3.
4*c**2*(c - 2)**2
What is t in 235*t + 5/3*t**3 - 350/3 - 120*t**2 = 0?
1, 70
Let b(s) = s**3 + 2*s**2 - 10*s - 1. Let y(z) = 2*z**3 + 4*z**2 + z - 2. Let r be y(-2). Let h be b(r). Factor -3*d**3 + 26*d**2 - h*d**3 + 6 + 55*d - 77*d.
-2*(d - 1)**2*(5*d - 3)
Let a(d) = -3*d**4 - 495*d**3 + 234*d**2 + 2796*d - 1104. Let w(m) = -99*m**3 + 47*m**2 + 560*m - 221. Let i(u) = -5*a(u) + 24*w(u). Solve i(s) = 0.
-6, -3, 2/5, 2
Let n(v) = -420*v - 5040. Let p be n(-12). Let f(k) be the third derivative of 0 + 0*k - 5/8*k**4 + 1/20*k**5 - 22*k**2 + p*k**3. Solve f(z) = 0 for z.
0, 5
Let -880*j - j**2 - 354 - 198 - 87 - 243 + 3*j**2 = 0. Calculate j.
-1, 441
Let x(r) = 30*r**5 + 425*r**4 + 760*r**3 - 1710*r**2 + 450*r + 45. Let y(z) = z**5 - z**3 - z**2 + 1. Let c(d) = -x(d) + 45*y(d). Suppose c(n) = 0. What is n?
-3, 0, 1/3, 1, 30
Let f(d) be the third derivative of -d**7/1050 + d**6/50 + 7*d**5/75 + 1100*d**2. Factor f(q).
-q**2*(q - 14)*(q + 2)/5
Let g = 1876 + -1876. Let h(y) be the third derivative of 50/3*y**4 + 0*y - 5/4*y**6 + g + 20*y**2 + 13/6*y**5 + 80/3*y**3 + 3/28*y**7. Factor h(l).
5*(l - 4)**2*(3*l + 2)**2/2
Let p(g) = 4*g**2 + 85*g + 29. Let r be p(-21). Let a(s) be the second derivative of 0 - r*s + 3/20*s**5 + 6*s**2 - 2*s**3 - 1/4*s**4. Factor a(q).
3*(q - 2)*(q - 1)*(q + 2)
Let a(t) be the third derivative of -t**5/330 - 3*t**4/11 - 28*t**3/3 - 23*t**2 - 6*t - 2. Suppose a(w) = 0. Calculate w.
-22, -14
Let m be (-15)/12 + 2187/1620. Let g = -5 + 7. Factor -1/10 - m*r**g + 1/5*r.
-(r - 1)**2/10
Let z(i) be the first derivative of -i**5/12 + 5*i**4/3 - 10*i**3 + 20*i**2 - i - 105. Let p(s) be the second derivative of z(s). Let p(k) = 0. What is k?
2, 6
Let z(a) be the third derivative of a**5/30 - 287*a**4/12 - 96*a**3 - 8*a**2 + 4*a + 4. Factor z(o).
2*(o - 288)*(o + 1)
Let w = 19727 - 19727. Let d(t) be the third derivative of 0*t**3 + 0*t + 0 + w*t**4 + 0*t**7 - 1/50*t**5 + 1/560*t**8 - 3/200*t**6 - 38*t**2. Factor d(j).
3*j**2*(j - 2)*(j + 1)**2/5
Let b(m) be the second derivative of 15*m**5/4 - 177*m**4/4 + 7*m**3 + 3*m + 137. Factor b(l).
3*l*(l - 7)*(25*l - 2)
Let v(g) be the second derivative of g**4/18 - 202*g**3/9 - 203*g**2/3 - 968*g. Factor v(i).
2*(i - 203)*(i + 1)/3
Let u be (4 + -1)/(6/(-6)) - -10. Suppose -19*n**2 + 2 + u*n - 28*n + 68*n**2 + 0 + 0 = 0. What is n?
1/7, 2/7
Let p = 51070 - 51068. Determine v, given that 2/3*v**3 + 4/3*v**p + 16 - 40/3*v = 0.
-6, 2
Let b be 23*3/90 - -8*(-51)/680. Let q(m) be the third derivative of 0*m**3 - 1/60*m**6 + b*m**4 + 0*m + 0 - 14*m**2 + 1/30*m**5. Find s, given that q(s) = 0.
-1, 0, 2
Let f(s) be the third derivative of 0*s**3 - 2/75*s**5 + 1/525*s**7 + 0*s + 1/1200*s**6 - 1/60*s**4 - 30*s**2 + 0. Suppose f(b) = 0. Calculate b.
-2, -1/4, 0, 2
Factor -581*j**3 + 425*j + 267 - 57 - 240*j**2 + 1188*j**3 - 582*j**3.
5*(j - 7)*(j - 3)*(5*j + 2)
Let a = 74 + -55. Suppose a*z - 42 = 5*z. Factor -13 + 26 + z*h**2 + 179 - 48*h.
3*(h - 8)**2
Let b(u) be the second derivative of -2/63*u**7 + 0*u**3 - 2 + 0*u**4 - 2/45*u**6 + 0*u**2 + 4*u + 2/15*u**5. Factor b(f).
-4*f**3*(f - 1)*(f + 2)/3
Solve -2/5*i**4 + 126/5*i + 54/5*i**2 - 14/5*i**3 - 324/5 = 0 for i.
-9, -3, 2, 3
Suppose -2153*m - 550 = -2158*m. Let p be m + -112 + 22/5. Solve p*b**3 + 16/5*b**2 + 0 - 16/5*b - 4/5*b**5 - 8/5*b**4 = 0.
-2, 0, 1
Let j(o) be the third derivative of -o**5/330 - 233*o**4/132 + 78*o**3/11 + 2*o**2 + 23*o - 2. Factor j(l).
-2*(l - 1)*(l + 234)/11
Suppose 0 = -208*r + 216*r - 24. Factor 3/2*p**2 + r*p + 3/2.
3*(p + 1)**2/2
Let o(s) be the second derivative of -4/27*s**3 + 0 + 1/27*s**4 + 39*s - 16/9*s**2. What is k in o(k) = 0?
-2, 4
Let s(b) be the third derivative of -b**6/120 - b**5/6 - 29*b**4/24 - 10*b**3/3 + 594*b**2. Find i, given that s(i) = 0.
-5, -4, -1
Let v = -28 + 60. Suppose 3*f - 8 = f, -5*f = 4*i - v. Solve -48*u + 9*u**i - 2*u**2 - 2*u**3 + 5*u**3 - u**2 + 12 = 0 for u.
-2, 1/4, 2
Suppose -5*k - 20*s + 16*s + 760 = 0, -424 = -3*k + 4*s. Suppose -36*c - 4 = -k. Factor 0*w + 0*w**3 + 0 + 2/9*w**c - 2*w**2.
2*w**2*(w - 3)*(w + 3)/9
Let y be 3/(-6)*((-2)/(-27) - (-424)/(-5724)). Factor -2/3*d**3 - 1/9*d**4 - 8/9*d + 5/3*d**2 + y.
-d*(d - 1)**2*(d + 8)/9
Let d = 770093 - 1540183/2. Factor -d*f + 3 - 3/2*f**2.
-3*(f - 1)*(f + 2)/2
Let g = 127 - 129. Let l be (g + 2)*-1 + 2. Factor 9584*b - 9584*b + 4*b**3 + 4*b**l.
4*b**2*(b + 1)
Find q, given that -33 + 124*q - 116*q**2 + 52 + 12 - 39 = 0.
2/29, 1
Let r(c) be the third derivative of 64*c**2 + 1/60*c**4 + 0*c + 0 + 1/30*c**3 + 1/300*c**5. Factor r(p).
(p + 1)**2/5
Let k(o) = 12*o - 180. Let i be k(19). Suppose -5*j - 49*t = -i*t - 11, 3*t = -j + 5. What is q in 22/3*q**3 - 8*q**2 - j*q**4 + 0 + 8/3*q = 0?
0, 2/3, 1, 2
Let u(f) be the second derivative of -f**5/4 + 155*f**4 - 58275*f**3/2 + 171125*f**2 + 30*f + 7. Factor u(q).
-5*(q - 185)**2*(q - 2)
Let r(k) be the third derivative of -k**5/60 - k**4/9 + k**3/6 - 2*k**2 + 190*k. Find x, given that r(x) = 0.
-3, 1/3
Let y(g) be the first derivative of -36 - 28*g - 3/13*g**3 + 1/13*g**4 + 4/13*g**2 - 1/130*g**5. Let a(q) be the first derivative of y(q). Factor a(n).
-2*(n - 4)*(n - 1)**2/13
Let c(t) be the first derivative of -4*t**2 - 2/3*t**3 + 102 + 0*t. Solve c(h) = 0 for h.
-4, 0
Let c(f) be the third derivative of 0 - 107*f**2 + 0*f**4 + 1/240*f**5 + 1/280*f**7 - f - 1/160*f**6 + 0*f**3 - 1/1344*f**8. Let c(b) = 0. Calculate b.
0, 1
Let q(a) = a**2 + 20 - a**2 - 40 - 48 + 36*a - a**2. Let t be q(34). Factor -2/19*m**2 - 4/19*m**4 + t*m + 6/19*m**3 + 0.
-2*m**2*(m - 1)*(2*m - 1)/19
What is t in -102/19*t + 2/19*t**2 + 0 = 0?
0, 51
Let q(c) be the second derivative of -25*c**7/231 - 799*c**6/33 - 3567*c**5/55 - 1898*c**4/33 - 632*c**3/33 + 492*c - 1. Let q(o) = 0. What is o?
-158, -1, -2/5, 0
Let b(a) = 6*a**3 + 6*a**2 - 11*a - 1. Let m(s) = -3*s**3 - 3 - 3*s**2 + 2 + 5*s + 3 - 1. Let o = -126 + 128. Let g(z) = o*b(z) + 5*m(z). Factor g(t).
-3*(t - 1)*(t + 1)**2
Let u(w) be the third derivative of -1/60*w**5 + 1/6*w**3 + 2 - 1/6*w**4 + 1/30*w**6 + 0*w - 4*w**2. Factor u(i).
(i - 1)*(i + 1)*(4*i - 1)
Let h be 10802/495 - 400/180. Factor -28/5*x - h - 2/5*x**2.
-2*(x + 7)**2/5
Let f(n) be the third derivative of -n**5/20 - 3137*n**4/4 - 9840769*n**3/2 - 4312*n**2. What is b in f(b) = 0?
-3137
Let h(f) be the second derivative of -8 + 5/2*f**3 + 1/10*f**6 - 3/4*f**5 + 4*f - 1/4*f**4 + 0*f**2. Factor h(v).
3*v*(v - 5)*(v - 1)*(v + 1)
Let k be (-77)/(-22) + -4 + 6/4. Let v(z) = -3*z**2 - 57*z - 6. Let l(a) = -a + 1. Let j(r) = k*v(r) + 6*l(r). Suppose j(y) = 0. Calculate y.
-21, 0
Let f(w) be the first derivative of -98000*w**3/3 - 700*w**2 - 5*w + 5135. Factor f(p).
-5*(140*p + 1)**2
Let s(f) = -f**2 - 34*f - 234. Let h be s(-10). Let j(v) be the first derivative of -2/9*v**2 + 0*v + h - 2/9*v**3 - 1/18*v**4. 