3 + 466/11*n**2 - 2/11*n**4 + 504/11*n = 0.
-28, -1, 0, 9
Let c be 124/42 + (-342)/3591. Factor -9/7*l + 0 - 4/7*l**5 - 37/7*l**3 + 30/7*l**2 + c*l**4.
-l*(l - 1)**2*(2*l - 3)**2/7
Let w(s) be the first derivative of -150*s - 5*s**3 - 235/2*s**2 + 103. Find x such that w(x) = 0.
-15, -2/3
Let z(d) be the second derivative of -5/6*d**7 - 2*d - 145/4*d**5 - 9*d**6 - 125/2*d**4 - 70/3*d**3 + 60*d**2 + 22. Suppose z(c) = 0. Calculate c.
-3, -2, -1, 2/7
Let o(a) be the first derivative of a**8/336 - 9*a**7/280 + 5*a**6/36 - 3*a**5/10 + a**4/3 + 5*a**3 - 6. Let w(i) be the third derivative of o(i). Factor w(x).
(x - 2)**2*(x - 1)*(5*x - 2)
Suppose 18 = -3*n + 2*z, n - 2*z = -35 + 13. Find w such that 6/5 - 2/3*w**n - 2/15*w**3 - 2/5*w = 0.
-3, 1
Let v(w) be the third derivative of 0*w**5 - 3*w**2 + 1/120*w**6 + 0*w**3 + 0*w + 0 + 0*w**4. Solve v(t) = 0 for t.
0
Let c(o) be the first derivative of o**6/2 + 144*o**5/5 + 1725*o**4/4 - 48*o**3 - 864*o**2 + 9165. Find g, given that c(g) = 0.
-24, -1, 0, 1
Suppose 2 = 17*a - 14*a + t, -5*a = -7*t - 90. Factor p**3 + 1/3*p**2 - p - 1/3*p**a + 0.
-p*(p - 3)*(p - 1)*(p + 1)/3
Let a(u) = -20*u**2 + 102*u + 2016. Let x(c) = 7*c**2 - 23*c - 672. Let w(k) = -6*a(k) - 17*x(k). Factor w(d).
(d - 224)*(d + 3)
Let x be (-15)/5 + -4*(-2710)/(-275). Let a = x + 213/5. Factor a*m**3 + 24/11*m - 12/11*m**2 - 16/11.
2*(m - 2)**3/11
Let a(w) be the first derivative of -w**4/22 - 16*w**3/33 + w**2/11 + 16*w/11 + 795. Factor a(b).
-2*(b - 1)*(b + 1)*(b + 8)/11
Let x(k) be the first derivative of k**6/810 - k**5/54 + 2*k**4/27 + 2*k**3/3 + 5*k**2/2 - 42. Let t(y) be the third derivative of x(y). What is z in t(z) = 0?
1, 4
Suppose -277*z + 84 + 184*z**2 + 24*z**3 + z**5 - 72*z**3 + z**4 + 5*z + 60 = 0. Calculate z.
-9, 2
Let p = 33672 - 33666. Let o(q) be the second derivative of -15*q + 4/21*q**3 + 5/21*q**4 + 0*q**2 + 0 - 1/70*q**5 - 1/42*q**p. Factor o(m).
-m*(m - 2)*(m + 2)*(5*m + 2)/7
Factor -4/5*u**2 + 24 - 4/5*u.
-4*(u - 5)*(u + 6)/5
Suppose 4*b = -u + 27 + 72, 0 = u - 4*b - 107. Let v = u + -101. Let -5*t**3 + 4*t**v + 5*t**5 + 768*t**4 + t**2 - 773*t**4 = 0. What is t?
-1, 0, 1
Let d be 266 + 6 + -10 + -2. Suppose 55*y - 70 = d. Solve -21 - 3/7*h**2 - y*h = 0.
-7
Let w = 39328 - 39328. Let u(o) be the second derivative of 0*o**4 + 0 - 1/126*o**7 - 1/20*o**5 - 2/45*o**6 - 12*o + w*o**2 + 0*o**3. Factor u(p).
-p**3*(p + 1)*(p + 3)/3
Suppose -258 - 1787/2*k**2 - 753/2*k**3 + 1/2*k**5 - 814*k - 77/2*k**4 = 0. Calculate k.
-6, -1, 86
Let -112/11*r - 49/11*r**2 - 2/11*r**3 - 4 = 0. Calculate r.
-22, -2, -1/2
Let q(v) = -v**4 - v**3 - 5*v**2 + v. Let z(k) = -10*k**4 + 42*k**3 + 162*k**2 - 818*k - 4200. Let n(x) = 12*q(x) - z(x). Factor n(r).
-2*(r - 4)*(r + 5)**2*(r + 21)
Let p(g) = -16*g**2 - 2*g. Let t(i) = -i**2. Suppose -2*j - o + 2 - 7 = 0, 2*j + 4*o + 8 = 0. Let y(a) = j*p(a) + 36*t(a). Let y(u) = 0. Calculate u.
0, 1
Solve -544*j + 8*j**3 - 32*j - 33*j**4 + 13*j**4 - 165*j**2 + 5*j**5 - 3*j**5 + 501*j**2 = 0 for j.
-4, 0, 2, 6
Let m(v) be the third derivative of v**6/1620 - v**5/60 + 2*v**4/27 - 143*v**3/6 + 15*v**2 - 3. Let u(b) be the first derivative of m(b). Solve u(p) = 0 for p.
1, 8
Suppose 106 + 4 = -62*n + 117*n. Let x(s) be the second derivative of -3/2*s**3 - 3/20*s**5 - 18*s + 3/4*s**4 + 0 + 3/2*s**n. Factor x(i).
-3*(i - 1)**3
Let v(w) = -20*w**4 - 240*w**3 + 180*w**2 + 290*w + 15. Let x(f) = f**4 + 2*f**2 - 2*f - 10. Let q(z) = v(z) + 25*x(z). Find r such that q(r) = 0.
-1, 1, 47
Let h(y) = -2*y**3 + 12*y**2 + 75*y + 128. Suppose 13*i + 54 = 22*i. Let p(o) = -9*o**3 + 47*o**2 + 300*o + 513. Let l(f) = i*p(f) - 26*h(f). Factor l(t).
-2*(t + 5)**3
Let b be (1 - (-8)/(-6))/((-12)/27828). Let z = -3861/5 + b. Find d such that 0*d - z*d**3 + 6/5*d**4 + 0 - 2/5*d**5 + 0*d**2 = 0.
0, 1, 2
Suppose -3*x - 24*r = -27*r - 18, -2*r = 4*x - 6. Factor -3*f**x + 13*f - 18*f + 13*f + f**3.
-2*f*(f - 2)*(f + 2)
Let w(h) be the first derivative of 1/3*h**2 + 0*h + 150 - 2/45*h**3. Find r such that w(r) = 0.
0, 5
Suppose -t + r + 3*r - 15 = 0, -10 = -2*r. Let g(z) = -6*z + 172. Let l be g(28). Find f such that -3*f**3 - 2*f**5 - f**5 + 4*f**t - l*f**5 - 6*f**4 = 0.
-1, 0
Find c, given that -206/7*c**2 - 208/7 - 415/7*c + 1/7*c**3 = 0.
-1, 208
Determine g so that 5/2*g + 0 - 1/6*g**3 + 7/3*g**2 = 0.
-1, 0, 15
Let o(n) be the third derivative of -n**8/84 - 4*n**7/15 + 7*n**6/6 + 544*n**5/15 - 1034*n**4/3 + 3872*n**3/3 + 97*n**2 - 10*n. Find d such that o(d) = 0.
-11, 2, 4
Suppose 6*c = 7*c + 6. Let b(l) = -15*l**2 + 48*l. Let z(i) = 17*i**2 - 49*i. Let h(m) = c*z(m) - 7*b(m). Factor h(a).
3*a*(a - 14)
Let p(s) be the third derivative of 2/15*s**4 + 0 - 2/75*s**5 + 0*s**3 + 0*s + 72*s**2 + 1/600*s**6. Let p(m) = 0. Calculate m.
0, 4
Let o(l) = -52*l**2 - 26*l + 24. Let s be o(1). Let t be (-21)/9 - 207/s. Factor 39/4*u + 27/4*u**3 - 15*u**2 - t.
3*(u - 1)**2*(9*u - 2)/4
Let y(g) be the second derivative of g**5/10 + 1085*g**4/2 + 1177225*g**3 + 1277289125*g**2 + 2*g - 62. Suppose y(u) = 0. Calculate u.
-1085
Let q(g) be the third derivative of g**6/780 + 551*g**5/390 + 6302*g**4/13 - 25392*g**3/13 - 2091*g**2. Factor q(f).
2*(f - 1)*(f + 276)**2/13
Let h(i) be the second derivative of -i**5/100 - 3*i**4/10 + 13*i**3/10 - 2*i**2 - 940*i. Factor h(s).
-(s - 1)**2*(s + 20)/5
Let q(u) = -72*u + 144. Let i be q(7). Let f be (-656)/i - 2/(-27)*-3. Factor -8*n - 10*n**2 - f.
-2*(5*n + 2)**2/5
Find c, given that -56*c**2 + 672 + 2/9*c**4 - 24*c - 38/9*c**3 = 0.
-6, 3, 28
Let i(d) = d**3 + 13*d**2 - 17*d - 18. Let a be i(-14). Let -a*x + 0*x**2 + 0*x**2 - 2*x**2 - 2*x**2 = 0. Calculate x.
-6, 0
Let o(y) be the second derivative of 2*y - 7/6*y**3 + 1/100*y**5 + 17/30*y**4 + 0*y**2 + 96. Factor o(c).
c*(c - 1)*(c + 35)/5
Factor -1/6*y**2 - 41067/2 - 117*y.
-(y + 351)**2/6
Let t(q) be the first derivative of -1/3*q**3 - 36*q + 45 + 6*q**2. Factor t(w).
-(w - 6)**2
Factor -2/5*k**2 + 48 + 52/5*k.
-2*(k - 30)*(k + 4)/5
Let m(h) = 4*h + 212. Let t be m(-50). Determine j, given that 11*j + 16 - t*j**4 + 4*j**3 - 152*j**2 + 37*j - 4*j**5 + 196*j**2 = 0.
-2, -1, 2
Let r(b) = -2*b**3 - 55*b**2 + 30*b + 56. Let t be r(-28). Let y(z) be the first derivative of 2*z**2 + 1/3*z**3 + t*z + 12. Factor y(d).
d*(d + 4)
Let t(n) = -n**4 - n**3 + n**2 - n - 1. Let z be 52/(-156) - 4/(-3). Let h(r) = r**4 + 13*r**3 - 19*r**2 + 11*r + 3. Let b(d) = z*h(d) + 3*t(d). Factor b(k).
-2*k*(k - 2)**2*(k - 1)
Suppose 4*u + 23 = -13*u + 108. Let a(y) be the first derivative of 3/4*y**4 - 2*y**3 + 0*y**2 + 3/5*y**u + 0*y + 10. Find d, given that a(d) = 0.
-2, 0, 1
Solve 8307*y**4 + 2 - 2*y**5 - 151*y**2 - 8256*y**4 + 102*y + 3*y**5 - 3*y**3 - 2 = 0 for y.
-51, -2, 0, 1
Let a(v) = -23*v**2 - 1718*v - 3344. Let t(f) = 8*f**2 + 573*f + 1114. Let q(r) = 3*a(r) + 8*t(r). Factor q(i).
-5*(i + 2)*(i + 112)
Let g(j) be the second derivative of j**5/40 - 10*j**4/3 + 77*j**3/3 - 76*j**2 + 7205*j. Suppose g(n) = 0. What is n?
2, 76
Suppose 2*z - 8 = 205*o - 206*o, 5*z = 3*o + 20. Let q(m) be the third derivative of o*m + 2/7*m**3 + 30*m**2 + 0 - 1/140*m**5 - 3/56*m**4. Factor q(u).
-3*(u - 1)*(u + 4)/7
Let n = -17 - -34. Suppose 5*g = 8 + n. Factor 2*s**3 - 72*s**5 + 76*s**g - 10*s + 10*s**3 + 16*s**4 - 16*s**2 - 6*s.
4*s*(s - 1)*(s + 1)*(s + 2)**2
Let s(j) be the first derivative of -j**4/32 + 4*j**3 - 2205*j**2/16 - 2401*j/4 + 861. Factor s(q).
-(q - 49)**2*(q + 2)/8
Suppose 69*k - 66*k - 66 = 0. Let d be (k/2 - 3) + 1. Factor -d*b**2 - 50*b**4 + 104*b**3 + 161*b**2 - 48*b**3 + 104*b**3 + 32*b.
-2*b*(b - 4)*(5*b + 2)**2
Let t(i) be the third derivative of 11/60*i**6 + 79/90*i**5 - 191*i**2 - 1/45*i**7 - 5/504*i**8 + 0 + 4/3*i**3 + 14/9*i**4 + 0*i. Suppose t(m) = 0. What is m?
-2, -1, -2/5, 3
Let s(t) be the second derivative of 7*t**4/12 - 8*t**3 + 94*t**2 + 92*t. Let p(z) = -36*z**2 + 240*z - 939. Let a(q) = 4*p(q) + 21*s(q). Factor a(h).
3*(h - 8)**2
Let o(g) be the first derivative of -40/3*g**2 - 41 - 320/3*g - 5/9*g**3. Factor o(r).
-5*(r + 8)**2/3
Let m be ((-38)/152)/((-2)/(-8)). Let w be 1 - (-31 + 32)/(1/m). Factor 0*h**w - 8/3*h + 0 + 2/3*h**3.
2*h*(h - 2)*(h + 2)/3
Let x(i) be the second derivative of -i**5/4 - 499*i**4/12 - 6200*i**3/3 + 1250*i**2 + 1823*i. 