20. Let r(z) = 1215*z**3 - 17137*z**2 + 51000*z + 69328. Let o(s) = -35*r(s) + 8*t(s). Solve o(u) = 0.
-1, 68/9
Let h(o) be the third derivative of o**6/660 - 13*o**5/330 + 5*o**4/22 - 2*o**2 - 2476. Find g such that h(g) = 0.
0, 3, 10
Let z(o) = 2*o**3 - 521*o**2 - 528*o - 65. Let g(f) = -10*f**3 + 2604*f**2 + 2640*f + 338. Let b(r) = -10*g(r) - 52*z(r). Factor b(p).
-4*p*(p - 264)*(p + 1)
Let h(y) be the second derivative of 4*y**2 + 11 - 8/3*y**3 + 1/5*y**5 - 1/15*y**6 + 1/2*y**4 - 2*y. Let h(l) = 0. What is l?
-2, 1, 2
Let m = -34341 + 34341. Let n(f) be the second derivative of 0 - 1/8*f**3 + 2*f + 1/48*f**4 + m*f**2. Solve n(j) = 0.
0, 3
Suppose -5*g + 10 = 5*q, -2*q + 4 = 3*g + 3*q. Let d be (2/4)/(29/116). Factor -15/2*y**d + 15/2 + 3/2*y - 3/2*y**g.
-3*(y - 1)*(y + 1)*(y + 5)/2
Let k = 71446/15 + -4763. Let f(a) be the second derivative of 0 - a**2 + 1/21*a**7 + 1/3*a**3 - 1/5*a**5 + 1/3*a**4 - k*a**6 + 19*a. Factor f(v).
2*(v - 1)**3*(v + 1)**2
Let r(n) = -40*n**4 + 55*n**3 - 903*n**2 - 1085*n + 1922. Let x(k) = 13*k**4 + 2*k**3 + 2*k**2. Let m(y) = 2*r(y) + 6*x(y). Find h, given that m(h) = 0.
-2, 1, 31
Let o = 202 + -196. Let v(n) = -16*n**3 - 11*n**2 - 6*n. Let p(i) = 2*i + i**2 + 3*i**3 - i + i**2. Let j(u) = o*v(u) + 33*p(u). Factor j(b).
3*b*(b - 1)*(b + 1)
Let k be (-6)/(-36) + (-2)/((-48)/44). Factor 47 + r**k - 6*r**2 + 69 + 4 + 115*r.
-5*(r - 24)*(r + 1)
Let x be ((-175)/(-20))/(14/16). Let q(t) be the first derivative of -2/9*t**3 + 1/6*t**4 + 1/9*t**2 + 0*t - 2/45*t**5 - x. Suppose q(z) = 0. Calculate z.
0, 1
Let n be 15/(-1) - (-1551)/99. Let j(p) be the first derivative of -p**4 + 4/3*p**3 + 0*p**2 - 4/5*p**5 + 0*p + n*p**6 - 8. Factor j(t).
4*t**2*(t - 1)**2*(t + 1)
Suppose 53*t - 335 = -14*t. Let q(r) be the first derivative of -4 + 2/3*r**6 + 8/3*r**3 - 8/5*r**t + 0*r + 0*r**4 - 2*r**2. Find p such that q(p) = 0.
-1, 0, 1
Let u = -458814 - -458816. Factor -24/11 + 2*f + 2/11*f**u.
2*(f - 1)*(f + 12)/11
Let y(p) be the third derivative of -1/80*p**5 + 5/48*p**4 - 1/480*p**6 - 109*p**2 + 0*p + 0*p**3 + 0. Determine i, given that y(i) = 0.
-5, 0, 2
Let x(z) be the second derivative of z**6/630 + 4*z**5/35 + 22*z**4/21 + 38*z**3/3 - 122*z. Let f(l) be the second derivative of x(l). Factor f(m).
4*(m + 2)*(m + 22)/7
Let c(z) be the second derivative of -162*z**2 - 1/10*z**6 - 39/20*z**5 - 135/2*z**3 + 22*z - 2 - 63/4*z**4. Let c(o) = 0. What is o?
-4, -3
Suppose 0 = -2*l + 87 - 51, 5*d + 2*l - 36 = 0. Factor d*k + 1/4*k**5 - k**4 + 0*k**2 + 0 + 0*k**3.
k**4*(k - 4)/4
Let u(g) = -6*g**2 - 10*g + 6. Let c(t) = 10 - 3 - t + t**2 - 4 + 0*t**2 - 2. Let b = -5 + -5. Let w(y) = b*c(y) - u(y). Suppose w(j) = 0. Calculate j.
1, 4
Suppose 26*z - 31*z = -35. Suppose -1 = z*a - 36. Find m, given that 5*m + a*m**3 - m**4 + 5*m**2 - 4 - 24*m - m**5 + 15*m = 0.
-2, -1, 1, 2
Factor -31/5 - 1/5*z**3 - 29/5*z**2 + 61/5*z.
-(z - 1)**2*(z + 31)/5
Let x = -28 + 28. Suppose 25 = q + 5*i + 3, x = q + 3*i - 18. Solve 3*c**2 - 19*c + q + 3*c + c**2 = 0.
1, 3
Let m = 297844 - 297844. What is c in m - 8/5*c**2 + 2/5*c**3 + 8/5*c = 0?
0, 2
Factor 192*z**2 - 1930*z - 769643 - 63552*z + 10328318 - 30310*z + 10112*z.
3*(8*z - 1785)**2
Suppose -14 = -2*w - 2*u, -4*w - 2*u + 3 = -15. Solve -11*x**w - 44*x + 2*x**3 + 3*x**2 + 50*x = 0.
0, 1, 3
Let b(j) = -58*j**2 + 4*j - 12. Let l be b(3). Let q = l + 524. What is v in 2/5*v**3 - 2/5*v**4 + 0*v + 0 + 0*v**q = 0?
0, 1
Let u(h) be the second derivative of -h**4/4 - 225*h**3 - 151875*h**2/2 - 2*h + 330. Factor u(y).
-3*(y + 225)**2
Let 4/3*q**5 + 2/3*q**2 + 4/3*q**3 + 0 - 4/9*q - 26/9*q**4 = 0. What is q?
-1/2, 0, 2/3, 1
Let g = -236 - -240. Let a(i) be the second derivative of 1/252*i**7 - 1/180*i**6 + 0 - 21*i + 1/36*i**g + 1/36*i**3 - 1/60*i**5 - 1/12*i**2. Solve a(y) = 0.
-1, 1
Let i = 20857 + -20833. Let c(k) be the second derivative of 0 - i*k - 1/2*k**3 + 3/20*k**5 + 1/60*k**6 - 5/4*k**2 + 1/6*k**4. Factor c(a).
(a - 1)*(a + 1)**2*(a + 5)/2
Suppose -15*j - 21*j + 28 = -29*j. Let p(v) be the first derivative of 0*v + 1/7*v**2 - 1/14*v**j + 0*v**3 + 26. Factor p(y).
-2*y*(y - 1)*(y + 1)/7
Suppose 5*d = -38 + 48. What is l in 5 + 1172*l - 1177*l - 4*l**2 + 5*l**3 - l**d = 0?
-1, 1
Let q = -1512 - -1512. Let k(r) be the first derivative of 2/9*r**6 - 16 + 0*r - 1/3*r**4 + q*r**2 + 4/9*r**3 - 4/15*r**5. Factor k(a).
4*a**2*(a - 1)**2*(a + 1)/3
Solve 207*h**3 - 206*h - 211*h**3 - 546*h - 484 - 144*h**2 - 500 + 24 = 0.
-30, -4, -2
Let a(u) be the third derivative of -u**6/1080 + u**5/45 - u**4/6 - 29*u**3/3 + u**2 - 7. Let g(x) be the first derivative of a(x). Factor g(t).
-(t - 6)*(t - 2)/3
Suppose -2*f = 4*r - 88, -3*r + f + 124 = 2*r. Factor 12*u - 5*u**4 - 3*u**4 - 51*u**2 + 35 + 5*u**4 + r*u**2 - 18*u**3 + 1.
-3*(u - 1)*(u + 2)**2*(u + 3)
Let a = 63 + -73. Let c be 5 + -2 + 5/a*-622. Factor -c + 23*r - 18*r**2 + 290 + 3*r**3 + 13*r.
3*(r - 2)**3
Let k(v) = -v**2 + 11*v - 23. Let m be k(6). Suppose -27 = m*l - 16*l. Factor -5*b**2 - b**l - b**4 + 5*b**5 - 4*b**3 + 6*b**4.
5*b**2*(b - 1)*(b + 1)**2
Let y = 1/149897 - -449683/1199176. Factor 39/4 + 45/8*w + y*w**2.
3*(w + 2)*(w + 13)/8
Let h(p) = -p**3 - p**2 - 2*p + 1. Let z(l) = l**4 + l**3 - 10*l + 5. Let a(j) = 5*h(j) - z(j). Factor a(v).
-v**2*(v + 1)*(v + 5)
Let c(m) be the third derivative of -m**7/840 + 13*m**6/240 - 9*m**5/10 + 81*m**4/16 + 243*m**3/8 - 2287*m**2. Let c(w) = 0. Calculate w.
-1, 9
Factor 2042*x**3 - 10693735 - 8786*x**3 - 2898645*x**2 - 622761 + 42593*x**2 - 4*x**4 + 3916838*x - 15260246*x.
-4*(x + 2)**2*(x + 841)**2
Let h(v) be the third derivative of 31 + v**2 - 1/15*v**4 + 1/100*v**5 + 0*v - 1/1050*v**7 + 2/15*v**3 + 1/300*v**6. Suppose h(n) = 0. What is n?
-2, 1, 2
Let d be (-20922)/122045*(-14)/4. Factor 6/5*b**3 + 3/5 - 9/5*b**4 - 9/5*b + 6/5*b**2 + d*b**5.
3*(b - 1)**4*(b + 1)/5
Let s(n) = -2*n**3 - 3*n**2 + n + 2. Let z(v) = -18*v**3 + 60*v**2 + 105*v + 27. Let x(j) = -3*s(j) + z(j). Suppose x(u) = 0. What is u?
-1, -1/4, 7
Let i(f) = -7*f**3 - 2365*f**2 - 1858111*f - 487443401. Let n(y) = 10*y**3 + 2367*y**2 + 1858113*y + 487443400. Let u(a) = 3*i(a) + 2*n(a). Factor u(b).
-(b + 787)**3
Let v be -1 + 7/3 - ((254 - 250) + (-10)/3). Determine k, given that -2/3*k + v*k**3 + 4 - 14/3*k**2 + 2/3*k**4 = 0.
-3, -1, 1, 2
Suppose -2*k + 3*c = -18, -2*k + 6*c + 22 = 2*c. Factor 0*g - 8*g**2 + k*g - 7 + 9*g - 5 + 8*g.
-4*(g - 1)*(2*g - 3)
Let u be (3/(-12))/((-1020)/34). Let k(g) be the third derivative of -1/9*g**3 + u*g**6 - 1/72*g**4 + 0 + 1/45*g**5 + 0*g - 4*g**2. Suppose k(t) = 0. What is t?
-1, 2/3
Let u be (-12)/14*(-40 - (-30 - 161/21)). What is n in 68/11*n**3 - 640/11*n**u + 0 + 1024/11*n - 2/11*n**4 = 0?
0, 2, 16
Let m(v) = -5*v**3 + 12*v**2 + 53*v + 48. Let k(w) = 16*w**3 - 38*w**2 - 160*w - 146. Let f(t) = -3*k(t) - 10*m(t). Let f(s) = 0. Calculate s.
-3, -1, 7
Let h(d) be the first derivative of d**6/3 + 2*d**5 - 2*d**4 - 40*d**3/3 - 1709. Determine q so that h(q) = 0.
-5, -2, 0, 2
Suppose 191 - 4571 = -12*p. Factor 85*j + 16*j**2 - 698 - 68*j + 610 - p*j.
4*(j - 22)*(4*j + 1)
Suppose 20*p + 10*p = 60. Suppose -14*y**p - 2*y + 19*y**2 + 32*y = 0. What is y?
-6, 0
Suppose -24 = -2*f, c + 5*f = -c - 23839 + 23899. Let -2/9*n**5 + c - 2/9*n**3 - 2/3*n**2 + 4/9*n + 2/3*n**4 = 0. Calculate n.
-1, 0, 1, 2
Let f be -2 + -1 - (-13 - (0 - -2)). Suppose d - 16 = f. Determine k so that 12*k**3 + 3*k**4 + 15*k**2 + 22*k**2 - d*k**2 = 0.
-3, -1, 0
Let x(t) = -116*t**4 + 8*t**3 - 25*t**2 + 16*t - 3. Let k(a) = -78*a**4 + 9*a**3 - 24*a**2 + 17*a - 4. Let r(d) = 3*k(d) - 2*x(d). Factor r(u).
-(u - 2)*(u - 1)**2*(2*u - 3)
Let c(p) be the first derivative of -3/4*p**4 - 864*p**2 - 164 + 48*p**3 + 0*p. Determine j so that c(j) = 0.
0, 24
Let c(q) be the second derivative of q**8/57120 - q**7/3570 + q**6/680 - q**4/4 - q**2/2 + 48*q. Let b(u) be the third derivative of c(u). Factor b(y).
2*y*(y - 3)**2/17
What is g in 3*g + 4*g**5 - 96 - g**5 - 34*g**3 - 34*g**3 - 96*g**4 + 192*g**2 + 62*g**3 = 0?
-1, 1, 32
Let k(g) = -16*g + 32. Let q(m) = 24*m - 49. Let v(t) = 8*k(t) + 5*q(t). Let z be v(1). Solve 9/7*x**2 + 1/7*x**z + 24/7*x + 16/7 = 0.
-4, -1
Let k(m) = 30*m**3 - 123*m**2 + 11*m + 6. Let z be k(4). Factor 1/5*v**2 - 9/5*v - z.
(v