*(b + 4)**2
Suppose 6*b + 14*g - 30 = 17*g, 4*b - 14 = g. What is j in -5/9*j + 5/9*j**4 + 10/9*j**b + 1/9 - 10/9*j**3 - 1/9*j**5 = 0?
1
Suppose -22*m**3 + 26*m**3 - 7346*m**2 - 212*m + 7146*m**2 + 408 = 0. Calculate m.
-2, 1, 51
Let f(r) be the third derivative of -r**7/5040 + r**6/288 - r**4/12 + 2*r**3 + 13*r**2 - 1. Let c(b) be the second derivative of f(b). Solve c(o) = 0.
0, 5
Let -13*z**4 - 47/2 - 331/4*z - 215/2*z**2 - 61*z**3 - 1/4*z**5 = 0. What is z?
-47, -2, -1
Suppose 11*r = 15*r - 20. Let s be -1 + 37 - (-1 - -2). Factor s*o + r + 7 - 22 + 20*o**2.
5*(o + 2)*(4*o - 1)
Let l(h) = 11*h**2 + 29*h + 46. Let v be l(-11). Let r be v/207 - (-50)/(-45). Factor -3*c**2 + 3/2*c**r + 3/2*c**5 - 3*c**3 + 3/2 + 3/2*c.
3*(c - 1)**2*(c + 1)**3/2
Let s(u) be the first derivative of -8/13*u**3 + 21/13*u**2 - 20/13*u + 73 + 1/26*u**4. Factor s(x).
2*(x - 10)*(x - 1)**2/13
Determine v so that 79*v**2 - v**4 - v + 4*v - 143*v**2 - 3*v**3 + 65*v**2 = 0.
-3, -1, 0, 1
Let u(y) be the third derivative of -y**5/240 + y**4/2 + 25*y**3/6 - 47*y**2 + 10. Suppose u(z) = 0. What is z?
-2, 50
Let k be ((-8)/1 - (-1276)/174)/(8/32*-2). Factor -8/9*w**2 + 22/9*w - 2/9*w**3 - k.
-2*(w - 1)**2*(w + 6)/9
Suppose -156 + 410 = -w. Let t = w + 256. Solve 0*x**t + 4/3 + 14/9*x - 2/9*x**3 = 0 for x.
-2, -1, 3
Let t be (176/20 + 2)*(-20)/8. Let i be 0 - (132/t)/11. Determine h so that -2/9*h**3 + i*h**2 - 2/9*h + 0 = 0.
0, 1
Factor -27/2*n - 1/2*n**2 + 62.
-(n - 4)*(n + 31)/2
Let -81725*q + 73*q**3 + 21*q**2 + 6*q**4 + q**5 - 48 - 5*q**4 + 26*q**4 + 81651*q = 0. What is q?
-24, -2, -1, 1
Let t(c) = -c**2 - 8*c + 2. Let o be t(-7). Solve -101 - i**2 - 12*i + o*i + 111 = 0 for i.
-5, 2
Let n(v) be the third derivative of 1/6*v**5 + 1/35*v**7 - 3/20*v**6 + 0 + 0*v**3 + 2*v + 0*v**4 + 1/168*v**8 - 21*v**2. Find k, given that n(k) = 0.
-5, 0, 1
Let d be 90/210 + 5283/21. Let z be (-168)/d*-2*(-6)/(-16). Find i, given that i - i**3 + 0 + 1/2*i**4 - z*i**2 = 0.
-1, 0, 1, 2
Let j be (-26)/(-8) - 2/8. Let d = 226 - 223. Factor m**j + 10 - 6 - d*m**2 + 8*m**2 + 8*m.
(m + 1)*(m + 2)**2
Let x be (-153)/(-12) + 2 - 6/8. Factor -15*q**2 - x*q**2 - 19*q**2 + 43*q**2.
-5*q**2
Let x(p) be the first derivative of -34*p + 0*p**2 + 1/20*p**5 - 2/3*p**3 + 1/4*p**4 + 27. Let t(h) be the first derivative of x(h). Factor t(d).
d*(d - 1)*(d + 4)
Let h(a) be the second derivative of -a**4/78 + 10*a**3/13 - 56*a**2/13 - 864*a. Solve h(c) = 0 for c.
2, 28
Let i(t) be the third derivative of t**8/8400 - t**7/525 + t**6/100 - 4*t**4/3 + 2*t**2 - t. Let d(f) be the second derivative of i(f). Factor d(y).
4*y*(y - 3)**2/5
Let j be (-64)/144*297/(-6). Let h be (-32)/(-56)*77/j. Determine u, given that -2/5*u**h + 0*u + 0 = 0.
0
Let -4/9*v - 2/9*v**2 + 0 = 0. Calculate v.
-2, 0
Let x = 12659 - 12659. Let i(j) be the third derivative of 2/105*j**7 - 1/3*j**4 + x*j + 0*j**3 + 0*j**6 - 1/5*j**5 + 0 - 44*j**2. Solve i(b) = 0.
-1, 0, 2
Let x be 420/504 + 20/(-24). Let g(v) be the third derivative of 1/9*v**3 - 1/24*v**4 + x*v + 0 + 1/180*v**5 + 31*v**2. Suppose g(w) = 0. Calculate w.
1, 2
Let u be ((-2)/(-49)*-14)/((-1)/(-7)). Let d be 0/(5 + -9) + 0/u. What is r in -8/13*r - 10/13*r**3 + d + 16/13*r**2 + 2/13*r**4 = 0?
0, 1, 2
Determine k, given that -36*k**2 - 1525 + 678 + 5236*k + 241 - 1044 - 670 = 0.
4/9, 145
Let i(g) = 7*g**3 - 2*g. Let j(v) = 23*v**3 - 245*v**2 - 2703*v - 8575. Let u(z) = -4*i(z) + j(z). Solve u(c) = 0.
-35, -7
Let n = -2875 - -2879. Let c(z) be the first derivative of -2/3*z**3 + 0*z - 1/2*z**2 - 1/4*z**n + 3. Let c(v) = 0. Calculate v.
-1, 0
Let w(j) be the third derivative of -j**8/3360 + j**6/120 - j**5/30 + 5*j**4/8 + 2*j**2 + 33. Let o(t) be the second derivative of w(t). Factor o(z).
-2*(z - 1)**2*(z + 2)
Let b(u) be the third derivative of -u**6/240 - 59*u**5/30 - 469*u**4/48 - 39*u**3/2 + 4036*u**2 + u. What is f in b(f) = 0?
-234, -1
Let g be 0/(-4) + (-316)/154 + 2. Let c = 142/231 - g. What is s in s + 1/3*s**2 + c = 0?
-2, -1
Factor 85375*z**3 + 222*z - 28*z**2 - 85377*z**3 - 212 - 148.
-2*(z - 3)**2*(z + 20)
Let s(v) be the third derivative of -v**6/480 + 13*v**5/48 + 133*v**4/96 + 67*v**3/24 + 2993*v**2. Find y, given that s(y) = 0.
-1, 67
Let k(x) = -x**3 - 10*x**2 - 8*x + 13. Let r be k(-9). Suppose 4*v - 5*s + r + 3 = 0, 0 = v - 5*s + 13. Factor 12*i - 3*i - 3*i - 2*i + i**v.
i*(i + 4)
Let q be 5/1 - 30*((-240)/126)/(-20). Factor -q*o**2 + 12/7 + 12/7*o - 9/7*o**3.
-3*(o - 1)*(o + 2)*(3*o + 2)/7
Let 18/5*t**5 + 384/5*t**2 + 0 + 328*t**3 - 392/5*t**4 + 0*t = 0. Calculate t.
-2/9, 0, 6, 16
Let u(f) be the first derivative of 4*f**3/9 - 66*f**2 + 392*f/3 - 4486. Solve u(b) = 0.
1, 98
Let h be (-60 + 12)/(-82 + 66). Factor -6/5*f**h + 1/5*f**2 + 0 + 0*f.
-f**2*(6*f - 1)/5
Let k(z) = -2*z**2 + z. Let i be 1 - (16*1/(-2) + 4). Let n(q) = -155*q**2 + 170*q - 10. Let r(a) = i*k(a) + n(a). Find x such that r(x) = 0.
2/33, 1
Let o(f) = 5*f**4 - 20*f**3 + 28*f**2 + 44*f - 140. Let d(u) = -u**4 + 2*u**3 + u**2 + u - 1. Let q(i) = -4*d(i) - o(i). Determine x so that q(x) = 0.
-2, 2, 6
Suppose 0 = 186*q - 254*q + 136. Let f(i) be the first derivative of 6/5*i - 1/5*i**3 - 3/10*i**q - 15. Factor f(p).
-3*(p - 1)*(p + 2)/5
Let v(x) = -3*x**2 - 5*x + 28. Let m be v(-4). Let h(q) be the first derivative of 0*q + 25/6*q**3 + m*q**2 - 17 - 5/4*q**4 + 1/10*q**5. Factor h(s).
s**2*(s - 5)**2/2
Let t = 71341 + -71339. Solve 3/7*l**5 + 0*l**t + 0*l**4 + 0*l - 12/7*l**3 + 0 = 0 for l.
-2, 0, 2
Determine p so that -50/7*p**2 + 2/7*p**3 + 254/7*p + 306/7 = 0.
-1, 9, 17
Let r be (-442)/(-130)*(1817/690 + 6/(-45)). Factor -r*w**4 + 0 + w + 21/2*w**3 - 11/2*w**2 + 5/2*w**5.
w*(w - 1)**3*(5*w - 2)/2
Let r(n) be the second derivative of 2/9*n**3 + 27 - 3/40*n**5 + 0*n**2 + 7/72*n**4 + 3*n + 1/252*n**7 - 7/180*n**6. Factor r(p).
p*(p - 8)*(p - 1)*(p + 1)**2/6
Suppose 4*g + 16 = 5*u, 0 = 2*u + 5*g - 4 - 9. Let x be (22/4 - 0) + (-1119)/746. Factor 0*a - 32*a**2 + 8*a + 35*a**2 + a**x - 4*a**3 - 4 - u*a.
(a - 2)**2*(a - 1)*(a + 1)
Let 684/5 - 834/5*l + 156/5*l**2 - 6/5*l**3 = 0. What is l?
1, 6, 19
Let g(i) be the third derivative of i**7/280 - 403*i**6/160 - 1233*i**5/20 - 1241*i**4/2 - 3320*i**3 - 22*i**2 - 2*i - 32. Factor g(y).
3*(y - 415)*(y + 4)**3/4
Factor 0 + 22*s**2 - 58/5*s**3 - 54/5*s + 2/5*s**4.
2*s*(s - 27)*(s - 1)**2/5
Let b(p) be the third derivative of -p**5/140 - 29*p**4/14 - 115*p**3/14 + p**2 + 297. Solve b(r) = 0.
-115, -1
Suppose 0 = 151*i - 154*i + 5*x - 8, 5*i - 32 = -3*x. Find z, given that 20/3*z**2 - 12 - i*z - 4/3*z**3 = 0.
-1, 3
Suppose -33*v + 302 - 236 = 0. Let z(i) be the first derivative of 19 + 0*i**v + 0*i - 2/21*i**3 - 1/14*i**4. Factor z(n).
-2*n**2*(n + 1)/7
Factor -3296*s - 616363 - 89237 - 1364*s + 1300*s + 43*s**2 - 47*s**2.
-4*(s + 420)**2
Suppose -16*u + 558 = -14*u. Let g be ((u/(-2))/3)/(4/(-24)). Suppose -4*k**2 - 4*k**4 + g*k - 8*k**3 - 279*k = 0. What is k?
-1, 0
Factor -3488*g - 546 + 3*g**2 + 1749*g + 1742*g.
3*(g - 13)*(g + 14)
Let q be 6*((-4)/14 - 295/21). Let y = 88 + q. Factor 157*j + 72*j**y + 2*j**4 + 24*j**3 - 157*j.
2*j**2*(j + 6)**2
Solve 1/4*o**4 + 3069*o**2 + 71114*o + 238328 + 95/2*o**3 = 0 for o.
-62, -4
Factor 437 + n**2 + 13*n - 3*n**2 + 99*n + 173 + 0*n**2.
-2*(n - 61)*(n + 5)
Let c(t) be the third derivative of -t**8/3360 - t**7/840 + 73*t**3/6 + 6*t**2 - 11. Let z(n) be the first derivative of c(n). Factor z(s).
-s**3*(s + 2)/2
Find s, given that -87/5 - 9/5*s**2 - 264/5*s = 0.
-29, -1/3
Suppose 0 = -4*x - 4, -3*q + 26 = -0*x + x. Suppose -q = -3*n - 6*n. Determine s so that -60*s**4 + 1 + 56*s**4 - n + 4*s**5 = 0.
0, 1
Let b(i) = -4 + 2 + 29*i - 3 - 33*i. Let n be b(-2). Factor -2*x**3 - 2*x**n + 128*x**2 - 128*x**2.
-4*x**3
Let j(u) = 18*u**4 - 631*u**3 + 404*u**2 + 379*u - 34. Let b(m) = 6*m**4 - 207*m**3 + 135*m**2 + 126*m - 12. Let r(l) = -17*b(l) + 6*j(l). Factor r(w).
3*w*(w - 44)*(w - 1)*(2*w + 1)
Let l = -143322 - -143322. Let u be (-19)/(-15) + (-3)/5. Find g such that 2/3*g**2 + l*g - u = 0.
-1, 1
Let c(s) = s**4 - s**3 - s**2 - 6*s. Let o(g) = g**4 + 168*g**3 + 1944*g**2 + 4825*g + 1083. Let d(w) = -6*c(w) - 2*o(w). Find j such that d(j) = 0.
-19, -3, -1/4
Let c(a) be the first derivative of 5*a**4/12 - 35*a**3/6 + 25*