2 - 450/(-66). Factor d + 3*d**2 + d**2 - o*d**3 - 4*d**3 + f*d**3.
-d*(d - 1)*(5*d + 1)
Let q(i) be the first derivative of i**6/2 - 6*i**5 + 45*i**4/2 - 40*i**3 + 75*i**2/2 - 18*i + 418. Find f, given that q(f) = 0.
1, 6
Let w be 2/3*(-1 - (-42)/15)*(-1229 + 1235). Suppose -w + 2/5*t**2 + 34/5*t = 0. Calculate t.
-18, 1
Let l(j) be the third derivative of j**8/1344 + 25*j**7/504 + 2*j**6/9 - 23*j**5/5 + 4*j**2 - 11*j. Let k(a) be the third derivative of l(a). Factor k(n).
5*(n + 16)*(3*n + 2)
Find d such that 559 - 389 + 378 + 544*d - 4*d**2 = 0.
-1, 137
Factor -100 - 2683255*z + z**2 + 0*z**2 + 2683207*z.
(z - 50)*(z + 2)
Suppose 2247*i + 129*i**4 - 11114 - 25095*i - 3*i**5 - 1857*i**3 + 28454 + 10311*i**2 = 0. Calculate i.
2, 5, 17
Let u(q) be the second derivative of q**6/120 - 17*q**5/80 - q**4/48 + 17*q**3/24 - 1428*q. Solve u(n) = 0 for n.
-1, 0, 1, 17
Let s(f) = -39*f - 114. Let j be s(-3). Let r(p) be the first derivative of 4 - 10/9*p**j + 7/3*p**2 + 1/6*p**4 - 2*p. Determine q, given that r(q) = 0.
1, 3
Factor m**3 - 11*m**2 - 2*m**4 + 5*m - 6*m + 5*m**4 + 10*m**2 - 2*m**2.
m*(m - 1)*(m + 1)*(3*m + 1)
Let t(i) be the first derivative of i**4/46 + 28*i**3/23 + 576*i**2/23 + 5184*i/23 + 1139. Factor t(k).
2*(k + 12)**2*(k + 18)/23
Let v(d) = 5*d**3 - 6*d**2 + 7*d - 6. Suppose 0 = 10*o + 13 - 23. Let n(r) = -r**3 - r + 2. Let b(t) = o*v(t) + 6*n(t). Factor b(q).
-(q - 1)*(q + 1)*(q + 6)
Let t(w) be the third derivative of -w**8/140 - 3*w**7/280 + w**6/30 + 3*w**5/40 - 23*w**3/2 + 56*w**2. Let j(n) be the first derivative of t(n). Factor j(a).
-3*a*(a - 1)*(a + 1)*(4*a + 3)
Let b(h) be the third derivative of 0*h**3 - 37*h**2 + 1/90*h**5 + 1/720*h**6 + 0*h**4 + 0 + 0*h. Determine r so that b(r) = 0.
-4, 0
Let v(p) be the second derivative of 1/3*p**5 + 11/6*p**3 - 25/6*p**4 - 7*p - 1/90*p**6 + 0*p**2 + 0. Let t(d) be the second derivative of v(d). Factor t(n).
-4*(n - 5)**2
Let -1495/3 + 1490/3*n + 5/3*n**2 = 0. What is n?
-299, 1
Let c = -4565 - -4570. Let d(z) be the third derivative of 0*z + 5/24*z**4 - 5/3*z**3 + 8*z**2 + 0 + 1/12*z**c. Factor d(q).
5*(q - 1)*(q + 2)
Suppose 8*q = 49 - 25. Find y, given that 30*y**2 - 21*y - q*y - 5*y**3 - y = 0.
0, 1, 5
Let h(c) = 10*c**5 + 21*c**4 - 63*c**3 + 68*c**2 - 9. Let i(r) = -r**5 - r**4 - 2*r**3 + 1. Let q(v) = 5*h(v) + 45*i(v). Find l, given that q(l) = 0.
-17, 0, 1, 4
Let 0*p**2 + 384*p + 0 - 3/2*p**3 = 0. Calculate p.
-16, 0, 16
Let b(h) = -h**3 + 6*h**2 + 16*h - 99. Let u be b(6). Let k(f) = -f**2 - 8*f - 5. Let n(w) = w**2 - 7*w - 5. Let z(y) = u*k(y) + 2*n(y). Solve z(j) = 0.
-1
Factor -126*m**3 + 47/3*m**4 - 32/3*m + 256*m**2 + 0.
m*(m - 4)**2*(47*m - 2)/3
Let u = -49 - -74. Solve 1 + 5*t**2 + 2 - 5*t + u*t + 17 = 0 for t.
-2
Let d = 6241663/8 + -780205. Factor -1/8*p**2 - 21/4 + d*p.
-(p - 21)*(p - 2)/8
Let q(a) be the second derivative of a**4/54 - 328*a**3/27 - 329*a**2/9 + 312*a - 2. Solve q(u) = 0 for u.
-1, 329
Let p(g) be the third derivative of g**7/2520 - 11*g**6/360 + 65*g**4/8 - 217*g**2. Let j(y) be the second derivative of p(y). Suppose j(w) = 0. Calculate w.
0, 22
Let a be (2/6)/((-4)/(-48)). Suppose -h = -a*f + 61, 2*h = 3*f - 2*h - 36. Factor -b + 10*b - 4*b + 15*b - f - 4*b**2.
-4*(b - 4)*(b - 1)
Suppose -3*s = -26 - 22. Let x be (-7)/((-189)/60)*6/s. Factor x*z**2 + 25/6*z + 10/3.
5*(z + 1)*(z + 4)/6
Suppose t - k - 5 = 0, t + k + 0*k = -1. Let 60*a**3 - 3418*a**t + 5*a + 12*a + 0*a + 3368*a**2 + 5*a**5 - 30*a**4 - 2*a = 0. What is a?
0, 1, 3
Let v(y) be the third derivative of 0*y + 113*y**2 - 17/20*y**5 + 2/15*y**6 + 0 + 0*y**3 - 1/210*y**7 + 3/2*y**4. Factor v(k).
-k*(k - 12)*(k - 3)*(k - 1)
Let j(n) = -5*n**3 + 473*n**2 - 55697*n + 55223. Let d(o) = -2*o**3 + o**2 - o - 1. Let u(c) = 10*d(c) - 5*j(c). Find p, given that u(p) = 0.
1, 235
Factor -2/13*q**3 - 54/13*q**2 + 56/13*q + 0.
-2*q*(q - 1)*(q + 28)/13
Let h be 4/(0 - (-15)/(-3))*-1020. Let r = 816 - h. Factor r + 0*q - 4/3*q**2 + q**4 - 1/3*q**5 + 0*q**3.
-q**2*(q - 2)**2*(q + 1)/3
Let r = 2941/2172 - 15/724. Let v(l) be the first derivative of -12 - 32*l - r*l**3 + 18*l**2. Find c, given that v(c) = 0.
1, 8
Let m(k) be the second derivative of 25/12*k**4 - 34*k + 2 - 85/12*k**3 + 10*k**2 - 1/8*k**5. Factor m(q).
-5*(q - 8)*(q - 1)**2/2
Let l(r) be the third derivative of 0*r**4 + 0 - 5*r - 1/60*r**5 + r**2 + 0*r**3 + 1/240*r**6 + 1/420*r**7. Factor l(d).
d**2*(d - 1)*(d + 2)/2
Let t = 40 + -38. Suppose 3*q + 5*n - 29 = 0, 2*q + 7*n - 26 = t*n. Determine o, given that -57*o**2 - 16*o + 149*o**3 - 128*o**q - 2*o = 0.
-2/7, 0, 3
Let w = 30093 - 150461/5. Factor -540*a - w*a**3 + 36*a**2 + 2700.
-4*(a - 15)**3/5
Factor -438/19*n + 216/19*n**2 + 2/19*n**3 + 220/19.
2*(n - 1)**2*(n + 110)/19
Suppose 136*b + 27*b**4 - 16*b**3 - 1315*b**2 + 1287*b**2 - 23*b**4 - 96 = 0. Calculate b.
-3, 1, 2, 4
Let i(d) be the second derivative of 10/3*d**3 + 2*d + 0*d**2 + 3/5*d**5 + 3*d**4 + 2 - 2/15*d**6. Let i(p) = 0. Calculate p.
-1, 0, 5
Let n(d) be the second derivative of -7/48*d**4 + 30*d + 0 + 0*d**2 + 1/6*d**3 + 1/120*d**6 + 1/40*d**5. Factor n(h).
h*(h - 1)**2*(h + 4)/4
Let u = -800677 - -800680. Factor -7/8*t**2 - 1/8*t**u + 17/8*t - 9/8.
-(t - 1)**2*(t + 9)/8
Let z = 6/527 + -5468/17391. Let u = 32/33 + z. Factor u*v**3 + 0*v**2 + 0 + 2/3*v**4 + 0*v.
2*v**3*(v + 1)/3
Let q(f) be the third derivative of f**5/30 - 7*f**4/6 - 5*f**3 + 2*f**2 + 2522*f. Factor q(l).
2*(l - 15)*(l + 1)
Let o(n) = 5*n**2 + 24*n - 74. Suppose 2*s + 18 = -12*b + 11*b, -5*b = 3*s + 41. Let h be o(s). Factor 50/9*y**2 + 0 + 2*y**h - 4/3*y.
2*y*(y + 3)*(9*y - 2)/9
Factor 35*s + 21*s + 249*s**3 + 53*s + 2*s + 132 - 252*s**3 - 24*s**2.
-3*(s - 4)*(s + 1)*(s + 11)
Let a(t) = t**3 - 8*t**2 - 3*t + 26. Let m be a(8). Let d be 28/10 + (-5 - m)/(-35). Factor 16*y - y**3 - 4*y**3 + y**d.
-4*y*(y - 2)*(y + 2)
Let q(o) be the second derivative of o**7/1400 - o**6/600 - o**5/100 - 4*o**3/3 - o**2/2 + 22*o + 1. Let d(b) be the second derivative of q(b). Factor d(j).
3*j*(j - 2)*(j + 1)/5
Suppose 32/11*m**2 + 38/11*m**3 - 72/11*m + 0 + 2/11*m**4 = 0. What is m?
-18, -2, 0, 1
Let p(g) = -13*g + 72. Let k(i) = 15*i - 72. Let c(b) = 6*k(b) + 5*p(b). Let o be c(3). Determine t so that -18/7*t**o - 120/7*t**2 - 74/7*t - 12/7 = 0.
-6, -1/3
Let z = 60 + -58. Factor -4*k**3 - 10*k**3 + 6*k**4 - 24*k**z + 46*k**3.
2*k**2*(k + 6)*(3*k - 2)
Suppose 0 = 4*j - c + 23, -j + 5*c - 6*c = 12. Let y be 54/189 - 12/j. Factor -2/7*g**3 - 6/7 + 10/7*g - 2/7*g**y.
-2*(g - 1)**2*(g + 3)/7
Factor 3*k**3 + 36 + 182*k + 64 - 185*k - 39 + 143 - 204*k**2.
3*(k - 68)*(k - 1)*(k + 1)
Let b(u) be the first derivative of -u**4/10 + 2*u**3 + 94*u**2/5 + 48*u - 9911. Factor b(k).
-2*(k - 20)*(k + 2)*(k + 3)/5
Factor 723404 - 723404 + 744*o + 24*o**3 + 376*o**2 - 22*o**3.
2*o*(o + 2)*(o + 186)
Suppose 5832*t - 15363/10*t**2 + 122/5*t**3 - 4320 - 1/10*t**4 = 0. Calculate t.
1, 3, 120
Let l(z) = 5*z**2 + 6*z - 77. Let p(h) = -10*h + 74 - 10*h**2 + 35 - 25 + 71. Let f(m) = 5*l(m) + 3*p(m). Factor f(y).
-5*(y - 4)*(y + 4)
Let s(m) = m**3 - 14*m - 4. Let q be s(-3). Factor 145*h - 2 - 19 - 2 - q - 10*h**2 - 101.
-5*(h - 1)*(2*h - 27)
Suppose -5*a - 4*b = -22, 5*a + 10*b - 165 + 125 = 0. Let o(n) be the third derivative of 7/27*n**4 + 0*n - 1/270*n**5 - 196/27*n**3 - 6*n**a - 3. Factor o(l).
-2*(l - 14)**2/9
Let u(j) = -j**3 - j**2 + j + 1. Let g(d) = -2*d**2 - 3*d - 1. Let i be g(-3). Let z(x) = 12*x**3 + 12*x**2 - 20*x - 4. Let v(o) = i*u(o) - z(o). Factor v(s).
-2*(s - 1)**2*(s + 3)
Let d(l) = -l**2 + 3662*l + 1119961. Let h(f) = -6*f**2 + 14646*f + 4479843. Let o(u) = 9*d(u) - 2*h(u). Factor o(w).
3*(w + 611)**2
Let u(q) = -q**2 + 1. Let l(y) = 6*y**2 - 6*y - 3. Let a(k) = 3*k + 17. Let w be a(-6). Let h(b) = w*l(b) - 3*u(b). Solve h(g) = 0 for g.
0, 2
Let x be (-28)/(-49)*((1 - 6) + 6)*7. Determine h so that 90/7*h + 0 + 2/7*h**x + 22/7*h**3 + 78/7*h**2 = 0.
-5, -3, 0
Factor 3819/7 - 258/7*l + 3/7*l**2.
3*(l - 67)*(l - 19)/7
Let n be (133/(-9) - 2/9)*(-1540)/7700. Factor 3/4*v**4 - 9/4*v**2 + 27/4*v**n - 27/2 - 87/4*v.
3*(v - 2)*(v + 1)**2*(v + 9)/4
Let a be 399/770 + (-16)/(-88) - (-6)/(-30). Find v, given that 4*v + a*v**2 - 33/2 = 0.
-11, 3
Let q(k) be the first derivative of 4*k**3