r**2 + 12*r - 7. Let c(n) = -1. Let w = -202 - -203. Let f(v) = w*j(v) + 2*c(v). Factor f(s).
-3*(s - 3)*(s - 1)
Factor 441 + 48*d - 63*d**2 + 105*d - 81 + 97*d + 48*d**2.
-5*(d - 18)*(3*d + 4)
Let i(w) = -4*w - 13. Let q be i(-7). Suppose q*g + 4 = 16*g. Solve 6*p**2 + 3*p**5 + 15*p**4 + 6*p - 4 + 15*p**2 + g + 27*p**3 = 0 for p.
-2, -1, 0
Let k(o) be the first derivative of o**3/2 - 531*o**2/4 + 783*o + 2530. Suppose k(p) = 0. Calculate p.
3, 174
Let y(c) = c**2 - 20*c - 380. Let b be y(32). Let k be ((-17)/(204/(-18)))/(10/b). Factor -6/5*p + 0 + 9/5*p**3 - k*p**2.
3*p*(p - 1)*(3*p + 2)/5
Let d be (105/(-42))/((-10)/4)*0. Factor -23*y + 54 - 5*y + d*y + 5*y**2 - 77*y + 46.
5*(y - 20)*(y - 1)
Let s(h) = -13*h**2 - 1047*h + 296. Let a(d) = -75*d**2 - 5236*d + 1479. Let j(q) = -2*a(q) + 11*s(q). Find n, given that j(n) = 0.
2/7, 149
Let x(j) = -2*j**3 + 4*j**2 + 18*j + 60. Let k be x(-5). Suppose 0 = k*r - 321*r + 4. Factor -8/9*w + 0 + 0*w**2 - 2/9*w**r + 2/3*w**3.
-2*w*(w - 2)**2*(w + 1)/9
Let -1/6*h**2 + 64*h + 386/3 = 0. What is h?
-2, 386
Suppose 105*u**2 - 4502*u**3 + 89*u - u**4 + 9*u + 4508*u**3 = 0. What is u?
-7, -1, 0, 14
Let n = -237265 + 474531/2. Determine l so that -169/2*l + 13*l**2 + 0 - n*l**3 = 0.
0, 13
Let f = -6526 - -6543. Let l(h) be the first derivative of 1/9*h**3 + 0*h + 1/2*h**2 - f. Factor l(q).
q*(q + 3)/3
Factor -g**2 + 17/2 + 135/4*g.
-(g - 34)*(4*g + 1)/4
Factor 100/13*d + 48/13 - 18/13*d**2.
-2*(d - 6)*(9*d + 4)/13
Suppose 22*q - 23*q = -16. Let a be (0/(q/(-12)*3))/2. Factor a*r**2 + 0*r + 1/6*r**5 + 1/6*r**3 + 0 - 1/3*r**4.
r**3*(r - 1)**2/6
Let z(i) be the first derivative of i**6/11 - 112*i**5/55 + 192*i**4/11 - 2372*i**3/33 + 1581*i**2/11 - 1260*i/11 + 4156. Solve z(k) = 0 for k.
2/3, 3, 5, 7
Factor 98003 - 3*p**5 + 2*p**5 + 330*p**4 + 476422 + 100740*p**2 + 10875*p**3 + 4*p**5 + 364560*p - 113433.
3*(p + 4)**3*(p + 49)**2
Let z(c) be the second derivative of c**7/6300 - c**6/180 + 181*c**4/12 + 15*c + 1. Let l(p) be the third derivative of z(p). Factor l(b).
2*b*(b - 10)/5
Let b = -694123 - -2082467/3. Determine u, given that b + 2/3*u**2 + 28/3*u = 0.
-7
Factor -22/7*w**2 + 162 + 2/7*w**3 - 90/7*w.
2*(w - 9)**2*(w + 7)/7
Suppose -2*t = -4*b + 8, 2*b - 2*t - 4 = -b. Let z = 12 - b. Determine o, given that 2*o**4 + 6 + 8*o**3 - 4*o**4 - z*o - o**2 - 3*o**2 = 0.
-1, 1, 3
Solve -472*c - 10839*c**2 + 5417*c**2 + 474 + 5420*c**2 = 0 for c.
-237, 1
Let d = -37410/7 - -489130/91. Factor 4/13*z**2 - d + 2/13*z**3 - 110/13*z.
2*(z - 8)*(z + 5)**2/13
Suppose -34*n = -44*n + 3310. Let i = -326 + n. Factor -1/6*x**4 + 5/6*x**2 + 0 - 1/2*x**3 - 1/3*x + 1/6*x**i.
x*(x - 1)**3*(x + 2)/6
Suppose -7*p = 162 - 449. Find j, given that -11 + 4*j**2 + 4*j + p + j**2 + 21*j = 0.
-3, -2
Let w(v) be the first derivative of 13/3*v + 11/12*v**2 + 161 - 1/18*v**3. Factor w(t).
-(t - 13)*(t + 2)/6
Suppose -115*m + 518 = 587 - 1104. Let u(x) be the third derivative of 0*x**4 + 0*x - 1/660*x**6 + 0*x**5 + 0*x**3 + m*x**2 + 0 - 1/1155*x**7. Factor u(a).
-2*a**3*(a + 1)/11
Suppose -3*a = 0, 4*a = 45*n - 49*n + 1312. Suppose 60*d - n = -22*d. Factor -4/5*s**2 + d*s - 24/5.
-4*(s - 3)*(s - 2)/5
Let w(f) be the first derivative of f**5/4 + 5*f**4/8 - 125*f**3 - 5005*f**2/4 + 11495*f/4 - 5691. Suppose w(k) = 0. What is k?
-11, 1, 19
Let r = 54929 + -54921. Factor 58/7 + r*q - 2/7*q**2.
-2*(q - 29)*(q + 1)/7
Suppose -114/11*n**3 - 18/11*n**4 + 58/11*n - 26/11*n**2 - 12/11 = 0. What is n?
-6, -1, 1/3
Suppose 15 = -a - 7. Let s = -20 - a. Let 4*d + 16*d**2 - 14*d**s - 8 + 2 = 0. What is d?
-3, 1
Let h = -5/69 + 27/161. Let j(c) be the first derivative of 2/7*c + 1/14*c**4 - 1/7*c**2 - h*c**3 + 12. Factor j(l).
2*(l - 1)**2*(l + 1)/7
Let u be (-1)/4 + (-252)/(-48). Determine t, given that -269*t**3 + 134*t**2 - 7*t**u + 56*t**4 - 3*t**3 + 52*t**2 + 11*t**5 + 102*t**2 = 0.
-18, 0, 2
Let p = -34503 + 517546/15. Let v(t) be the first derivative of 0*t + 1/10*t**2 + 1/25*t**5 - p*t**3 - 1/20*t**4 - 17. Factor v(o).
o*(o - 1)**2*(o + 1)/5
Let d = 124671 - 498681/4. Factor -d*k + 0 + 1/4*k**3 - 1/2*k**2.
k*(k - 3)*(k + 1)/4
Suppose -238 = -7*f - 189. Suppose 5*i + c - f = 0, -i - 4*c + 8 = -6*c. Factor 0*d - 4/7*d**i - 10/7*d**4 - 2*d**3 + 0.
-2*d**2*(d + 1)*(5*d + 2)/7
Suppose -6 = -12*o + 6*o. Let y be o/12 - (-10)/(-120). Factor -5/4*c**2 + 0 + y*c.
-5*c**2/4
Suppose -41*w + 68 = -24*w. Factor 53*n**2 + 96*n - 43*n**2 + n**4 + 102*n**3 + 17*n**w + 166*n**2.
2*n*(n + 3)*(3*n + 4)**2
Factor 0*n - 14/17*n**3 + 124/17*n**2 + 0.
-2*n**2*(7*n - 62)/17
Let 24/7*z**4 - 132/7*z**2 + 0 - 26/7*z**3 - 2/7*z**5 - 80/7*z = 0. Calculate z.
-1, 0, 4, 10
Let i(y) be the second derivative of y**7/14 + 11*y**6/10 - 213*y**5/20 + 137*y**4/4 - 55*y**3 + 48*y**2 + 214*y - 2. Find m, given that i(m) = 0.
-16, 1, 2
Let m be (-12)/(-4) - ((-3)/(-1) + -2). Factor -i - 7 - 3*i + 6*i**2 + 5 - 8*i**m.
-2*(i + 1)**2
Suppose 3*n + 4*g = 436, 4*n - 575 = -0*g + g. Suppose 2*j = -n + 148. Factor 0 + 3/8*u + 1/8*u**3 + 1/2*u**j.
u*(u + 1)*(u + 3)/8
Solve -1248*q**2 - 2487/2*q + 9/2 = 0.
-1, 3/832
Let d be 63/24 - -1 - 3/(-8). Suppose -4*m + m = d*m. Suppose 16/3*z + 44/3*z**3 + 10/3*z**4 + m + 56/3*z**2 = 0. What is z?
-2, -2/5, 0
Find w such that -1539/4 - 15/4*w**2 - 3849/2*w = 0.
-513, -1/5
Let z(t) be the second derivative of 0*t**3 + 0*t**2 + 3/20*t**5 - 43*t + 0*t**6 - 1/42*t**7 - 1/6*t**4 + 0. Factor z(s).
-s**2*(s - 1)**2*(s + 2)
Let k(f) be the first derivative of -f**4/22 + 14*f**3/33 - 2*f**2/11 - 80*f/11 - 944. Factor k(v).
-2*(v - 5)*(v - 4)*(v + 2)/11
Determine p, given that -1/8*p**2 - 89042 - 211*p = 0.
-844
Let l(w) = -54*w + 237. Let o(q) = q**2 - 162*q + 713. Let u(c) = -8*l(c) + 3*o(c). Factor u(v).
3*(v - 9)**2
Let k = -63 + 66. Let y be k*8/(-24)*-4. Suppose 16/3*s**2 + 4/3*s**3 - 16/3*s - 4/3*s**y + 0 = 0. What is s?
-2, 0, 1, 2
Find w such that -29/3*w**5 - 137/3*w**4 - 179/3*w**2 - 79*w**3 - 50/3*w + 0 = 0.
-50/29, -1, 0
Suppose -1599*x + 1793*x - 582 = 0. Determine v, given that 4/7*v + 0*v**x + 0 + 6/7*v**2 - 2/7*v**4 = 0.
-1, 0, 2
Let d be ((-44)/(-748))/((-95)/(-969)). Factor -3072/5 - d*t**2 + 192/5*t.
-3*(t - 32)**2/5
Let i be ((-228)/(-2470))/(21/910). Suppose 0 + 44/13*c + 330/13*c**3 - 14/13*c**5 - 122/13*c**i - 238/13*c**2 = 0. What is c?
-11, 0, 2/7, 1
Let i(v) be the first derivative of -9*v**6/2 - 2358*v**5/5 + 1581*v**4/4 - 88*v**3 + 2122. Factor i(w).
-3*w**2*(w + 88)*(3*w - 1)**2
Solve 0*u + 8/11*u**3 + 0 - 24/11*u**2 + 2/11*u**4 = 0.
-6, 0, 2
Let w = -2/3699 + 824/3699. Determine x so that -2/9*x - 2/9*x**4 + w*x**3 + 0 + 2/9*x**2 = 0.
-1, 0, 1
Let a(j) be the first derivative of j**6/540 + 7*j**5/90 - 5*j**4/12 + 5*j**3 + 2*j + 52. Let v(c) be the third derivative of a(c). Factor v(l).
2*(l - 1)*(l + 15)/3
Factor 1/8*y**3 - 149/8*y + 71/8*y**2 - 219/8.
(y - 3)*(y + 1)*(y + 73)/8
Let f = 257 - 138. Suppose 0 = -5*y - f + 129. Factor 2*j**3 + 2*j**y + 2/3*j + 0 + 2/3*j**4.
2*j*(j + 1)**3/3
Let z(d) be the third derivative of -d**7/10080 + d**6/160 + 23*d**4/8 - 10*d**2 + 3*d. Let v(b) be the second derivative of z(b). What is p in v(p) = 0?
0, 18
Let k = -721 - -724. Suppose 498*w**4 + 0*w**k - 500*w**4 + 10*w**2 - 8*w**3 = 0. What is w?
-5, 0, 1
Let -14*s**2 - s + s**3 + 1633 + 1648 - 3267 = 0. Calculate s.
-1, 1, 14
Factor -44/13 - 10*d - 126/13*d**2 + 2/13*d**4 - 38/13*d**3.
2*(d - 22)*(d + 1)**3/13
Let c(u) be the third derivative of 14/3*u**3 + 7*u**2 + 0 - 14*u + 1/6*u**4 - 1/30*u**6 - 7/15*u**5. Find p, given that c(p) = 0.
-7, -1, 1
Let w(x) be the second derivative of x**6/60 - x**5/10 - 119*x**4/8 + 282*x**3 - 756*x**2 + 770*x + 7. Determine m, given that w(m) = 0.
-21, 1, 12
Let g(p) be the second derivative of -84*p - 25/8*p**2 + 5/12*p**3 + 0 - 1/48*p**4. Determine k, given that g(k) = 0.
5
Let i = -491/2 + -407/6. Let y = 314 + i. Determine w so that 4/3*w**3 + y*w**4 + 0*w + 2/3*w**2 + 0 = 0.
-1, 0
Determine p so that 4/19*p**3 - 2/19*p**5 - 4/19 - 4/19*p**4 - 2/19*p + 8/19*p**2 = 0.
-2, -1, 1
Suppose -32/3*k**2 + 0 - 4/3*k**4 + 44/3*k**3 - 80/3*k = 0. Calculate k.
-1, 0, 2, 10
Let y(j) be the second derivative of -3*j**5/140 - 73*j**4/21 - 97*j**3/42 - 2046*j. Find f, given that y(f) = 0.
-97, -1/3, 0
Let m(t) = 6*t - 1