t -21/8*q**4 - 9/4*q**3 - 45/8 + 33/4*q**2 + 21/8*q - s*q**5 = 0.
-5, -3, -1, 1
Let h(d) = 15*d + 15. Let z be h(-1). Suppose -13*i + 35 - 9 = z. Determine x, given that -33/8*x - 23/4*x**i - 9/8*x**4 - 1/8*x**5 - 9/8 - 15/4*x**3 = 0.
-3, -1
Let z(b) be the third derivative of b**8/560 + b**7/70 - 7*b**6/200 - 41*b**5/100 - 3*b**4/4 - b**2 + 52*b. What is d in z(d) = 0?
-5, -2, -1, 0, 3
Let g be ((-986)/(-1015) + -1)*(-5)/1. Let 30/7*f**2 - g*f**3 - 225/7*f + 0 = 0. Calculate f.
0, 15
Let 14/9*u**4 - 2/9*u**5 - 86/9*u**2 + 2/9*u**3 + 0*u + 8 = 0. Calculate u.
-2, -1, 1, 3, 6
Let c(o) be the first derivative of o**6/1020 + o**5/102 - o**4/34 - o**2 - 22. Let v(b) be the second derivative of c(b). Find s, given that v(s) = 0.
-6, 0, 1
Suppose 0*h - 2*h - 50 = -2*a, 83 = 3*a + h. What is r in 37329*r**2 + a*r**3 - 37329*r**2 - 3*r**4 = 0?
0, 9
Let s(r) be the second derivative of 0*r**2 - 1/2*r**6 - 2*r**5 + 0 - 35/12*r**4 - 5/3*r**3 + 20*r. Factor s(i).
-5*i*(i + 1)**2*(3*i + 2)
Let i = 11972 + 412. Factor 60*d - 5*d**4 + i - 28*d**2 - 37*d**2 - 12404 + 30*d**3.
-5*(d - 2)**2*(d - 1)**2
Suppose -4*z = -n - 2*z + 30, 3*n - 4*z = 96. Factor -872*i + 10*i**2 + 18*i**2 + 864*i + n*i**3.
4*i*(i + 1)*(9*i - 2)
Let j be 208/(-364)*147/(-6). Let z(y) be the first derivative of -4/13*y**2 + 2/39*y**3 + 6/13*y - j. Factor z(p).
2*(p - 3)*(p - 1)/13
Let g be 3 + 1*(-33)/9 + (-93)/(-27). Let f(i) be the second derivative of 0 + 1/54*i**4 - 10/27*i**3 + 9*i + g*i**2. Determine x, given that f(x) = 0.
5
Suppose 0*l + 2*l - 112 = 0. Let m = 58 - l. Factor 50*w + 15*w + 26*w**3 - 120*w**2 + 7*w + m*w**5 + 20*w**4.
2*w*(w - 1)**2*(w + 6)**2
Let o(t) be the first derivative of 140/3*t**3 + 25/2*t**4 + t**5 - 129 + 60*t**2 + 0*t. Suppose o(g) = 0. What is g?
-6, -2, 0
Let u(k) = 2*k**5 + k**4 + k**3 + 2*k + 1. Let f(o) = -17*o**5 - 14*o**4 - 7*o**3 + 8*o**2 - 18*o - 9. Let r(b) = 4*f(b) + 36*u(b). Factor r(i).
4*i**2*(i - 4)*(i - 2)*(i + 1)
Let y = -15483/77 + 2259/11. Find f, given that 2/7*f**2 - y*f - 32/7 = 0.
-1, 16
Suppose -3*i = r - 432 - 552, 0 = 3*i - 4*r - 969. Suppose 321*x - i*x = -18. Let -3/2*a**4 + 3*a**2 - 3/2*a**5 + x*a**3 - 3/2 - 3/2*a = 0. What is a?
-1, 1
Let j(y) be the second derivative of -y**6/1800 - 7*y**5/150 + 29*y**4/120 - 50*y**3 - 4*y - 41. Let x(c) be the second derivative of j(c). Factor x(r).
-(r - 1)*(r + 29)/5
Let n(r) be the third derivative of r**5/270 + 37*r**4/108 + 160*r**3/27 - 2307*r**2. Factor n(b).
2*(b + 5)*(b + 32)/9
Let k(r) be the second derivative of 53*r**4/54 + 104*r**3/27 - 4*r**2/9 + 6*r + 20. Suppose k(x) = 0. Calculate x.
-2, 2/53
Let z(x) be the third derivative of -x**5/360 + 37*x**4/144 - 40*x**3/9 - 89*x**2 - 4*x + 7. Factor z(b).
-(b - 32)*(b - 5)/6
Let x(v) = -3*v**4 + 96*v**3 + v**2 - 96*v + 4. Let p(h) = 4*h**4 - 96*h**3 - h**2 + 96*h - 6. Let m(c) = 2*p(c) + 3*x(c). Determine g, given that m(g) = 0.
-1, 0, 1, 96
Let q(x) be the second derivative of 5*x**7/42 - 19*x**6/12 + 25*x**5/8 - 5*x**4/3 - 331*x + 1. Suppose q(n) = 0. What is n?
0, 1/2, 1, 8
Let k(o) be the first derivative of o**4/2 + 242*o**3/3 + 4047*o**2 + 45486*o + 2463. Solve k(i) = 0.
-57, -7
Let g(w) be the third derivative of -w**6/120 - w**5/60 - w**4 - 28*w**2. Let m(k) = -k**3 - k**2 + k. Let x(u) = g(u) - 6*m(u). Let x(a) = 0. Calculate a.
-3, 0, 2
Factor -1/6*f**2 - 175/3 - 19/2*f.
-(f + 7)*(f + 50)/6
Let h(v) = -v**2 + 22*v - 40. Let s be h(20). Suppose -k = c - 6*k - 14, -4*c - 2*k + 12 = s. Suppose c*r**2 - 30 + 0*r + 46 + 16*r = 0. Calculate r.
-2
Let h(s) be the second derivative of -s**4/3 - 800*s**3 - 720000*s**2 - 8*s - 1. What is p in h(p) = 0?
-600
Let g(b) be the third derivative of -b**5/120 - 16*b**4/3 - 4096*b**3/3 - 50*b**2 + 9. Factor g(m).
-(m + 128)**2/2
Let c be 147 + 1 + 2 + 0 + 0. Let n = c + 17. Find f, given that 0 - 3*f + 0 + 164*f**2 - n*f**2 = 0.
-1, 0
Let w(s) = 3*s - 1. Let a be w(1). Factor 466 - 103 + 3*d**a + 43*d + 23*d.
3*(d + 11)**2
Let h(v) be the first derivative of 2*v**3/3 - 7*v**2 - 88*v + 1130. Factor h(i).
2*(i - 11)*(i + 4)
Find w such that -56169 + 5*w**2 - 6*w**2 - 233*w + 113*w - 265*w - 89*w = 0.
-237
Let y be (-1209)/(-99) - 154/(-66). Let p = y + -988/77. Let 0 + p*v - 22/7*v**2 - 2/7*v**5 + 6/7*v**4 + 6/7*v**3 = 0. What is v?
-2, 0, 1, 3
Let c(n) be the second derivative of n**5/30 - 11*n**4/3 + 21*n**3 + 4*n + 501. Factor c(a).
2*a*(a - 63)*(a - 3)/3
Let j(g) be the first derivative of 3*g**4/4 + 15*g**3 - 24*g**2 - 55. Factor j(s).
3*s*(s - 1)*(s + 16)
Suppose -239*q = -c - 235*q - 2, 0 = -q + 2. Let r be c/3 - (-143)/231*-3. Determine v, given that -6/7 + r*v**2 + 1/7*v = 0.
-3, 2
Let x be (-50)/(10/2) + 9 + (-3375)/(-175). Let 7*f**5 + 0 - 32/7*f + x*f**2 - f**4 - 138/7*f**3 = 0. What is f?
-2, 0, 4/7, 1
Solve -155*b + 1/6*b**2 + 72075/2 = 0 for b.
465
Let l be (6 - 1) + -5 + 4. Suppose 2 = 11*u - 12*u + l*y, 0 = 4*u - 2*y - 6. Factor -4/11 + 2/11*k**u - 2/11*k.
2*(k - 2)*(k + 1)/11
Factor -13/3*k**3 + 13/3*k - 1/3*k**4 + 1/3*k**2 + 0.
-k*(k - 1)*(k + 1)*(k + 13)/3
Let s be 16 + (4*17/(-204))/(2/78). Factor 2/3*y**s + y**4 - 3*y**5 + 0*y + 0 + 0*y**2.
-y**3*(3*y - 2)*(3*y + 1)/3
Let t(n) = 2*n**2 - 14*n + 20. Let b = -9 - -29. Let g be t(b). Factor 147 - g - 120*j - 327 - 5*j**2.
-5*(j + 12)**2
Suppose -312*n = -54*n. Let a(o) be the second derivative of -10/3*o**3 + n + 4*o - 8*o**2 + 3*o**4. Factor a(k).
4*(k - 1)*(9*k + 4)
Let d(a) be the second derivative of -a**5/40 + 23*a**4/24 - 43*a**3/12 + 21*a**2/4 - 956*a. Factor d(z).
-(z - 21)*(z - 1)**2/2
Let r(p) be the third derivative of -2*p**7/945 - 2*p**6/135 - p**5/27 - p**4/27 + p**2 - 100*p. Factor r(q).
-4*q*(q + 1)**2*(q + 2)/9
Suppose 31*j - 30 = -5*d + 28*j, d = -2*j + 6. Let k be (-100)/(-350) + (-2)/d*0. Find w, given that k*w + 17/7*w**2 + 37/7*w**3 + 0 - 48/7*w**5 - 8/7*w**4 = 0.
-2/3, -1/4, 0, 1
Let x(d) be the second derivative of d**5/220 + 71*d**4/132 - 4*d - 160. Find r, given that x(r) = 0.
-71, 0
Let h be (-3)/3 + (0 + -5)/(-1). Find p, given that h*p**2 - 9 - 24*p + 19 + 22 = 0.
2, 4
Let u(v) be the first derivative of 2*v**6/3 - 32*v**5/5 + 23*v**4 - 112*v**3/3 + 24*v**2 - 813. What is j in u(j) = 0?
0, 1, 2, 3
Let s be 2*(3 + 2 + -5 + 1). Factor -195 - 3*j**2 + 168 + 2*j**s + 45*j + 37*j - 2*j**2.
-(j - 27)*(3*j - 1)
Determine u so that 291 - 70*u + 3*u**3 + 67*u - 52*u**2 - 89*u**2 - 51*u**2 - 99*u**2 = 0.
-1, 1, 97
Let r(p) = p**2 - 678*p + 619. Let c(j) = 2*j. Let y(d) = -116*c(d) - 4*r(d). Factor y(z).
-4*(z - 619)*(z - 1)
Let r(x) be the second derivative of 3*x**6/2 + 321*x**5/20 + 26*x**4 + 6*x**3 - 204*x. Factor r(j).
3*j*(j + 1)*(j + 6)*(15*j + 2)
Let t = -26 + 44. Suppose 5*x - 20 = y, -2*y - t = -x - 5. Factor -2*r**x + 3*r**2 - 18 + r**3 + 33 - 19.
-(r - 2)**2*(r + 1)
Let q(y) be the second derivative of y**6/30 - 7*y**5/20 - 199*y**4/12 - 533*y**3/6 - 171*y**2 + 4*y - 132. Solve q(b) = 0 for b.
-9, -2, -1, 19
Let t(d) = -9*d**3 + 224*d**2 - 266*d + 131. Let b(y) = -7*y**3 + 206*y**2 - 267*y + 132. Let g(z) = -5*b(z) + 4*t(z). Factor g(v).
-(v - 1)**2*(v + 136)
Let y = 73918 - 73908. Factor -35/2*m + y*m**2 - 245/3 - 5/6*m**3.
-5*(m - 7)**2*(m + 2)/6
Let j(d) be the third derivative of 0 + 0*d**6 + d**2 - 1/840*d**8 - 2/75*d**5 + 0*d**4 + 1/175*d**7 - 38*d + 0*d**3. Determine u so that j(u) = 0.
-1, 0, 2
Let s = 16/157 - 1592/3297. Let b = 23/42 + s. Suppose -1/2*r**2 - 1/6 - b*r**3 - 1/2*r = 0. What is r?
-1
Let d(c) be the second derivative of -10*c**4/3 + 2*c**3/3 + 18*c**2 - 2696*c. Suppose d(i) = 0. What is i?
-9/10, 1
Let l(o) = -o**2 - 2077*o + 4160. Let d be l(2). Factor -2/17*u**d + 12/17 - 2/17*u.
-2*(u - 2)*(u + 3)/17
Let l(v) be the second derivative of v**8/224 + v**7/140 - 3*v**6/80 - v**5/8 - v**4/8 + 3*v**2/2 - 77*v. Let k(a) be the first derivative of l(a). Factor k(b).
3*b*(b - 2)*(b + 1)**3/2
Let q(h) be the second derivative of -h**4/12 - 2*h**3/3 + 1569*h. Solve q(m) = 0.
-4, 0
Let w(n) = -9*n**2 - 73*n - 122. Let b(u) = -u**2 - 6*u - 1. Let k(s) = 24*b(s) - 3*w(s). Factor k(j).
3*(j + 6)*(j + 19)
Let r = 662100 + -662097. Factor -31/9*f + 5/3 - 1/9*f**r + 17/9*f**2.
-(f - 15)*(f - 1)**2/9
Suppose 351 + 117 = q. Let s(f) = -13*f - q - 4*f**2 + 544 + 36*f. Let h(i) = -5