285/3. Let 1/3*o**5 - 7/3*o**4 + l*o - 6*o**3 + 3 - 2/3*o**2 = 0. Calculate o.
-1, 1, 9
Suppose 676 = -2283*b + 2309*b. Let o(w) be the second derivative of 0 + 0*w**3 - b*w + 0*w**2 - 5/12*w**4 + 1/4*w**5. Find t, given that o(t) = 0.
0, 1
Let r be (-2)/(-13 - 876/(-68)). Let g(x) be the third derivative of 1/160*x**5 - 3/16*x**3 + 0 + 0*x - 1/32*x**4 + r*x**2. Determine c, given that g(c) = 0.
-1, 3
Determine w so that 79*w**4 - 100*w**3 + 41*w - 9*w + 69*w**4 - 22*w**3 - 134*w**4 + 76*w**2 = 0.
-2/7, 0, 1, 8
Find c such that 0 + 72*c - 158*c**3 + 204*c**2 - 7/3*c**5 + 103/3*c**4 = 0.
-2/7, 0, 3, 6
Factor -5808/7*p - 2/7*p**2 - 4216608/7.
-2*(p + 1452)**2/7
Let t(y) = 6*y**3 + 144*y**2 + 282*y + 136. Let d(s) = s**3 + s**2 + 2*s. Let a(g) = -4*d(g) + t(g). Factor a(b).
2*(b + 1)**2*(b + 68)
Let u = 174090 + -870446/5. Solve 56/5*b**2 - u*b**3 + 0*b + 0 = 0 for b.
0, 14
Let z(g) be the second derivative of -g**4/20 - 5*g**3 - 423*g**2/10 - 1163*g. Factor z(m).
-3*(m + 3)*(m + 47)/5
Factor -140*y + 31*y**4 - 1068*y**2 + 485*y**3 + 341*y + 139*y - 16*y**4 + 228*y**2.
5*y*(y - 1)*(y + 34)*(3*y - 2)
Let j(y) be the third derivative of y**8/336 - y**7/35 + y**6/15 + y**2 - 397. Factor j(r).
r**3*(r - 4)*(r - 2)
Let o(c) be the second derivative of 3*c**5/140 + 25*c**4/14 - 52*c**3/7 + 1314*c + 1. Factor o(d).
3*d*(d - 2)*(d + 52)/7
Let y = 1876 - 1544. Let v be (-120)/16*(y/(-100) - -3). Suppose -v + 9/5*o**3 + 21/5*o + 42/5*o**2 = 0. What is o?
-4, -1, 1/3
Let u(i) be the second derivative of -i**7/210 + i**6/90 + 4*i**5/15 - 2*i**4 + 53*i**3/6 + 30*i + 1. Let o(x) be the second derivative of u(x). Factor o(v).
-4*(v - 2)**2*(v + 3)
Let o(h) be the first derivative of h**4/2 + 298*h**3 + 446*h**2 + 2946. Factor o(g).
2*g*(g + 1)*(g + 446)
Let g(m) be the first derivative of -m**5/330 - 5*m**4/44 - m**2 - 58. Let k(u) be the second derivative of g(u). Determine a, given that k(a) = 0.
-15, 0
Let v(b) be the second derivative of -b**4/16 + 121*b**3 - 403*b. Factor v(u).
-3*u*(u - 968)/4
Let x(l) be the second derivative of -23*l + 0*l**3 - 7/108*l**4 - 1/270*l**5 + 0 + 16*l**2. Let b(v) be the first derivative of x(v). Solve b(g) = 0 for g.
-7, 0
Let k(h) be the second derivative of h**7/105 - 8*h**6/15 + 213*h**5/50 - 51*h**4/5 - 6636*h. Suppose k(f) = 0. Calculate f.
0, 3, 34
Let f(o) be the first derivative of -8/7*o**2 + 0*o + 1/14*o**4 - 178 - 2/3*o**3. Factor f(n).
2*n*(n - 8)*(n + 1)/7
Let m be (160/(-60) - 17)*(0 + -3). Suppose -s = -j + 5, 57*j + 1 = m*j + s. Determine i so that 2/3*i**3 + 0*i + 0 + j*i**2 = 0.
-3, 0
Let w(u) = 6*u**2 - 32*u + 16. Suppose 5*p - 4*f = 19, 3*p - f + 8 = 6*p. Let d(o) = 2*o**2 - 11*o + 5. Let q(b) = p*w(b) - 8*d(b). Find r such that q(r) = 0.
2
Let u be (-418)/(-51) - 6 - 2. Let s = u - 1/34. Find n, given that 1/2*n**2 + 0 + s*n**4 - 1/6*n - 1/2*n**3 = 0.
0, 1
Let r(t) be the third derivative of -t**8/80640 + t**7/1008 - 5*t**6/144 - t**5/20 - 91*t**2. Let a(k) be the third derivative of r(k). Factor a(x).
-(x - 10)**2/4
Let n(s) = -3*s**2 - 340*s - 8744. Let o be 1/(-4) - (-153)/36. Let a(l) = 9*l**2 + 1016*l + 26233. Let v(y) = o*a(y) + 11*n(y). Suppose v(u) = 0. What is u?
-54
Suppose 4*q - 6 - 2 = 5*d, -4*q + 8 = -2*d. Factor -3*b - 9*b + q*b + b**2 + 14*b.
b*(b + 4)
Let i be -6 + 4*(-4)/(-16) + 125/25. Let h(c) be the first derivative of -2/45*c**5 + 0*c**3 - 42 + 0*c**2 - 1/18*c**4 + i*c. Solve h(l) = 0.
-1, 0
Let s be ((-37)/(3 - 225))/(20/64). Suppose s + 16/15*w + 2/5*w**2 = 0. Calculate w.
-2, -2/3
Let c(b) = -8*b**3 + 2*b**2 - 7*b. Let s = -4 - 3. Suppose 0 = -0*z - 5*z - 30. Let d(v) = 7*v**3 - 2*v**2 + 6*v. Let k(y) = s*d(y) + z*c(y). Factor k(o).
-o**2*(o - 2)
Let x(q) = 4*q**3 - 116*q**2 + 106*q + 212. Let w(r) = 8*r**3 - 234*r**2 + 215*r + 422. Let v(s) = 2*w(s) - 5*x(s). Factor v(a).
-4*(a - 27)*(a - 2)*(a + 1)
Let k(d) be the third derivative of d**7/210 - 13*d**5/30 + 2*d**4 - 32*d**3/3 - 251*d**2. Let o(a) be the first derivative of k(a). Factor o(g).
4*(g - 3)*(g - 1)*(g + 4)
Suppose 506*j - 46 = 504*j. Factor -2*m**5 + m**3 + 16*m - 146*m + 92*m**2 + 50 + 0*m**4 - j*m**4 + 3*m**3 + 9*m**4.
-2*(m - 1)**3*(m + 5)**2
Let i be (5/16)/((-3366)/(-6336)). Let 8/17*r**2 - i*r + 0 + 2/17*r**3 = 0. What is r?
-5, 0, 1
Let q(y) = -2*y**2 - 2 + y**2 - 5*y - 3 + 2. Let z be q(-3). Factor -20*a + 495 - 30*a**4 - 495 - 65*a**z - 5*a**5 - 60*a**2.
-5*a*(a + 1)**2*(a + 2)**2
Factor 85*g**2 + 172*g**2 + 362*g**3 + 62*g**2 - 112*g**3 - 67*g**2 - 2*g**4.
-2*g**2*(g - 126)*(g + 1)
Let o(f) = -f - 6*f**3 + 5*f**3 - 265 + 266. Suppose -a - 6 = -5. Let c(i) = 3*i**2 + 4*i - 2. Let r(l) = a*c(l) - 2*o(l). Factor r(n).
n*(n - 2)*(2*n + 1)
Suppose 4*o - 23 = 2*n - 19, 3 = 3*o. Let l(v) be the third derivative of 0*v**4 + 1/105*v**7 + n*v - 1/60*v**6 + 0*v**3 - 1/15*v**5 + 0 - 2*v**2. Factor l(s).
2*s**2*(s - 2)*(s + 1)
Let l(c) be the second derivative of -c**4/12 + 13*c**3/3 - 69*c**2/2 + 971*c. Factor l(u).
-(u - 23)*(u - 3)
Determine j, given that 1408/9*j**3 - 3818/3*j**2 - 486 + 1/3*j**5 + 148/9*j**4 - 1899*j = 0.
-27, -1, -1/3, 6
Suppose 42*v = 43*v + 43. Let m = v + 51. Find x, given that 4*x**3 + 14*x**4 + 16*x**5 - m*x**2 - 12*x**5 + 4*x**3 = 0.
-2, 0, 1/2
Let j(s) be the second derivative of 7*s**7/30 - 21*s**6/50 - 129*s**5/50 + 47*s**4/30 + 31*s**3/2 + 45*s**2/2 - 13019*s. What is x in j(x) = 0?
-1, 15/7
Suppose 221 = -45*a + 141*a - 180 + 305. Factor 1/4*z**2 + a - z.
(z - 2)**2/4
Let p(d) = 121*d + 125. Let o be p(-1). Let w be o/(-102)*3 - (-207)/459. Solve -2/3 + 1/3*i + 2/3*i**2 - w*i**3 = 0.
-1, 1, 2
Let p(j) = -j**4 - j**2 + 4*j + 1. Let n(o) = -o**5 + 126*o**4 + 241*o**3 + 128*o**2 - 28*o - 7. Let d(w) = -3*n(w) - 21*p(w). Factor d(z).
3*z**2*(z - 121)*(z + 1)**2
Let a = 106 + -106. Suppose -8 = -2*n - a*n. Solve 7*d**3 + 5*d**2 + 858*d - 863*d - 5*d**n - 2*d**3 = 0.
-1, 0, 1
Let t(p) be the third derivative of -p**6/40 - 74*p**5/5 + 167*p**2 - 11. What is s in t(s) = 0?
-296, 0
Suppose 9*a = 2 + 79. Factor -4*j**2 - 2*j + a*j**2 - j**3 - 8*j**2.
-j*(j + 1)*(j + 2)
Let g(f) be the third derivative of 1/5*f**6 - 4/105*f**7 + 3*f - 8/15*f**5 + 7*f**2 + 0*f**3 + 0 + 2/3*f**4 + 1/336*f**8. Factor g(x).
x*(x - 2)**4
Let r = -1064 + 1064. Suppose -3*u + 8 + 1 = r. Let 0*t - 1/8*t**u + 0 + 1/8*t**4 + 0*t**2 = 0. Calculate t.
0, 1
Let l = -221 + 224. Factor -h**l - 3*h**3 - 287*h + h**4 + 4*h**2 + 287*h.
h**2*(h - 2)**2
Let k = -418200 - -5436602/13. Factor 36/13 - k*u**3 - 4/13*u**2 + 18/13*u.
-2*(u - 3)*(u + 2)*(u + 3)/13
Let y be 1*(-44)/(-6)*(-32)/(-176). Let r = 358/81 - 7/81. Suppose -1/3 + r*o**3 - y*o**4 - 5*o**2 + 7/3*o = 0. What is o?
1/4, 1
Let s(v) be the first derivative of -16/5*v + 2*v**2 - 4/15*v**3 + 69. Factor s(p).
-4*(p - 4)*(p - 1)/5
Factor -2/7*x**3 - 170/7*x + 264/7 - 92/7*x**2.
-2*(x - 1)*(x + 3)*(x + 44)/7
Let y = -153/70 - -81/14. Solve -6/5*l**4 + 1/5*l**3 - 3*l + 2/5 + y*l**2 = 0 for l.
-2, 1/6, 1
Let d(v) be the second derivative of 0 + 100*v**2 - 25/2*v**4 + 198*v + 7/4*v**5 + 10/3*v**3 + 1/6*v**6. Factor d(o).
5*(o - 2)**2*(o + 1)*(o + 10)
Let v(i) be the third derivative of i**6/1080 - 7*i**5/540 + 7*i**4/108 - 4*i**3/27 + 10*i**2 - 64*i. Factor v(k).
(k - 4)*(k - 2)*(k - 1)/9
Factor -210*l**3 - 21840*l - 9104*l**2 - 796*l**2 - 1119*l**2 - l**4 - 10816 - 214*l**2.
-(l + 1)**2*(l + 104)**2
Let w be (-12932)/(-854) - (-2 - 8). Let f(h) be the first derivative of 81/14*h**4 - w*h**2 - 246/7*h**3 + 18 - 40/7*h. Let f(t) = 0. Calculate t.
-2/9, 5
Let q(p) be the first derivative of 3*p**5/20 + p**4 - 3*p**3/2 + 46*p**2 + 57. Let s(t) be the second derivative of q(t). Let s(c) = 0. What is c?
-3, 1/3
Let q(o) be the first derivative of 3*o**5/20 + 33*o**4/2 + 726*o**3 + 15972*o**2 + 60*o - 163. Let c(p) be the first derivative of q(p). Factor c(k).
3*(k + 22)**3
Factor -129/2*f + 1/2*f**2 - 198.
(f - 132)*(f + 3)/2
Let q(x) be the first derivative of 5*x**3/6 - 355*x**2/2 + 700*x - 585. What is o in q(o) = 0?
2, 140
Suppose -2*f = -3*z + 810, -4*f - 3*z = -9*f - 2043. Let s = f + 5347/13. Factor 6/13*j - s - 2/13*j**2.
-2*(j - 2)*(j - 1)/13
Let o(l) be the second derivative of l**6/420 + 13*l**5/210 + l**4/7 + 25*l**2 - l + 56. Let w(t) be the first derivative of o(t). L