. Calculate n.
-3/2, 1
Suppose 137/5*s - 22 - 28/5*s**2 + 1/5*s**3 = 0. What is s?
1, 5, 22
Let q be (-7)/(23 + 5)*36/(-63). Let 22/7*b + 3 + q*b**2 = 0. Calculate b.
-21, -1
Suppose 14/19*c**4 + 1008/19 - 2536/19*c - 830/19*c**3 - 3236/19*c**2 = 0. Calculate c.
-2, 2/7, 63
What is g in -8786*g - 1608*g - 889524*g**3 - 5746*g - 67195*g**3 + 144674*g**3 + 40 + 1632150*g**2 = 0?
2/403, 2
Let s(w) be the first derivative of w**5/105 + 5*w**4/42 + 8*w**3/21 + 76*w**2 + 138. Let p(b) be the second derivative of s(b). What is c in p(c) = 0?
-4, -1
Let k(l) = -16*l + 68. Let i be k(4). What is j in 21 - 13 + i*j**2 - 15*j + 3*j = 0?
1, 2
Let y(o) be the second derivative of 13*o**6/105 - 3*o**5/7 - 26*o**4/21 + 40*o**3/7 - 2*o - 252. Let y(c) = 0. What is c?
-2, 0, 2, 30/13
Let b be 0 - ((7 - 14) + 17). Let s be -8 - (-12 + (b - -14)). Factor 4/9 + s*n - 1/9*n**2.
-(n - 2)*(n + 2)/9
Let -17*c**2 - 2*c + 0*c - 23*c**2 + 19*c + 39*c**2 = 0. What is c?
0, 17
Find m such that 0*m - 3*m + 868*m**2 + 16*m + 18 - 866*m**2 = 0.
-9/2, -2
Suppose 0*b - 22 = -2*r - 2*b, -r + 4*b + 6 = 0. Let n be ((-12)/r)/((-5)/(200/12)). Factor q - 5*q**2 - 4*q + n*q**2.
-q*(q + 3)
Let u be (-6 - -20)/(-1) - -21. Let t(b) be the third derivative of 0 + 1/525*b**u + 0*b**4 + 0*b**3 - 5*b**2 + 0*b - 1/100*b**6 + 1/75*b**5. Solve t(h) = 0.
0, 1, 2
Let z(k) be the third derivative of -k**8/952 - 41*k**7/1785 - 61*k**6/510 + 46*k**5/255 + 134*k**4/51 + 96*k**3/17 + 6*k**2 - 5*k. Solve z(f) = 0 for f.
-9, -4, -2, -2/3, 2
Let r(w) be the third derivative of w**6/160 - 87*w**5/80 + 43*w**4/16 - 8*w**2 - 390*w. Solve r(f) = 0.
0, 1, 86
Let w = 29564 + -29562. Let -44*k**w + 74/3*k**3 - 5*k**4 + 1/3*k**5 + 24*k + 0 = 0. Calculate k.
0, 1, 2, 6
Let t(g) be the third derivative of -g**6/540 - 257*g**5/270 - 16891*g**4/108 - 16129*g**3/9 - 2577*g**2. What is p in t(p) = 0?
-127, -3
Let k(b) = 2*b**4 - 8*b**3 - 121*b**2 - 129*b. Let m(w) = -2*w**4 + 6*w**3 + 120*w**2 + 128*w. Let p(h) = -8*k(h) - 9*m(h). Suppose p(u) = 0. Calculate u.
-10, -1, 0, 6
Let w(s) be the third derivative of -s**6/6 + 54*s**5/5 + 113*s**4/6 - 308*s**3 - 1996*s**2. What is c in w(c) = 0?
-2, 7/5, 33
Determine l so that 0 + 961*l**5 - 9/4*l - 93*l**4 - 3835/4*l**3 + 93*l**2 = 0.
-1, 0, 3/62, 1
Let r(k) = -k**3 - 17*k**2 - 35*k - 1385. Let i be r(-19). Factor 0 + 0*w**2 + 1/2*w**5 + 0*w**4 - i*w**3 + 0*w.
w**3*(w - 2)*(w + 2)/2
Let l = 10034/39015 - -3/1445. Let n(i) be the first derivative of -5/18*i**2 - 24 + l*i**3 + 1/18*i**4 - 4/9*i. Factor n(v).
(v - 1)*(v + 4)*(2*v + 1)/9
Suppose 0 = -2*v + 3*v. Let s be (-65)/(-35)*1 - 3/(-21). Find u such that 6*u**2 + 0*u + 0*u**s - 3*u**3 + v*u - 3*u = 0.
0, 1
Let j(m) be the third derivative of -4*m**5/15 + 643*m**4/6 + 322*m**3/3 - m**2 - 19*m. Let j(s) = 0. Calculate s.
-1/4, 161
Let s(q) = -55*q**3 + 5900*q**2 + 5850*q - 70. Let n(h) = 3*h**3 - 347*h**2 - 344*h + 4. Let o(d) = -35*n(d) - 2*s(d). Factor o(c).
5*c*(c + 1)*(c + 68)
Let o(c) be the third derivative of -c**5/120 - 85*c**4/24 - 167*c**3/4 + 12*c**2 - 188. Suppose o(r) = 0. What is r?
-167, -3
Let i(t) be the first derivative of -2*t**6/3 - 104*t**5/5 + 30*t**4 + 320*t**3/3 - 58*t**2 - 216*t + 5399. Let i(h) = 0. Calculate h.
-27, -1, 1, 2
Suppose 782*s - 4325*s - 4 = 3577*s - 4. Factor 2*t**2 + s*t - 1/2*t**4 + 1/2*t**5 + 0 - 2*t**3.
t**2*(t - 2)*(t - 1)*(t + 2)/2
Let n = 13 - 11. Let g be 1540/(-630) + (-6)/(-3) + 2. Let 8/9 - 32/9*m + g*m**n = 0. Calculate m.
2/7, 2
Let x(s) be the first derivative of s**2 + 71. Let d(j) = -j**2 + 7*j - 2. Let f(p) = -2*d(p) + 10*x(p). Factor f(o).
2*(o + 1)*(o + 2)
Let r(q) be the second derivative of 3*q**5/4 + 72*q**4 - 358*q**3 + 360*q**2 - q + 1309. Factor r(c).
3*(c - 2)*(c + 60)*(5*c - 2)
Let s(q) = q**4 + q**3 + q**2 - q. Let b(g) = 5*g**5 - 6*g**4 - 21*g**3 + 4*g**2 + 6*g. Let k = 380 - 381. Let o(m) = k*b(m) - 6*s(m). Solve o(a) = 0.
-2, 0, 1
Suppose -7*k = -128 - 180. Suppose -13*i = -9*i - k. Factor -8*o**2 - 6*o**2 + 40*o + 25*o**4 - 5*o**5 + 5*o**2 - 30*o**3 - i*o**2.
-5*o*(o - 2)**3*(o + 1)
Factor 16/9*m - 32/3 + 2/9*m**2.
2*(m - 4)*(m + 12)/9
Let s = 578 - 488. Suppose 102 = 6*o + s. Factor -6 - 4*k + 11/6*k**o - 1/6*k**3.
-(k - 6)**2*(k + 1)/6
Let g = -61147/51 + 20388/17. Factor 0*s + 1/6*s**5 + 0*s**4 + 0 + g*s**2 - 1/2*s**3.
s**2*(s - 1)**2*(s + 2)/6
Let x be -7*(-150)/(-105) - (-903)/86. Factor x*l - 1/2*l**4 + 3/2*l**2 - 1 - 1/2*l**3.
-(l - 1)**2*(l + 1)*(l + 2)/2
Let a(q) be the second derivative of 0*q**2 + 3 - 15*q + 1/50*q**5 + 0*q**3 + 37/15*q**4. Factor a(p).
2*p**2*(p + 74)/5
Suppose -4*c - s + 34 = 0, -c + 6*c - 2*s = 36. Factor 4*z**4 + c*z**4 + 25*z**3 + 4*z**3 + 2*z - 6*z**3 + 13*z**2 + 0*z**2.
z*(z + 1)*(3*z + 2)*(4*z + 1)
Suppose -31*r + 138 = -8*r. Let f(v) = 2*v**2 - 19*v + 24. Let y(k) = k**2 - 10*k + 12. Let d(a) = r*f(a) - 14*y(a). Suppose d(s) = 0. What is s?
1, 12
Let w be (-26)/(-52) - (-190)/4. Factor -9*h**2 + 16*h**2 + w + 48 - 10*h**2 - 42*h.
-3*(h - 2)*(h + 16)
Suppose -4*r + 368 = 344, 0 = 3*d - 3*r + 6. Factor 0*f**3 + 0*f + 2/5*f**d - 4/5*f**2 + 2/5.
2*(f - 1)**2*(f + 1)**2/5
Let u(q) = 3*q**2 - 12*q + 9. Let p be u(3). Suppose p = 4*y + 4*y + 3*y. Factor -3/7*c + 3/7*c**3 + 3/7*c**2 + y - 3/7*c**4.
-3*c*(c - 1)**2*(c + 1)/7
Let q = 500 + -485. Suppose -3*w**2 + q + 3*w**3 - 8*w - 7 - w - 18*w + 19 = 0. Calculate w.
-3, 1, 3
Let q(x) = 2*x**3 + 13*x**2 - 8*x - 5. Suppose 3*a - 5*b + 36 = 0, -27 = 3*a - 4*b + 2*b. Let i be q(a). Factor 44/9*h**i - 8/9 + 20/9*h + 16/9*h**3.
4*(h + 1)*(h + 2)*(4*h - 1)/9
Let n(k) be the first derivative of -k**4/36 - k**3/18 + k**2/3 - 14*k + 80. Let z(q) be the first derivative of n(q). Let z(w) = 0. What is w?
-2, 1
Let q = 195540/7 + -27934. Let 44/7*c - q*c**2 - 242/7 = 0. What is c?
11
Let i be (((-9)/(-6))/(24/224))/2. Let -4*p**2 + i*p**2 + 15*p - 3*p = 0. What is p?
-4, 0
Let a(k) be the second derivative of -5*k**7/42 + 27*k**5/4 - 45*k**4/2 - 6466*k. Determine w, given that a(w) = 0.
-6, 0, 3
Let t be 30/(-36)*-6*-1 + 7. Let u(v) be the first derivative of 0*v + 12 + 1/6*v**3 + v**t. Solve u(z) = 0 for z.
-4, 0
Let g(i) = -7*i**3 + 2020*i**2 - 13*i - 2080. Let t(k) = -6*k**3 + 2019*k**2 - 12*k - 2073. Let h(b) = -9*g(b) + 10*t(b). Factor h(w).
3*(w - 1)*(w + 1)*(w + 670)
Suppose -2*i + 14 + 8 = 0. Suppose -4*g = -5*k - i, 5*g - 5*k + 2*k = 17. Determine w, given that 4/3*w**g + 4*w - 8/3 - 4*w**3 + 4/3*w**2 = 0.
-1, 1, 2
Let a = 49 - 26. Suppose -2*x + 6*j = 8*j - 14, a = x + 5*j. Factor -5*w**4 - 3*w**4 - 2129*w + 2129*w + 4*w**5 - 4*w**x + 8*w**2.
4*w**2*(w - 2)*(w - 1)*(w + 1)
Let g(t) = 20*t**4 + 18*t**3 - 33*t**2 - 25*t + 6. Let n(q) = 20*q**4 + 17*q**3 - 32*q**2 - 25*q + 4. Let a(z) = -2*g(z) + 3*n(z). Solve a(f) = 0.
-1, 0, 5/4
Let o(f) be the first derivative of -40 - 45/2*f - 1/4*f**3 + 93/8*f**2. Let o(y) = 0. Calculate y.
1, 30
Let 3/2*p**2 + 957/2*p - 480 = 0. Calculate p.
-320, 1
Let u(q) be the first derivative of -3*q**3 + 141*q**2 - 93*q - 6153. Let u(l) = 0. What is l?
1/3, 31
Let j be (17 - (-222)/(-12)) + (-38)/(-12). Factor -j*i - 4/3 - 1/3*i**2.
-(i + 1)*(i + 4)/3
Let k(a) = a**2 - 7*a - 148. Let x be k(16). Let z be 14/16 - (-2)/x. Solve -z*f**2 - 3/4 - 9/8*f = 0.
-2, -1
Let i = 0 - -5. Let p = 366 - 260. Solve -g**4 - 3*g + 60*g**2 - i*g - 148*g**3 - 36*g**5 + p*g**4 + 27*g**4 = 0 for g.
0, 1/3, 1, 2
Let w(m) be the second derivative of -m**5/12 + m**4/6 + 2*m**3 - 11*m**2 + 6*m. Let c(v) be the first derivative of w(v). Factor c(x).
-(x - 2)*(5*x + 6)
Let g(p) be the first derivative of 5*p**3/3 - 155*p**2/2 + 420*p + 676. Find d such that g(d) = 0.
3, 28
Let l be (-52)/24 + (-12 + 18)*1/2. Let k(g) be the third derivative of 1/8*g**6 - 7*g**2 + l*g**3 + 2/21*g**7 + 0 - 5/12*g**5 + 0*g - 5/8*g**4. Factor k(h).
5*(h - 1)*(h + 1)**2*(4*h - 1)
Let s = -156 + 212. Let t be 18/s - (-33)/132. Factor -48/7*y - 8/7*y**2 + t*y**4 - 32/7 + 12/7*y**3.
4*(y - 2)*(y + 1)*(y + 2)**2/7
Let u = -385 - -389. Suppose 68*s**2 - 24 + 55*s**4 - u*s**4 + s**4 - 8*s**5 - 108*s**3 + 20*s = 0. Calculate s.
-1/2, 1, 2, 3
What is x in 63504/11 - 14868/11*x - 1/11*x**3 - 248/11*x**2 = 0?
-126, 4
Determine v, given that -81225/8*v + 0 - 285/4*v**2 - 1/8*v**3 = 0.
-285, 0
Let r be (1