, 1
Let b(v) be the second derivative of 4/33*v**4 - 1/3*v**3 - 35*v + 3/11*v**2 + 2/55*v**5 + 0. Suppose b(w) = 0. What is w?
-3, 1/2
Suppose -99 = -77*k - 195*k + 717. Let c(j) be the second derivative of -3/4*j**5 - 55/12*j**4 - 20/3*j**k + 10*j**2 + 8*j + 0. Factor c(h).
-5*(h + 2)**2*(3*h - 1)
Let a(u) be the first derivative of 2*u**5/65 + 9*u**4/26 + 16*u**3/13 + 20*u**2/13 + 3141. Factor a(n).
2*n*(n + 2)**2*(n + 5)/13
Let b(q) be the second derivative of q**7/14 - q**6/5 - 6*q**5/5 + 1239*q. Determine c, given that b(c) = 0.
-2, 0, 4
Let a be (-1)/8*(-3984)/1494. Find k, given that 31/3 - a*k**2 + 10*k = 0.
-1, 31
Suppose -3/4*v**5 - 33/4*v**2 + 0 + 9/4*v**4 + 9/2*v + 9/4*v**3 = 0. What is v?
-2, 0, 1, 3
Let r = 1/111 - 577/2442. Let k = r + 13/33. Find y such that -k*y**2 + 0 - 1/3*y = 0.
-2, 0
Let r(i) be the third derivative of -i**5/270 - 161*i**4/108 - 1459*i**2. Solve r(u) = 0 for u.
-161, 0
Let t(c) = -c + 16. Let q be t(8). Let i(u) = -6*u + 69. Let p be i(11). Factor -5*y**2 + 10 + 5*y**4 - 13*y**p + q*y**3 + 5*y**5 - 10.
5*y**2*(y - 1)*(y + 1)**2
Let m be ((-3773)/(-6468))/((-7)/(-2)). Solve -1/6*d**5 + m*d**3 - 2/3*d**2 + 0 + 2/3*d**4 + 0*d = 0 for d.
-1, 0, 1, 4
Let l be 17 + ((-956)/16 - -44). Factor 3/4*b**2 + 0 + 1/4*b**4 + 9/4*b - l*b**3.
b*(b - 3)**2*(b + 1)/4
Let g(l) be the first derivative of 40 + 5/12*l**3 - 1/10*l**5 + 1/16*l**4 + 1/4*l**2 + 0*l. Let g(h) = 0. What is h?
-1, -1/2, 0, 2
Let v(j) be the third derivative of 0*j - 15/28*j**4 + 0 + 1/210*j**5 - 3/7*j**3 - 159*j**2 + 1/84*j**6. Factor v(d).
2*(d - 3)*(d + 3)*(5*d + 1)/7
Factor 5773531*d**3 + 135*d - 5773406*d**3 + 2*d**4 - 7*d**4 + 265*d**2.
-5*d*(d - 27)*(d + 1)**2
Determine i, given that 0*i**2 + 8*i**4 + 0*i + 5/4*i**5 + 11*i**3 + 0 = 0.
-22/5, -2, 0
Find z such that 2864*z - 98235 - 13*z**2 + 2148859 + 14*z**2 = 0.
-1432
Suppose -23*c + 21*c + 5 = 3*b, -c = 3*b - 1. Determine i, given that -28*i**3 - 8 - 48*i - c*i**4 + 8 + 96*i**2 - 160*i**2 = 0.
-3, -2, 0
Let s(y) = -189*y + 567. Let z be s(3). Let t(n) be the third derivative of n**2 - 1/2*n**3 + 0*n**4 + z*n + 1/80*n**5 + 0. Factor t(q).
3*(q - 2)*(q + 2)/4
Factor -62*s**4 - 3*s**2 + 33*s**2 + 63*s**4 - s**3 - 10*s**3.
s**2*(s - 6)*(s - 5)
Suppose 169 = 5*j - 2*v + 152, -3*j - v = -8. Factor 0 + 0*s + 3/8*s**4 + 3/4*s**2 - 9/8*s**j.
3*s**2*(s - 2)*(s - 1)/8
Let k = -67 - -70. Let u be (-7)/(-2) - k/6. Find h such that h**3 - h**5 - 7*h**4 + 8*h**4 + 7*h**2 - u - 4*h**4 - 1 = 0.
-2, -1, 1
Let l(j) be the third derivative of -j**10/756000 + j**9/30240 - j**8/11200 - 11*j**5/4 + 2*j**2 + 3. Let n(v) be the third derivative of l(v). Factor n(k).
-k**2*(k - 9)*(k - 1)/5
Let x(y) be the second derivative of -y**6/240 - y**5/20 + y**4/48 + y**3/2 - 20*y**2 - 24*y - 2. Let j(q) be the first derivative of x(q). Factor j(m).
-(m - 1)*(m + 1)*(m + 6)/2
Let f be ((-2)/(-5))/(50/(-750)). Let v(g) = g**3 + 9*g**2 + 20*g + 7. Let p(j) = j**3 + 9*j**2 + 20*j + 6. Let m(o) = f*v(o) + 5*p(o). Factor m(u).
-(u + 1)*(u + 2)*(u + 6)
Let s(g) be the second derivative of 30*g + 0*g**3 + 9/80*g**5 - 1/40*g**6 + 0*g**2 - 1/168*g**7 + 0 - 5/48*g**4. Factor s(n).
-n**2*(n - 1)**2*(n + 5)/4
Factor 3*t + 110/7 + 1/7*t**2.
(t + 10)*(t + 11)/7
Let w be 44/18 - (-51)/153. Let k(f) be the first derivative of -1/18*f**4 - 13 - w*f**2 + 20/27*f**3 + 0*f. Suppose k(n) = 0. Calculate n.
0, 5
Suppose 100 - 240 = 10*r. Let t be (-6)/9*(r + -1). Factor -17*c**2 - 3*c**3 + 16*c**4 + 6*c**2 - 2*c + t*c**2 + 35*c**3.
c*(c + 2)*(4*c - 1)*(4*c + 1)
Let z = 5720 + -5716. Let u(r) = r**2 + r. Let i(s) be the second derivative of 5*s**4/12 + s**3/2 - s**2 - s. Let q(d) = z*u(d) - i(d). Factor q(l).
-(l - 2)*(l + 1)
Let k = -761/12 - -257/4. Factor 0 + 4/3*o**2 + k*o**3 + 2/3*o + 1/6*o**4.
o*(o + 1)*(o + 2)**2/6
Let i(d) be the third derivative of -10/21*d**4 - 2*d**2 - 1/15*d**5 + 0 - 128*d + 2/7*d**3. Factor i(s).
-4*(s + 3)*(7*s - 1)/7
Suppose -4*u - 4*v - 32 = 0, v - 5*v = 32. Let q be (-10)/7*(-28)/52. Suppose q*r - 2/13*r**2 + u = 0. What is r?
0, 5
Let f = -35 + 97. Let m(q) be the first derivative of 50*q + q**4 + f*q - 18 + 54*q**2 - 4*q + 12*q**3. Factor m(t).
4*(t + 3)**3
Let -11/2*n**4 + 0*n + 0 + 3/2*n**5 - 6*n**2 - 20*n**3 = 0. Calculate n.
-2, -1/3, 0, 6
Suppose 5*o - 23 = 57. Suppose 0 = 5*g + 5*u + 5, g + 0*u + 4*u + o = 0. Factor 5 - g*y + 11 - 32*y - 10*y**2.
-2*(y + 4)*(5*y - 2)
Let q(m) be the second derivative of m**6/6 + 295*m**5 + 867295*m**4/6 - 581150*m**3 + 1746405*m**2/2 - 67*m + 1. Factor q(h).
5*(h - 1)**2*(h + 591)**2
Suppose -304 = -15*q - 4. Solve -2 + 64*u**2 - 18 - q*u - 69*u**2 = 0 for u.
-2
Let w(m) be the third derivative of m**6/720 + m**5/72 - 61*m**4/144 + 55*m**3/36 - 14*m**2 - 29. Factor w(o).
(o - 5)*(o - 1)*(o + 11)/6
Let i(d) be the third derivative of -7*d**6/40 + 9*d**5/20 + 5*d**4 - 6*d**3 + 301*d**2 - 2*d. Determine c so that i(c) = 0.
-2, 2/7, 3
Let q be 2/12 + -10 + 638/(-352)*-8. Factor -q*d + 0 - 1/3*d**2.
-d*(d + 14)/3
Let a = 208510/312759 + -4/312759. Suppose 5/2*d**3 + 8/3*d**2 + 1/2*d + a*d**4 - 1/3 = 0. What is d?
-2, -1, 1/4
Suppose -216*h + 3150 = 1359*h. Factor -4*q**h + 0*q + 0 + 4/3*q**4 + 8/3*q**3.
4*q**2*(q - 1)*(q + 3)/3
Let g be (-15)/330 - (-9514)/3124. Factor 39/4*s**2 - 15/4 + 33/4*s - 9/4*s**g.
-3*(s - 5)*(s + 1)*(3*s - 1)/4
Let b = 32 + -27. Let g(k) be the first derivative of 7 - 13*k**5 + b*k**6 + 1 + 10*k**3 - 5*k + 5*k**4 - 5*k**2 + 3. What is w in g(w) = 0?
-1/2, -1/3, 1
Determine j so that -8/3*j**3 + 27*j**2 + 8 - 202/3*j = 0.
1/8, 4, 6
Let q = 33/4870 + 7239/9740. Factor 0 + 3*u - 15/4*u**2 + q*u**3.
3*u*(u - 4)*(u - 1)/4
Let h(b) = -b**2 + 36*b - 31. Let i be h(35). Suppose -4*v + i*n = -32, -v - 5*n - 13 - 9 = 0. Factor 3/2*k + v*k**2 + 0 + 3/2*k**3.
3*k*(k + 1)**2/2
Let x(j) be the second derivative of -j**5/80 - 113*j**4/48 - 39*j**3 + 9*j - 73. What is g in x(g) = 0?
-104, -9, 0
Let y(l) be the third derivative of 1/20*l**6 - 1/4*l**4 + 1/20*l**5 + 0*l**3 - 1/70*l**7 + l**2 + 0*l - 7. Factor y(w).
-3*w*(w - 2)*(w - 1)*(w + 1)
Let x(l) be the second derivative of 0 - 110*l + 1/5*l**5 + 1/5*l**4 - 6/5*l**3 + 0*l**2 + 2/75*l**6. Factor x(q).
4*q*(q - 1)*(q + 3)**2/5
Let v be 1 + 2 + 170 - 6. Determine k so that 10 - 22*k + 67 + 23 + v*k + 30*k**2 = 0.
-4, -5/6
Suppose 1611*g - 613*g - 4*g**3 + 112*g**2 - 505*g + 1520 - 1257*g = 0. Calculate g.
4, 5, 19
Let g be 10/2 - ((-1976)/(-40) + 7). Let h = -251/5 - g. Find x such that 9/5*x + h + 3/5*x**2 = 0.
-2, -1
Let r = -103731 - -518656/5. Suppose r*n**5 + 0 + 1/5*n**4 - 1/5*n**3 + 0*n - 1/5*n**2 = 0. What is n?
-1, 0, 1
Determine f, given that 46977*f - 51597*f + 4356 - 20*f**2 - 4*f**3 + 288*f**2 = 0.
1, 33
Let q(u) be the second derivative of -115*u**4/4 - 56*u**3 + 9*u**2/2 + 2548*u. Determine h, given that q(h) = 0.
-1, 3/115
Let c be 4 - (-12 - -8) - 2*2. Determine d, given that -214*d - 3*d**2 + 232*d + 4 - c = 0.
0, 6
Determine k so that 19/2*k**4 - 35*k**3 - 44*k**2 + 0*k + 0 + 1/2*k**5 = 0.
-22, -1, 0, 4
Factor 1/3*m**3 - m**2 + 28 - 40/3*m.
(m - 7)*(m - 2)*(m + 6)/3
Let o(t) = -12*t**4 - 15*t**3 + 143*t**2 - 235*t - 5. Let s(z) = 5*z**4 + 7*z**3 - 72*z**2 + 118*z + 2. Let p(c) = -2*o(c) - 5*s(c). Solve p(w) = 0.
-12, 0, 2, 5
Suppose 49 = 4*p - 5*b, -5*p + 0*b = -2*b - 74. Determine i so that -7 + 11*i**4 - 5*i**4 - p*i**2 - 13*i - 38*i**3 + 43*i + 4*i**5 + 17*i**4 + 4*i = 0.
-7, -1, 1/4, 1
Let k(i) be the first derivative of 5*i**4/4 - 60*i**3 + 870*i**2 - 2800*i + 144. Factor k(z).
5*(z - 20)*(z - 14)*(z - 2)
Suppose 3*x - 2*g + 2 = 2*g, 5*x = g + 8. Suppose -4*z - x*d = -8, 2*z - 1 = -2*d + 1. Factor 2*w**2 + 6*w**5 + 3*w**z + 11*w**5 - 18*w**5.
-w**2*(w - 2)*(w + 1)**2
Let s = 22877/2 + -11438. Let y(m) be the second derivative of 0 + 0*m**2 + s*m**3 + 15*m - 3/20*m**5 - 3/8*m**4. What is v in y(v) = 0?
-2, 0, 1/2
Let w(n) = 354*n**2 + 348*n + 7373. Let j(k) = 85*k**2 + 87*k + 1844. Let g(p) = 25*j(p) - 6*w(p). Factor g(c).
(c + 38)*(c + 49)
Let y(f) be the second derivative of f**4/24 - 31*f**3/3 + 61*f**2 - 4038*f. Factor y(s).
(s - 122)*(s - 2)/2
Suppose 19 + 71 - 76986*g**3 - 6*g**2 + 76985*g**3 + 37*g = 0. Calculate g.
-9, -2, 5
Let x = -316 - -318. Find t, given that -20*t + 243*t**2 - 123