 Calculate x.
-1, 0, 2/7
Suppose -5*r = -2*s - 506, r - 3*s - 96 = -0*r. Let u = -100 + r. What is d in 2/3*d + 4/3 - 2*d**u = 0?
-2/3, 1
Suppose 0 = -4*i - 3*q + 20, 0 = -3*q + 18 - 6. Solve 3/2*y**i - 3/4 - 3/8*y**5 - 3/4*y**4 + 3/4*y**3 - 3/8*y = 0 for y.
-2, -1, 1
Let v = -2596/963 + 336/107. Let w(z) be the second derivative of -1/45*z**5 + v*z**2 - 10/27*z**3 + 27*z + 4/27*z**4 + 0. Factor w(n).
-4*(n - 2)*(n - 1)**2/9
Let s = -5321/6 - -1775/2. Let i(w) be the first derivative of 4*w + 2 + s*w**3 + 3*w**2. Factor i(j).
2*(j + 1)*(j + 2)
Let l(t) be the third derivative of -t**6/180 + 7*t**5/5 - 203*t**4/12 + 484*t**3/9 - 11*t**2 - 30. Suppose l(c) = 0. Calculate c.
1, 4, 121
Factor 49127 + 431*x - 336*x**2 + 172*x**2 + 116761 + 721*x + 166*x**2.
2*(x + 288)**2
Factor -2/3*k**2 + 54*k - 2440/3.
-2*(k - 61)*(k - 20)/3
Let z(q) be the second derivative of -2*q**7/189 + 2*q**6/45 - q**5/45 - q**4/9 + 4*q**3/27 + 780*q + 1. Let z(r) = 0. Calculate r.
-1, 0, 1, 2
Let u(d) = 4*d + 122. Suppose -20*r - 91 - 509 = 0. Let q be u(r). Factor 0 - 2/3*m**4 + 4/3*m**3 - 2/3*m**q + 0*m.
-2*m**2*(m - 1)**2/3
Let d be (140/(-160))/(1/(-8)). Factor c**2 - 136*c**3 + 62*c**2 - 10*c**4 - d*c**2.
-2*c**2*(c + 14)*(5*c - 2)
Factor 4128/5*n - 4/5*n**3 - 8384/5 - 492/5*n**2.
-4*(n - 4)**2*(n + 131)/5
Let l = 4/10271 + 41024/154065. Let q(h) be the second derivative of 9*h + 0 + 1/50*h**5 + 0*h**2 - 2/15*h**4 + l*h**3. Factor q(i).
2*i*(i - 2)**2/5
Find s, given that 81 - 3/8*s**4 - 153/2*s + 21/8*s**3 + 57/4*s**2 = 0.
-6, 2, 9
Let r(c) = 17*c + 86. Let g be r(-6). Let v be (-9)/(-42)*g/(-12). Solve -4/7 - 6/7*j**2 + 10/7*j + 2/7*j**4 - v*j**3 = 0 for j.
-2, 1
Suppose 11*h - 3 - 41 = 0. Factor 34*j - 3*j**2 + 5*j**2 - 7826*j**4 + 7824*j**h - 10*j**3 + 0*j - 24.
-2*(j - 1)**2*(j + 3)*(j + 4)
Factor -648/17 + 78/17*j - 2/17*j**2.
-2*(j - 27)*(j - 12)/17
Suppose -5*c = a - 662, 2*a - 11*c = -12*c + 1297. Factor -p**2 + 108*p + 1061 + 1044 + 3*p**2 - a.
2*(p + 27)**2
Solve -h**2 + 368/5*h + 148/5 = 0.
-2/5, 74
Let t(s) = -21*s**3 + 94*s**2 - 98*s + 5. Let m(g) = 4*g**3 + g**2 - 1. Let q(h) = 10*m(h) + 2*t(h). Let q(p) = 0. What is p?
0, 1, 98
Factor 0 - 2/19*j**4 + 2300/19*j**3 + 0*j - 661250/19*j**2.
-2*j**2*(j - 575)**2/19
Let d(j) be the first derivative of 5*j**3/3 - 445*j**2/2 + 440*j - 121. Factor d(q).
5*(q - 88)*(q - 1)
Let l be 114/10*((-4844)/(-336) + -14) + -1. Let 1/4*y**3 + 3/2*y**2 + 2 - l*y = 0. Calculate y.
-8, 1
Suppose 0 = 17*x - 53 + 19. Let w(j) = -2*j**3 - 27*j**2 - 27*j - 2. Let f(r) = 9*r**2 + 1 + r + r**3 + 0*r**2 + 8*r. Let l(h) = x*w(h) + 7*f(h). Factor l(v).
3*(v + 1)**3
Let i(f) be the third derivative of -f**7/42 - 388*f**6/3 - 301088*f**5 - 1168221440*f**4/3 - 906539837440*f**3/3 + 2268*f**2. Suppose i(r) = 0. Calculate r.
-776
Let w(l) be the third derivative of -l**6/160 - 7*l**5/160 - l**4/8 - 6*l**3 - 61*l**2. Let t(j) be the first derivative of w(j). Suppose t(a) = 0. What is a?
-4/3, -1
Let b be (-4)/14 - 529/(-161). Let z(r) = -5*r**2 - 15*r - 10. Let p(l) = 24*l**2 + 74*l + 50. Let i(j) = b*p(j) + 14*z(j). Factor i(y).
2*(y + 1)*(y + 5)
Suppose 34653 = -17*j + 1180. Let n = -1967 - j. Let 0 + 0*x - 1/9*x**4 + 5/9*x**3 - 2/3*x**n = 0. What is x?
0, 2, 3
Let x(a) be the second derivative of 3/10*a**5 + 1/3*a**4 - 1/42*a**7 - 5/6*a**3 + 0*a**2 - 55*a - 1 - 2/15*a**6. Find k, given that x(k) = 0.
-5, -1, 0, 1
Suppose 11*o = -59*o - 162*o + 25*o. Factor 0 + 32/7*i**3 - 2/7*i + o*i**2.
2*i*(4*i - 1)*(4*i + 1)/7
Let n = -1054321 + 5271608/5. Factor -54/5*y**3 + 72*y**2 + 225 - 210*y + n*y**4.
3*(y - 5)**3*(y - 3)/5
Suppose 0 = 3*y + 2*y - 3*v - 37, -v - 15 = -2*y. Let o be (0 - (-6)/y)/(1/4). Factor 19*a**4 - 5*a**2 - 4*a**4 - 10*a**o - 3 + 3.
5*a**2*(a - 1)*(3*a + 1)
Let i(z) be the first derivative of -z**8/560 + z**7/70 - 3*z**6/100 - 97*z**2/2 - 24. Let u(a) be the second derivative of i(a). Factor u(t).
-3*t**3*(t - 3)*(t - 2)/5
Let z(k) be the third derivative of 0 + 1/840*k**8 + 0*k + 49*k**2 + 2/15*k**3 + 1/75*k**5 - 4/525*k**7 + 1/75*k**6 - 1/12*k**4. Suppose z(n) = 0. Calculate n.
-1, 1, 2
Let w(v) = 102*v**3 + 6*v**2 - 17*v + 30. Let z be w(2). Suppose 0 = z*p - 850*p + 42. Suppose 0*u + 0 + 3/5*u**p - 6/5*u**2 + 3/5*u**4 = 0. What is u?
-2, 0, 1
Let c(q) be the second derivative of -q**7/18 - q**6/18 + q**5/30 - 47*q - 3. Suppose c(d) = 0. What is d?
-1, 0, 2/7
Let a(i) be the third derivative of -17/20*i**5 - 40*i**2 + 3/4*i**4 + 1/8*i**6 + 0*i**3 + 0 + 0*i. Factor a(g).
3*g*(g - 3)*(5*g - 2)
Let j(o) be the first derivative of 1/3*o**6 + 0*o + 4*o**2 + 6/5*o**5 - 2*o**3 - 32 - 5/2*o**4. Factor j(g).
2*g*(g - 1)**2*(g + 1)*(g + 4)
Let i(c) = c**3 + 12*c**2 + 14*c + 43. Let k be i(-11). Solve -36 - 33 - k*x + 4*x**2 + 63 - 5*x**2 + 3*x = 0 for x.
-6, -1
Let t = -4/7517 + 248221/300680. Let j = t + 1609/280. Solve -4/7 + 48/7*y**3 - 30/7*y - j*y**2 + 32/7*y**4 = 0 for y.
-2, -1/4, 1
Solve 392 - 130/3*f**2 + 50/3*f**3 - 448/3*f = 0.
-3, 14/5
Let m be (-5 + 2)*(6 + (-4 - 3)). Suppose -5*v**m + 5*v**4 - 4*v**5 + 6*v**4 - 11*v**4 + 9*v**5 = 0. What is v?
-1, 0, 1
Determine o so that -1262*o - 3*o**2 - 3*o**2 + 3422*o + 5*o**2 + 5*o**2 + 291600 = 0.
-270
Suppose -30*v**2 + 180*v**4 - 12891*v**5 + 12856*v**5 + 6*v**3 + 179*v**3 = 0. Calculate v.
-1, 0, 1/7, 6
Let b = -39/5 - -283/35. Let k = 3105694/7 + -443666. Factor 128/7 + k*z + b*z**2.
2*(z + 8)**2/7
Let p(k) be the third derivative of -9*k**6/40 - 41*k**5/20 - 17*k**4/4 + 12*k**3 + 2017*k**2. Solve p(l) = 0 for l.
-3, -2, 4/9
Let w(y) be the second derivative of -y**6/45 + 77*y**5/90 - 124*y**4/27 + 44*y**3/9 + 19*y + 2. Determine o, given that w(o) = 0.
0, 2/3, 3, 22
Let u(m) be the first derivative of m**6/66 - 181*m**5/55 + 6407*m**4/22 - 147330*m**3/11 + 7405425*m**2/22 - 48205125*m/11 + 749. Let u(w) = 0. Calculate w.
23, 45
Let n(p) be the second derivative of -49/36*p**3 + 1/120*p**5 - 1/72*p**4 + 49/12*p**2 - 265*p + 0. Factor n(u).
(u - 7)*(u - 1)*(u + 7)/6
Let o(u) = -u**3 - 278*u**2 - 799*u + 7153. Let r be o(-275). Factor -152/5*n**2 + 2/5*n**r - 5476/5 + 3034/5*n.
2*(n - 37)**2*(n - 2)/5
Determine d so that 50*d - 4*d + 42*d**2 - 43*d**2 - 3*d - 2*d = 0.
0, 41
Suppose -7*w - 2*t = -3*w + 10, 4*w - 4*t = 8. Let q be 6*(0 + w/(-2)). Factor 272 - q*v**2 - 272 + 3*v**3.
3*v**2*(v - 1)
Factor 16*z**3 + 12*z**2 - 32*z - 71*z**3 + 18*z**3 + 21*z**3 + 15*z**3.
-z*(z - 8)*(z - 4)
Let x(d) be the second derivative of 5*d**7/42 + d**6 - 2*d**5 - 5*d**4/2 + 35*d**3/6 - 11*d - 130. Factor x(q).
5*q*(q - 1)**2*(q + 1)*(q + 7)
Let m(n) be the first derivative of -3*n**5/20 + 209*n**4/16 + 283*n**3/12 + 71*n**2/8 - 7711. Let m(o) = 0. What is o?
-1, -1/3, 0, 71
Let v(q) = 54*q**2 + 191*q. Let r(b) = -21*b**2 - 95*b. Let f(m) = 5*r(m) + 2*v(m). Factor f(p).
3*p*(p - 31)
Let z be (-22)/(-44)*(-30)/(-20). Let f(m) be the first derivative of 0*m - 22 - z*m**2 - 3/8*m**4 - m**3. Factor f(n).
-3*n*(n + 1)**2/2
Suppose -140/3*q**2 - 5/3*q**3 + 1100/3*q + 38720/3 = 0. Calculate q.
-22, 16
Let w = 100 + -100. Suppose -96 = 2*b - 3*b. Determine s so that b + w*s - 3*s**2 - 96 - 3*s = 0.
-1, 0
Let b(n) be the second derivative of 96*n**2 + 1/30*n**5 - n + 64/3*n**3 + 13/9*n**4 - 93. Suppose b(g) = 0. Calculate g.
-12, -2
Let p(l) = l**3 + 4*l**2 + 4*l + 3. Let g be p(-2). Suppose 0 = 4*f - b - 9, 2*f + b - 2*b = 3. Factor -f*u - 3*u**2 - g*u - 2*u + 2*u - 3.
-3*(u + 1)**2
Let w(k) = -4*k**4 - 32*k**3 + 26*k**2 - 10*k + 10. Let c(x) = -5*x**4 - 32*x**3 + 25*x**2 - 12*x + 12. Let d(p) = -5*c(p) + 6*w(p). Factor d(n).
n**2*(n - 31)*(n - 1)
Let i(k) be the second derivative of -k**6/150 - k**5/4 - 19*k**4/60 + 39*k**3/10 - 36*k**2/5 + 43*k - 11. Factor i(p).
-(p - 1)**2*(p + 3)*(p + 24)/5
Let c(q) be the first derivative of 1/20*q**5 - 3 + 1/12*q**4 + 0*q**2 + 4*q - 1/3*q**3. Let p(x) be the first derivative of c(x). Find u, given that p(u) = 0.
-2, 0, 1
Let c be 19/(4 - (-14)/(-4)). Let h = c + -8. Find n such that h*n**2 - 2 - 16*n**2 - 15*n**2 + 3*n = 0.
1, 2
Suppose 3*k + x + 4 = 0, 168*x + 20 = 5*k + 163*x. Factor 2/9*q**5 - 4/9*q**4 - 2/3*q**3 + k*q**2 + 0 + 0*q.
2*q**3*(q - 3)*(q + 1)/9
Let a(w) = 14*w**3 + 3*w**2 + w - 2. Let f be a(1). Let o(t) = -t + 25. Let u be o(f). Solve -8