, 1
Let b(c) = c**2 - c**3 - 6*c**2 - 11*c + c**2 - c**2 + 2 - 5*c**2. Let a(p) = p**3 + p**2 + p - 1. Let o(i) = 4*a(i) + 2*b(i). Solve o(j) = 0 for j.
-1, 0, 9
Let b(t) be the first derivative of 3*t**4/4 - 12*t**3 - 4021. What is a in b(a) = 0?
0, 12
Let a(q) be the third derivative of -1/10*q**3 + 2*q + 0 - 1/300*q**5 - 26*q**2 - 1/600*q**6 + 1/24*q**4. Let a(l) = 0. What is l?
-3, 1
Let n = -50190 + 50190. Find b such that 4/3*b**4 - 32/3*b**2 + n + 0*b + 8/3*b**3 = 0.
-4, 0, 2
Let t(j) = 5*j**5 - j**4 + 3*j**3 - 3*j**2 - 4*j. Let z = 155 + -159. Let c(x) = -x**5 - x**3 + x**2 + x. Let d(q) = z*c(q) - t(q). Factor d(g).
-g**2*(g - 1)**2*(g + 1)
Let q(j) be the first derivative of j**4 + 0*j + 17 - 20/3*j**3 + 8*j**2. Suppose q(m) = 0. What is m?
0, 1, 4
Suppose -57*u + 29*u = -21*u + 44*u + 51*u. Factor -1/2*v**2 + 0*v - 5/6*v**3 + u.
-v**2*(5*v + 3)/6
Let n(w) be the second derivative of w**4/42 + 209*w**3/7 - 248*w - 8. Solve n(p) = 0.
-627, 0
Suppose -1082*o + 1087*o = 1605. Suppose 10*y - o = -291. What is x in -3/4*x**y + 1/4*x**5 + 1/4*x**4 + 1/2*x + 0 - 1/4*x**2 = 0?
-2, -1, 0, 1
Let j(w) be the first derivative of -w**3/3 - 24*w**2 + 265*w + 1553. Factor j(n).
-(n - 5)*(n + 53)
Let f(o) be the third derivative of 0*o - 1/420*o**6 + 0*o**3 + 0 + 1/21*o**4 + 41*o**2 - 1/70*o**5. Factor f(v).
-2*v*(v - 1)*(v + 4)/7
Let f(x) be the third derivative of -x**8/1680 - x**7/210 + 2*x**6/75 + 14*x**5/75 - 2*x**4/5 - 24*x**3/5 - 440*x**2. Solve f(t) = 0 for t.
-6, -2, 2, 3
Let t(b) be the second derivative of b**7/168 + 53*b**6/30 - 213*b**5/80 - 1591*b. Factor t(q).
q**3*(q - 1)*(q + 213)/4
Let a(j) be the third derivative of j**8/9240 - j**7/660 + j**6/165 + 65*j**3/3 + 9*j**2. Let z(b) be the first derivative of a(b). Factor z(f).
2*f**2*(f - 4)*(f - 3)/11
Let v be 10*(-4)/((-34 - -6)/7). Suppose -v*d = 4*d + 8*d. Factor 0*p - 2/7*p**4 + 2/7*p**3 + 0*p**2 + d.
-2*p**3*(p - 1)/7
Let r be 1 + 2 + (-1)/1. Let k = 0 + r. Factor -25*t**4 + 61*t**k - 53*t**3 + 18*t**3 - 71*t**2.
-5*t**2*(t + 1)*(5*t + 2)
Let k(o) be the second derivative of -7*o - 2/3*o**3 + 1/180*o**6 + 0*o**2 - 2/15*o**5 + 4/3*o**4 + 0. Let c(f) be the second derivative of k(f). Factor c(v).
2*(v - 4)**2
Let s(m) be the third derivative of 1/240*m**6 - 1/12*m**4 + 2 + 0*m**3 + 1/30*m**5 + 6*m**2 - 1/420*m**7 + 0*m. Factor s(l).
-l*(l - 2)*(l - 1)*(l + 2)/2
Let h be (-855)/(-760) + (-3)/8. Let r(t) = t**2 - 30*t - 132. Let j be r(34). Suppose -11/8*b - h + 3/8*b**3 - 3/8*b**2 + 1/8*b**j = 0. Calculate b.
-3, -1, 2
Let i = 65263/326265 + -2/65253. Solve 6 + i*u**2 + 17/5*u = 0.
-15, -2
Let m be 65/39 - 5*(-4)/60. Let o be (-6)/(-4) - 9/6. Factor 3/7*b - 3/7*b**3 + o*b**m + 0.
-3*b*(b - 1)*(b + 1)/7
Let a(c) be the first derivative of 5/3*c**3 - 10*c - 26 + 5/2*c**2. Factor a(h).
5*(h - 1)*(h + 2)
What is v in -144*v + 66*v**3 + 192 - 237*v**2 - 3332*v**5 + 3335*v**5 + 0*v**4 + 75*v**3 - 2*v**4 + 47*v**4 = 0?
-8, -1, 1
Let -72 + 75 + 0*o**2 + 3*o**2 + 393 - 84*o = 0. What is o?
6, 22
Suppose -6*d - 108 = -2*d. Let r = 32 + d. Factor 4 + r + 11 - 15*c**2 - 5*c**3.
-5*(c - 1)*(c + 2)**2
Let d(k) be the first derivative of 4*k**5/5 - 22*k**4 + 648. Find b such that d(b) = 0.
0, 22
Let n be 7/(112/192) - 9. Let k(s) be the first derivative of 0*s**2 - 20 + 0*s - 1/6*s**4 - 2/45*s**5 + 8/27*s**n. Suppose k(b) = 0. Calculate b.
-4, 0, 1
Let a(q) be the second derivative of -q**4/12 - 47*q**3 - 19881*q**2/2 - 138*q + 17. Factor a(g).
-(g + 141)**2
Let y(b) be the third derivative of -b**7/525 + b**6/20 - 7*b**5/75 - 304*b**2 + b. Factor y(z).
-2*z**2*(z - 14)*(z - 1)/5
Let t(z) be the second derivative of -z**7/126 + z**6/90 + 11*z**5/60 - z**4/4 - z**3 - 46*z - 11. Suppose t(i) = 0. Calculate i.
-3, -1, 0, 2, 3
Let o = 113 - 109. Let v(p) = -p**4 - 45*p**3 + 27*p**2 + 40*p - 31. Let w(i) = -44*i**3 + 28*i**2 + 40*i - 32. Let d(a) = o*v(a) - 5*w(a). Factor d(j).
-4*(j - 9)*(j - 1)**2*(j + 1)
Let c(v) = -433*v**2 - 17318*v + 82. Let i be c(-40). Factor 2/3*f**5 - i*f**4 + 8/3*f**2 + 0*f + 0*f**3 + 0.
2*f**2*(f - 2)**2*(f + 1)/3
Factor 225*y**2 - 10*y**3 + 0*y - 5/3*y**4 + 0.
-5*y**2*(y - 9)*(y + 15)/3
Suppose -750*a - 2203 + 2106 + 7597 = 0. Let -16/3 - a*z - 4*z**2 + 2/3*z**3 = 0. What is z?
-1, 8
Suppose 6 = -4*j - 3*s, -5 = -5*j + 3*s + 1. Let t = -961039/3 - -320347. Solve 8/3*f**4 - t*f**5 - 10/3*f**3 + 0*f + j + 4/3*f**2 = 0 for f.
0, 1, 2
Let m(w) be the first derivative of -108 + 9/14*w**6 + 8/7*w**3 - 27/7*w**4 - 6/35*w**5 + 0*w + 0*w**2. Suppose m(q) = 0. What is q?
-2, 0, 2/9, 2
Let o = 647 - 656. Let y(h) = h**2 + 8*h - 9. Let t(f) = -3*f**2 + 2*f + 20 - 35*f + 16. Let x(z) = o*y(z) - 2*t(z). Factor x(v).
-3*(v - 1)*(v + 3)
Let l(b) be the first derivative of 2*b**6/15 - 4*b**5/5 + b**4 - 20*b - 69. Let t(z) be the first derivative of l(z). Solve t(o) = 0.
0, 1, 3
Let k(j) be the first derivative of -5*j**4/12 - 5*j**3/2 + 45*j**2 - 54*j + 230. Let m(g) be the first derivative of k(g). Determine a, given that m(a) = 0.
-6, 3
Let v(l) be the first derivative of -4*l**3 - 6*l**2 + 2*l - 3/20*l**5 - 4 - 5/4*l**4. Let u(p) be the first derivative of v(p). Factor u(m).
-3*(m + 1)*(m + 2)**2
Let f = -327 + 329. What is s in -9*s + 6*s**2 - 2 - 8*s**2 + 2*s - s**f = 0?
-2, -1/3
Let q(n) = 4*n**2 - 3*n - 6. Let m(r) = 2*r**2 + 4. Let x(j) = -6*j**2 + j - 9. Let i(a) = 5*m(a) + 2*x(a). Let f(c) = -5*i(c) - 2*q(c). Factor f(p).
2*(p - 1)**2
Let l(f) be the third derivative of f**6/480 - 19*f**5/120 + 35*f**4/96 + 37*f**3/12 + 5*f**2 - 193. Factor l(v).
(v - 37)*(v - 2)*(v + 1)/4
Find c such that -28 + 4576/9*c**4 - 722/3*c + 2504/9*c**3 - 4324/9*c**2 - 338/9*c**5 = 0.
-1, -3/13, 1, 14
Let o(q) be the third derivative of -q**5/24 + 1451*q**4/96 - 145*q**3/24 + q**2 - 1490. Suppose o(k) = 0. What is k?
1/10, 145
Suppose -8*g + 5*g - 141 = 0. Let q = g - -61. Suppose -q + 2*w**2 - 43*w + 18*w + 13*w = 0. What is w?
-1, 7
Let p(a) be the third derivative of -1/100*a**5 + 3/10*a**3 + 0*a + 1/20*a**4 - 52*a**2 + 0. Solve p(l) = 0 for l.
-1, 3
Let b(d) be the first derivative of -4*d**6 + 10*d**5 - 5*d**4/2 - 10*d**3 + 5*d**2 + 4*d - 1440. Solve b(w) = 0.
-2/3, -1/4, 1
Determine b so that 0*b**2 + 0*b + 16/5*b**4 - 14/5*b**3 - 2/5*b**5 + 0 = 0.
0, 1, 7
Let h(u) = -28*u**3 - 1719*u**2 - 14220*u + 3511. Let a(k) = -19*k**3 - 1146*k**2 - 9480*k + 2347. Let f(q) = 8*a(q) - 5*h(q). Factor f(z).
-3*(z + 11)*(z + 37)*(4*z - 1)
Factor 3*k**3 + 18861*k**2 + 18866*k**2 - 22*k - 35*k - 37751*k**2 - 30.
3*(k - 10)*(k + 1)**2
Let o(p) be the first derivative of -3/10*p**4 - 76 - 4/15*p**3 - 2/25*p**5 + 0*p**2 + 0*p. Factor o(y).
-2*y**2*(y + 1)*(y + 2)/5
Let u(x) be the third derivative of 0 + x + 13/6*x**4 + 169/3*x**3 + 1/30*x**5 - 2*x**2. Find n such that u(n) = 0.
-13
Let l(j) be the first derivative of -j**8/5040 + j**6/270 + 2*j**3/3 - j**2 - 43. Let s(h) be the third derivative of l(h). Factor s(y).
-y**2*(y - 2)*(y + 2)/3
Let y = 7081/924 + -333/44. Let 4/21 + 2/21*b - y*b**2 = 0. Calculate b.
-1, 2
Suppose -3*g + f - 21 + 34 = 0, 0 = -5*g + f + 21. Find p, given that p**2 + 131*p**4 - g - 2*p**3 - 4*p**2 + 8*p - 130*p**4 = 0.
-2, 1, 2
Let s(r) be the second derivative of r**7/273 - 56*r**6/65 - 51*r**5/13 - 256*r**4/39 - 57*r**3/13 + 225*r + 3. Factor s(l).
2*l*(l - 171)*(l + 1)**3/13
Let p be (-7)/(-49) + 1/7. Let x(f) = -f**3 + 5*f**2 + 14*f - 46. Let t be x(6). Factor -p - 6/7*b - 4/7*b**t.
-2*(b + 1)*(2*b + 1)/7
Let c(x) be the third derivative of x**6/40 - 19*x**5/20 - x**4/8 + 19*x**3/2 + 1543*x**2. Determine b so that c(b) = 0.
-1, 1, 19
Let z(o) = 47*o**2 - 570*o - 572. Let n(l) = -267*l**2 + 3420*l + 3432. Let k(s) = -6*n(s) - 34*z(s). Suppose k(v) = 0. Calculate v.
-1, 286
Let o(k) be the third derivative of -k**5/60 - 7*k**4/8 - 52*k**3/3 + 632*k**2. Determine d, given that o(d) = 0.
-13, -8
Suppose -20*x + 96 = -12*x. Factor 29*l**2 - 106*l**5 + 3*l**2 - 6*l**3 + 108*l**5 + 24*l - x*l**4.
2*l*(l - 6)*(l - 2)*(l + 1)**2
Let 708/11*c - 598/11*c**2 - 128/11 + 18/11*c**3 = 0. Calculate c.
2/9, 1, 32
Suppose -257 + 271 = 2*r, -5*r = -2*t - 27. Factor 1/6*q**2 + 1/6*q**t + 0 + q - 2/3*q**3.
q*(q - 3)*(q - 2)*(q + 1)/6
Let i be (-90)/(-54)*18/30. Let v(a) be the first derivative of 3/7