3 + c*p**3 - p**4 + p.
-p*(p - 1)**3
Solve -49/5*q + 49/5*q**3 + 51/5*q**2 - 1/5*q**4 - 10 = 0 for q.
-1, 1, 50
Let c(l) be the third derivative of -289*l**7/105 - 4267*l**6/60 - 101*l**5 + 223*l**4/3 - 56*l**3/3 + 140*l**2 + 1. Determine k so that c(k) = 0.
-14, -1, 2/17
Let f = -192 + 1348/7. Let w = 16510/7 + -2358. Factor -f - 8/7*g - w*g**2.
-4*(g + 1)**2/7
Let s = -283/10 - -289/10. Factor -2/5*f + f**2 + s*f**3 + 0.
f*(f + 2)*(3*f - 1)/5
Let h = 14 - 11. Solve 3*d**h - 6*d + 4 - 21*d + 0 - 19 - 9*d**2 = 0 for d.
-1, 5
Let v(t) be the third derivative of -5*t**8/336 - 5*t**7/21 - 7*t**6/8 + 3*t**5 + 45*t**4/2 - 385*t**2. What is d in v(d) = 0?
-6, -3, 0, 2
Suppose 20 = 5*x - x. Suppose -13*w = -5*w. Factor 0 + 0*k**4 + w*k - 1/3*k**3 + 0*k**2 + 1/3*k**x.
k**3*(k - 1)*(k + 1)/3
Let y = -40 - -122. Suppose -5*v + y = -3*d + 6*d, 8 = 2*v - 5*d. Factor -5*h + v*h + 4 + 1 - 10*h**3 + h - 5*h**4.
-5*(h - 1)*(h + 1)**3
Let t = 59 - 48. Suppose -10*d = t*d - 63. Factor c**2 + 1/4*c**4 + 0 + 0*c + c**d.
c**2*(c + 2)**2/4
Suppose 7*n - n = 72. Let s be n/(-18) + (-40)/(-42). Factor s*k - 2/7*k**2 + 0.
-2*k*(k - 1)/7
Let b(j) be the third derivative of 5/8*j**4 + 0 + 3/2*j**3 + 1/20*j**5 + 17*j**2 + 0*j - 1/40*j**6. Find t, given that b(t) = 0.
-1, 3
Let h = -7095 - -163191/23. Find w, given that 4/23 + h*w + 2/23*w**2 = 0.
-2, -1
Determine o, given that -386*o**3 - 3645*o**2 - 5*o**4 + 116*o**3 + 0*o**4 = 0.
-27, 0
Let b(r) = 10*r**2 + 32*r - 28. Let p be b(-4). Factor 12/5*o**p - 4/5*o**5 - 12/5*o**3 + 4/5*o**2 + 0*o + 0.
-4*o**2*(o - 1)**3/5
Let c be -2 + 0 - (-48)/24. Factor -4/3*n + c*n**3 - 8/3*n**2 + 4/3*n**5 + 0 + 8/3*n**4.
4*n*(n - 1)*(n + 1)**3/3
Let x be 236/1764 + (-2)/(-18). Let o = 393/196 + x. Factor -o*f - 3/2 + 0*f**2 + 3/4*f**3.
3*(f - 2)*(f + 1)**2/4
Let b = -5707 + 5711. Find l, given that -1/5*l**b + 4/5*l**2 + 0*l**3 + 0 + 0*l = 0.
-2, 0, 2
Find m, given that -12*m**2 - 24*m - 23*m + 0*m**2 + 165 - 113*m + 7*m**2 = 0.
-33, 1
Suppose 0 = -17*t + 1113 - 195. Suppose 21*g - 3*g = t. Factor l**2 + 1/2*l + 1/2*l**g + 0.
l*(l + 1)**2/2
Let x be ((-2)/(-3))/((-910)/(-126) - 7). Let p = 3 - -1. Factor 5*u + 3*u - 2*u**x + p - 2*u.
-2*(u - 2)*(u + 1)**2
Let o(l) = -5*l**5 - 26*l**4 + l**3 + 101*l**2 + 79*l + 1. Let c(x) = -x**4 + x**3 + x**2 - x + 1. Let z(v) = -c(v) + o(v). Determine r so that z(r) = 0.
-4, -2, -1, 0, 2
Let d(n) be the third derivative of -n**6/60 - 13*n**5/15 + 29*n**4/12 + 18*n**3 + 223*n**2. Let d(t) = 0. What is t?
-27, -1, 2
What is k in -3/7*k**3 + 3*k**2 + 27/7 - 45/7*k = 0?
1, 3
Let s(u) be the first derivative of u**4/4 + 11*u**3/3 + 12*u**2 - 36*u - 78. Determine k, given that s(k) = 0.
-6, 1
Let l be (8 - -1)*12/18. Let h(x) = 2*x - 2. Let a be h(2). Factor -l*t**a - 16*t**3 + 3*t**2 + 13*t**3.
-3*t**2*(t + 1)
Suppose 2*h + 5*f = -0*f + 3, -3*h + 17 = -5*f. Suppose 8 = h*k - 8. Factor -16/5 + 12/5*y**2 + 16/5*y - 4/5*y**k - 8/5*y**3.
-4*(y - 1)**2*(y + 2)**2/5
Let d = 337 - 335. Let m(o) be the first derivative of 6 + d*o - 1/3*o**3 + 1/2*o**2. Suppose m(w) = 0. What is w?
-1, 2
Suppose -6*c = -2*c + 4*r - 92, 0 = 5*c - 3*r - 91. Factor -20*a - 75*a**5 + c - 55*a + 80*a**5 + 100*a**2 - 50*a**3.
5*(a - 1)**4*(a + 4)
Let v(j) be the second derivative of -j**6/60 + 2*j**5/15 - j**4/3 + j**2/2 - 14*j. Let z(x) be the first derivative of v(x). Determine w so that z(w) = 0.
0, 2
Suppose -s - 1 = -9. Suppose -u - 45 = -4*d, 5*d - u = 3*u + 48. Find v, given that -d*v - 12*v**2 + 2 - 3*v**3 + 6 - s = 0.
-2, 0
Let q(r) be the third derivative of 5/336*r**8 + 1/12*r**6 + 0*r + 0*r**4 + 0*r**5 + 0 + 1/14*r**7 - 7*r**2 + 0*r**3. Factor q(c).
5*c**3*(c + 1)*(c + 2)
Let s(k) be the second derivative of -k**6/45 + 41*k**5/30 - 133*k**4/6 - 49*k**3 + 16*k. Factor s(q).
-2*q*(q - 21)**2*(q + 1)/3
Suppose -4*v - 200 = 4*v. Let j be (3 + 77/v)*(-12 + 2). Factor -2/5*h**2 + 0 + j*h.
-2*h*(h - 2)/5
Let q = 59 - 57. Factor -9 + 4*m**3 + 2979*m**q - 2974*m**2 - 3*m**3 + 3*m.
(m - 1)*(m + 3)**2
Let p(c) be the third derivative of c**6/75 - 11*c**5/25 - 31*c**4/10 - 76*c**3/15 - 3*c**2 - 15*c. Factor p(r).
4*(r - 19)*(r + 2)*(2*r + 1)/5
Let p(s) = -2*s**2 + 25*s - 6. Let c be p(12). Let a be 48/72*c/16. Factor a*h**5 - 3/4*h**4 + 1/4*h**3 + 3/4*h**2 + 0 - 1/2*h.
h*(h - 2)*(h - 1)**2*(h + 1)/4
Suppose 0 = -q - 2*q - 0*q. Let p(a) be the third derivative of q*a - 5*a**2 + 0 - 2/15*a**3 - 1/300*a**5 + 1/30*a**4. Factor p(n).
-(n - 2)**2/5
Let u(q) be the third derivative of q**7/7560 - q**6/1080 - q**4/8 - 10*q**2. Let n(h) be the second derivative of u(h). Solve n(s) = 0 for s.
0, 2
Let f(d) be the third derivative of d**6/200 + d**5/10 + 23*d**4/40 + 7*d**3/5 + d**2 - 109*d. Factor f(u).
3*(u + 1)*(u + 2)*(u + 7)/5
Let o(i) be the second derivative of -i**5/5 + 2*i**4 + 14*i**3/3 - 2*i + 70. Factor o(k).
-4*k*(k - 7)*(k + 1)
Let b be (0 - (-6)/(-3)) + 4. Factor f**3 - b*f**2 + 41*f**2 + 3*f**3 + 256*f + 25*f**2.
4*f*(f + 8)**2
Let w = -2/483 - -503/4830. Let i(p) be the third derivative of 3/40*p**6 + 0*p**3 + 0 + 0*p**4 - 2*p**2 + 0*p - 1/70*p**7 - w*p**5. Factor i(d).
-3*d**2*(d - 2)*(d - 1)
Factor -159/2*a - 75/2*a**2 - 81/2 + 3/2*a**3.
3*(a - 27)*(a + 1)**2/2
Factor 23*r**3 - 49*r**3 + 36*r**2 + 162 + 23*r**3 - 135*r.
-3*(r - 6)*(r - 3)**2
Let k(n) = -2*n**2 - 16*n. Let t = -97 + 76. Let i(q) = -9*q**2 - 63*q. Let c(r) = t*k(r) + 5*i(r). Determine x, given that c(x) = 0.
0, 7
Suppose -r + 27 - 7 = 0. Let a = -14 + r. Factor 6*v**4 - 8*v**3 - 18*v - a*v**3 + 30*v**2 + 4 - 8*v**3.
2*(v - 1)**3*(3*v - 2)
Let j(z) be the third derivative of -z**5/210 - z**4/12 - 338*z**2. Find v, given that j(v) = 0.
-7, 0
Let z(i) be the first derivative of 2*i**3/27 + i**2/9 - 4*i/9 - 77. Factor z(h).
2*(h - 1)*(h + 2)/9
Let m be (633/1055)/(-2*(-2)/20). Solve 15/7*k**m + 0 - 3*k**2 - 3/7*k**4 + 9/7*k = 0.
0, 1, 3
Factor 1764 - 42*t + 1/4*t**2.
(t - 84)**2/4
Suppose 0 = 9*v - 20*v + 33. Let u be 1/(-1 - 0) - -4. Find s, given that 7*s**5 - 5*s**5 - s**u + 3*s**v + 4*s**4 = 0.
-1, 0
Suppose 0 = -26*x + 28 + 76. Let b(u) be the first derivative of -4 - 1/3*u**2 + 0*u - 4/9*u**3 - 1/6*u**x. Factor b(p).
-2*p*(p + 1)**2/3
Let x(u) be the first derivative of 3*u**4/4 - 27*u**3/5 + 9*u**2 - 24*u/5 + 198. Let x(b) = 0. Calculate b.
2/5, 1, 4
Let d(i) be the third derivative of 2*i**7/35 - i**6/15 - i**5/15 - i**2 - 12*i. Factor d(p).
4*p**2*(p - 1)*(3*p + 1)
Let j(v) be the second derivative of -v**6/75 - 13*v**5/50 - 332*v. What is r in j(r) = 0?
-13, 0
Let w(p) be the first derivative of 11*p**3/18 + p**2/6 + 48. Factor w(q).
q*(11*q + 2)/6
Let u(i) be the first derivative of 0*i**3 - 6*i**2 - 15*i + 32 - 2*i**3 + 3*i**3. Find s such that u(s) = 0.
-1, 5
Let u(c) = 126*c + 759. Let k be u(-6). Let y(q) be the first derivative of -20*q**k - 6 + 15/2*q**4 - 15*q - q**5 + 25*q**2. Solve y(d) = 0.
1, 3
Let z(w) be the third derivative of -w**8/84 - 3*w**7/70 + 7*w**6/60 + w**5/5 - 5*w**4/12 - w**3/2 - w**2 + 455. Let z(t) = 0. Calculate t.
-3, -1, -1/4, 1
Suppose 8*a - 7 = 9. Let j(d) be the first derivative of 0*d**4 - 7 + 1/3*d**3 - 1/10*d**5 + 0*d**a - 1/2*d. Factor j(f).
-(f - 1)**2*(f + 1)**2/2
Let p(y) be the first derivative of y**6/10 + 3*y**5/20 - y**4/4 - y**3/2 + 29*y - 11. Let b(q) be the first derivative of p(q). Factor b(z).
3*z*(z - 1)*(z + 1)**2
Suppose -5*m + 44 = 34. Let u(c) be the third derivative of 0*c + 1/27*c**4 - 4*c**m - 1/9*c**3 - 1/270*c**5 + 0. Factor u(k).
-2*(k - 3)*(k - 1)/9
Determine z, given that 6*z**2 - 25*z - 30*z + 80*z - 30*z - 5*z**2 = 0.
0, 5
Let o(v) be the first derivative of -2*v**3/33 - 4*v**2/11 - 8*v/11 + 62. Factor o(p).
-2*(p + 2)**2/11
Let a be -32*(10/(-4) + -2 + 4). Let l be (-25)/(-8) + (-2)/a. Factor 2/9 + 2/3*s**2 - 2*s**l + 10/9*s.
-2*(s - 1)*(3*s + 1)**2/9
Suppose 4*r = 17 - 5. Suppose 3*i - 54 = 4*o, i - 3*o + 0 - 13 = 0. Suppose r + 2*j**3 + 12*j**2 - 9 + 10*j + i + 14*j = 0. Calculate j.
-2
Factor 52*g - 22*g + 6*g**4 - 5*g**4 + 25 - 30*g**3 - 20*g**2 - 6*g**4.
-5*(g - 1)*(g + 1)**2*(g + 5)
Let n(z) be the third derivative of -12*z**2 - 1/18*z**3 - 1/72*z**4 + 1/180*z**5 + 0 + 1/360*z**6 + 0*z. Factor n(u).
(u - 1)*(u + 1)**2/3
Let u(o) be the first derivative of 5*o**6/6 + 4*o**5 + 15*o**4/4