et v be (-285)/228 + 25/20. Determine p, given that -34/5*p**3 - 2/5*p**5 - 12/5*p - 14/5*p**4 + v - 34/5*p**2 = 0.
-3, -2, -1, 0
Let r(i) = -i**2 - 3*i + 30. Let n be r(-7). Factor -38*q**n - 2*q**2 + 96*q - 80 + 4*q**3 + 4*q**2.
4*(q - 5)*(q - 2)**2
Let u(n) = -n**2 - 4*n - 2. Let s be u(-4). Let b(k) = k**2 + 1. Let o be b(s). Factor -1 - 8*j - j**3 + o*j - 3*j**2 + 0*j**2.
-(j + 1)**3
Let c(j) be the first derivative of j**4 + 98*j**3/3 - 132*j**2 + 162*j - 3525. Factor c(o).
2*(o - 1)*(o + 27)*(2*o - 3)
Let n(i) = 3059*i + 73418. Let y be n(-24). Factor 3/4*a**3 - 1/2*a**y + 0 + 0*a - 1/4*a**4.
-a**2*(a - 2)*(a - 1)/4
Let z be 131058/1215 - 108 - (-37)/15. Let -10*b + z*b**2 + 8/3 = 0. Calculate b.
2/7, 4
Let q be ((-2)/4)/(-3 - 127/(-42)). Let r be 5/(-35) - (3 + 150/q). Factor 2820 - 2*c**r - 2820 - c**4 + 3*c**3.
-3*c**3*(c - 1)
Suppose 459*d**4 + 708*d**3 - 468*d**4 - 2685*d**2 + 1602*d - 456 + 840*d**2 = 0. What is d?
2/3, 1, 76
Let h(s) be the third derivative of 0*s**3 + 0*s**4 - 13/30*s**6 + 0*s + 148*s**2 + 0 - 9/10*s**5 + 1/105*s**7. Determine b, given that h(b) = 0.
-1, 0, 27
Let u(t) = 53*t**4 - 493*t**3 + 651*t**2 + 7245*t. Let y(m) = 30*m**4 - 282*m**3 + 372*m**2 + 4140*m. Let s(b) = 9*u(b) - 16*y(b). Factor s(x).
-3*x*(x - 23)*(x - 5)*(x + 3)
Let b be (1/5 - 13/(-35)) + (-123136)/(-8736). Factor -16*a + 8/3*a**3 - 48 + b*a**2 - 4/3*a**4.
-4*(a - 3)**2*(a + 2)**2/3
Let r be (-5 - (-424)/88)*(-19 - 3). Let l = 56 + -164/3. What is y in 2/3*y**r + 2/3 - 2/3*y - 2/3*y**5 - l*y**2 + 4/3*y**3 = 0?
-1, 1
Let a(w) be the second derivative of -w**5/6 + 41*w**4/12 - 8*w**3/3 - 101*w**2/2 + 81*w. Let d(b) be the first derivative of a(b). Factor d(z).
-2*(z - 8)*(5*z - 1)
Let s(n) be the third derivative of 0 - 1/588*n**8 + 0*n + 4/245*n**7 - 3/70*n**6 + 0*n**4 + 0*n**3 - 31*n**2 + 4/105*n**5. Find b such that s(b) = 0.
0, 1, 4
Suppose 2*t - 5*d = 0, 0 = 39*t - 43*t + 4*d. Factor -34*k**2 - 10 + 3*k**3 + 12*k + 10 + t*k + 11*k**3.
2*k*(k - 2)*(7*k - 3)
Let g(h) be the second derivative of -h**4/72 - 341*h**3/36 - 85*h**2/3 - 605*h + 1. Determine u, given that g(u) = 0.
-340, -1
Let h(p) = p**2 - 5*p - 2. Let w(s) = s - 3. Let x be w(-3). Let y(m) = -3*m**2 + 11*m + 5. Let r = -2038 + 2023. Let k(t) = r*h(t) + x*y(t). Factor k(a).
3*a*(a + 3)
Let t(w) be the first derivative of 1/16*w**3 + 1/160*w**5 + 5/8*w**2 - 1 + 32*w - 1/16*w**4. Let q(n) be the first derivative of t(n). Factor q(g).
(g - 5)*(g - 2)*(g + 1)/8
Let l(s) = 2*s**2 + 48*s - 6. Let j(r) = -2*r**2 - 58*r + 5. Let m(u) = -4*j(u) - 5*l(u). Factor m(x).
-2*(x - 1)*(x + 5)
Let c(u) = 8*u**3 - 5560*u**2 + 968835*u - 963294. Let h(g) = 2*g**3 - 1390*g**2 + 242209*g - 240824. Let j(q) = -3*c(q) + 11*h(q). Let j(l) = 0. Calculate l.
1, 347
Let h be ((-4)/1 - -1) + (-4)/(-4). Let o(v) = -v**2 - v - 1. Let c(t) = t**2 + 15*t - 9*t + 5 + 5*t**2 - 11. Let b(s) = h*o(s) - c(s). Factor b(d).
-4*(d - 1)*(d + 2)
Let p(j) be the first derivative of j**6/14 - 6*j**5/35 - 9*j**4/2 + 44*j**3/7 + 123*j**2/14 - 18*j + 9414. Find y such that p(y) = 0.
-6, -1, 1, 7
Let u(j) be the second derivative of -j**5/210 + 5*j**4/84 + 2*j**3/7 - 47*j**2 - 9*j. Let a(c) be the first derivative of u(c). Factor a(t).
-2*(t - 6)*(t + 1)/7
Let k(l) be the second derivative of l**4/42 - 190*l**3/21 + 9025*l**2/7 + 64*l. Factor k(h).
2*(h - 95)**2/7
What is d in -4116 - 714*d**2 - 3483*d + 3*d**4 - 1795*d + 658*d - 114*d**3 - 465*d**2 - 342*d**2 = 0?
-7, -2, 49
Let p(j) be the third derivative of -j**5/210 - 15*j**4/4 + 634*j**3/21 + 1579*j**2. Determine m so that p(m) = 0.
-317, 2
Let n(x) be the first derivative of -16807*x**5/5 + 34643*x**4/2 - 2772*x**3 + 1180*x**2/7 - 32*x/7 + 837. Solve n(d) = 0.
2/49, 4
Let 16*h**2 - 24/5*h + 0 - 54/5*h**3 + 2*h**4 = 0. What is h?
0, 2/5, 2, 3
Factor 218*q**2 - 4301*q + 921600 + 461*q - 214*q**2.
4*(q - 480)**2
Determine c, given that 118*c + 8/9*c**2 - 266/9 = 0.
-133, 1/4
Determine p, given that 150/11*p**2 - 756/11 + 6/11*p**4 + 6*p**3 - 234/11*p = 0.
-7, -3, 2
Let -7*v**2 + 50*v + 2*v**2 + v**2 + 55 + 5*v**2 - 6*v**2 = 0. What is v?
-1, 11
Let c(x) be the second derivative of -x**4/32 - 155*x**3/8 - 927*x**2/16 + 2523*x - 1. Factor c(m).
-3*(m + 1)*(m + 309)/8
Let t be 4/26 + (-1)/(117/(-9186)). Let y = -232/3 + t. Suppose y - 4/3*k**2 - 4/3*k**3 + 4/3*k = 0. Calculate k.
-1, 1
Let x(l) = -15*l - 128. Let n be x(-9). Let -11 + 11*w - 5 + 4 + 3*w**2 + 5*w - n*w**2 = 0. What is w?
1, 3
Factor 0*x**2 - 2/13*x**5 + 0 + 42/13*x**4 - 108/13*x**3 + 0*x.
-2*x**3*(x - 18)*(x - 3)/13
Let f(k) = 8*k**3 - 154*k**2 - 1092*k - 1728. Let o(d) = 31*d**3 - 618*d**2 - 4369*d - 6906. Let g(n) = -11*f(n) + 3*o(n). Solve g(c) = 0 for c.
-3, 38
Let u(p) be the second derivative of -p**6/10 + 21*p**5/20 + 7*p**4 + 10*p**3 - 31*p - 23. Factor u(i).
-3*i*(i - 10)*(i + 1)*(i + 2)
Let m(h) be the second derivative of h**4/6 - 5*h**3 + 56*h**2 + 1640*h + 2. Solve m(v) = 0 for v.
7, 8
Let h be 210/49 + (-4)/14 + 12/(-9). Let r(x) be the second derivative of -2*x**2 + 7/5*x**5 + 1/21*x**7 - h*x**4 + 16*x + 3*x**3 + 0 - 2/5*x**6. Factor r(m).
2*(m - 2)*(m - 1)**4
Let k(q) be the first derivative of q**8/336 + q**7/420 - q**6/72 - q**5/60 + 191*q**3/3 + 50. Let o(n) be the third derivative of k(n). Factor o(d).
d*(d - 1)*(d + 1)*(5*d + 2)
Let f(c) be the third derivative of -c**5/40 - 67*c**4/16 + 17*c**3 + c**2 + 375*c. Factor f(b).
-3*(b - 1)*(b + 68)/2
Let s be ((-5)/(-3))/(0 - 5/(-18)) - (10 + -6). Factor 10*o - 7 - 11/4*o**s - 1/4*o**3.
-(o - 2)*(o - 1)*(o + 14)/4
What is x in 93/5*x - 18*x**3 - 6*x**2 - 33/5*x**4 - 3/5*x**5 + 63/5 = 0?
-7, -3, -1, 1
Let h = 368 - 365. Suppose -12*p + 60 = h*p. Factor 2/3 + 2/3*c**5 - 4/3*c**3 + 2/3*c + 2/3*c**p - 4/3*c**2.
2*(c - 1)**2*(c + 1)**3/3
Factor 0 + 1/11*z**5 - 6/11*z**3 + 1/11*z**4 + 0*z**2 + 0*z.
z**3*(z - 2)*(z + 3)/11
Suppose 366 = 14*m - 11*m. Let j = m + -112. What is f in -5*f**2 - 5*f + 6*f - 7*f + j + f = 0?
-2, 1
Let r = 13233 + -13191. Let l(x) be the first derivative of 61/3*x**3 + 30 + 36*x + 7/2*x**4 + 1/5*x**5 + r*x**2. Factor l(k).
(k + 1)**2*(k + 6)**2
Factor -73/4*i + 1/4*i**3 - 105 + 3*i**2.
(i - 7)*(i + 4)*(i + 15)/4
Let k = 139 + -136. Determine d, given that -14*d**3 - 10*d**2 + 24*d**3 + 20*d + 40 - 15*d**k = 0.
-2, 2
Suppose 0 = s - 0*s - 2*s. Let k be (21/2)/(-7) + 145/(-350)*-5. Factor -5/7*i**2 + 2/7*i + k*i**3 - 1/7*i**4 + s.
-i*(i - 2)*(i - 1)**2/7
Let l(d) be the first derivative of -d**5/5 - 6*d**4 - 21*d**3 + 1716. Let l(w) = 0. Calculate w.
-21, -3, 0
Let a be 22/6 + -1 - (-38)/(-57). Factor -21*n - 27*n + 5 + 0*n**2 + n**a + 42*n.
(n - 5)*(n - 1)
Factor 873*v**2 - 5*v**2 + 4*v**3 + 4020*v + 13659*v + 25703*v + 4138*v + 46656.
4*(v + 1)*(v + 108)**2
Let g(v) = -8 + 5 - 7*v - v**3 - 8*v - 8 + 17*v**2. Let s be g(16). What is p in 8*p**5 - 4*p**5 - 3*p**3 + p**2 - s*p**5 - 36*p**4 + 39*p**4 = 0?
0, 1
Suppose 340/7*h**2 + 9/7 - 129/7*h + 128/7*h**3 = 0. Calculate h.
-3, 3/32, 1/4
Suppose 8*x = 22*x + 294. Let a be 96/36*(-3 - 0)/x. Factor -2/21 - a*z - 4/7*z**2 - 2/21*z**4 - 8/21*z**3.
-2*(z + 1)**4/21
Let j(b) be the first derivative of 2*b**3/45 + 3968*b**2/15 + 7872512*b/15 + 8593. Suppose j(p) = 0. Calculate p.
-1984
Let d = -11 - -19. Suppose 2*l - 50 = -d*l. Factor 6*n**4 - n**2 - n**2 - n**3 + 3*n**3 - 9*n + n**l - 4 + 6*n**3.
(n - 1)*(n + 1)**3*(n + 4)
Suppose 5*v + 5 = 0, 2*z + 3*v - 1 = -0*z. Factor -23291*a + 20*a**z - 2*a**5 - 4*a**4 - 2*a**5 + 23299*a + 12*a**3.
-4*a*(a - 2)*(a + 1)**3
Let v(g) be the third derivative of g**6/280 - 33*g**5/140 - g**4/56 + 33*g**3/14 - 6*g**2 + 243*g - 1. Find f such that v(f) = 0.
-1, 1, 33
Factor -300 - 87*a**2 + 7257*a**3 - 188*a - 124*a - 7260*a**3.
-3*(a + 2)**2*(a + 25)
Suppose 12*p - 38 + 2 = 0. Factor -14*d**p - 54*d**5 - 12*d - 26*d**2 + 28*d**5 + 2*d**4 + 28*d**5.
2*d*(d - 3)*(d + 1)**2*(d + 2)
Suppose 0*t + 2*r = t - 8, 0 = 4*t - r - 53. Let h be (t - 14)/(5/(-1)). Factor 1/2*j**5 + j**4 - 2*j**3 + h - j**2 + 3/2*j.
j*(j - 1)**2*(j + 1)*(j + 3)/2
Let r = 890426/53 - 4556244228/271201. Let g = -2/301 + r. Suppose -10/17*o**4 + 2/17*o**2 - 2/17*o + 6/17*o**3 + g*o**5 + 0 = 0. What is o?
-1/2, 0, 1
Let q be (13*40/130)/(0 + 1). Let j(n) be the third derivative of