- 12. Let s(v) = -4*h(v) - 5*r(v). Find j such that s(j) = 0.
-3, 2
Let p be (-10)/(-28)*(-8 + (-112)/(-10)). Suppose -8*h + 16*h**3 + 66/7*h**2 + p + 32/7*h**4 = 0. What is h?
-2, 1/4
Let g(d) be the third derivative of d**8/840 + d**7/175 + d**6/300 - d**5/50 - d**4/30 + d**2 + 40*d. Determine r, given that g(r) = 0.
-2, -1, 0, 1
Suppose -1/2*k**2 + 23/2*k + 70 = 0. Calculate k.
-5, 28
Let h = -31 + 25. Let u(a) = -a**5 - a**4 - a**3 + 1. Let q(g) = 3*g**5 - 7*g**4 - 9*g**3 + 4*g**2 + 3. Let b(d) = h*u(d) + 2*q(d). Find l such that b(l) = 0.
-1, 0, 2/3, 1
Suppose -26*y + 23*y - 28*y = 34*y. Factor 18/11*x + 2/11*x**3 - 12/11*x**2 + y.
2*x*(x - 3)**2/11
Factor -3/2*n**2 + 195/2*n + 0.
-3*n*(n - 65)/2
Let h(u) = -18*u - 52. Let m be h(-10). Let l = 904/7 - m. Find b such that l*b**4 - 4/7*b**5 + 0 + 0*b + 0*b**2 - 4/7*b**3 = 0.
0, 1
Let r be (-27)/(-24)*64/96. Solve 0*h - r*h**3 + 0 - 9/4*h**2 = 0.
-3, 0
Let x be (1075/75 - 15) + (-76)/(-42). Solve 2/7*o**3 + 8/7*o + x*o**2 + 0 = 0.
-2, 0
Let o(y) = 2*y**4 + 54*y**3 - 182*y**2 + 242*y - 116. Let f(g) = g**4 + 36*g**3 - 121*g**2 + 161*g - 77. Let k(b) = -8*f(b) + 5*o(b). Find q such that k(q) = 0.
1, 2, 3
Let w = 101/18 + -11/2. Let q(f) be the first derivative of -4 - w*f**3 + 0*f**2 + 1/3*f. Factor q(i).
-(i - 1)*(i + 1)/3
Let v be (-3 + (-7 - -12))/((-1)/(-2)). Let r be (24/(-112))/((-2)/v). Factor r*d**3 - 3/7*d**5 + 0*d + 3/7*d**4 - 3/7*d**2 + 0.
-3*d**2*(d - 1)**2*(d + 1)/7
Let r be (13/65)/((-1)/5). Let i be (-3)/6*54/(-1 + r). Factor 1/2*k**3 + 9/2*k**2 + 27/2*k + i.
(k + 3)**3/2
Let n(v) = 8*v**4 - 14*v**3 + 38*v**2 + 12*v + 6. Let d(p) = 7*p**4 - 14*p**3 + 35*p**2 + 10*p + 5. Let f(i) = -6*d(i) + 5*n(i). Factor f(t).
-2*t**2*(t - 5)*(t - 2)
Let y(j) be the third derivative of j**9/60480 - j**8/2240 + j**7/630 + j**5/15 - 3*j**2. Let m(u) be the third derivative of y(u). Let m(z) = 0. Calculate z.
0, 1, 8
Suppose 4/7*a**5 + 537824 + 117604/7*a**3 + 1184/7*a**4 + 1092112*a + 570920*a**2 = 0. Calculate a.
-98, -1
Suppose -4*r + 5*k - 2 = -1, 0 = 4*r - k + 13. Let p be ((-2)/(-6))/(r/(-24)). Factor -t**2 + 2 + 5*t**2 - 4*t**4 - p.
-4*t**2*(t - 1)*(t + 1)
Let y = -26478723/28805 - 186/4115. Let n = 921 + y. Factor -n*x**2 - 2/7 - 2/7*x**4 + 8/7*x + 8/7*x**3.
-2*(x - 1)**4/7
Let n(i) be the first derivative of 5*i**4/12 - 5*i**3/6 - 5*i**2 + 36*i - 28. Let k(u) be the first derivative of n(u). Suppose k(y) = 0. What is y?
-1, 2
Suppose -3*n = -6*n - 4*t + 156, n = 5*t + 33. Suppose -17*x + 5*x = -n. What is i in 0*i - 26/3*i**x - 14*i**5 + 0 - 4/3*i**3 + 0*i**2 = 0?
-1/3, -2/7, 0
Let t = 55 - 65. Let k = -20/3 - t. Factor k*d**4 + 2/3*d**5 + 0 + 16/3*d**3 + 8/3*d**2 + 0*d.
2*d**2*(d + 1)*(d + 2)**2/3
Suppose -4*l + 8*l + 4*h = 0, 21 = -3*l + 4*h. Let n be (120/(-50))/((l/5)/3). What is k in 44/7*k + 20/7*k**4 + 68/7*k**3 + 8/7 + n*k**2 = 0?
-1, -2/5
Factor 45/2*p**2 - 35/2*p + 5/2*p**4 - 25/2*p**3 + 5.
5*(p - 2)*(p - 1)**3/2
Factor 77*v + 54033 + 473*v - 54158 - 605*v**2.
-5*(11*v - 5)**2
Suppose 5*n - o = o, 5*o - 25 = 0. Suppose -58*h = -57*h - 3. Factor 5 - k**3 - 5*k - h - 4*k**4 + n*k**2 + k**5 + 5*k**3.
(k - 2)*(k - 1)**3*(k + 1)
Let t(i) = 15*i**3 + 5*i**2 - 35*i + 20. Let o(n) = -8*n**3 - 3*n**2 + 18*n - 10. Let v(u) = 6*u + 37. Let w be v(-7). Let s(y) = w*o(y) - 3*t(y). Factor s(h).
-5*(h - 1)**2*(h + 2)
Let t = 51790/3 + -17258. Determine s, given that -t*s**2 + 4/3*s**3 + 4*s + 0 = 0.
0, 1, 3
Let u(l) be the second derivative of 1/70*l**5 - 4*l - 2/7*l**3 + 0*l**2 - 1/42*l**4 + 0. Let u(o) = 0. What is o?
-2, 0, 3
Let r = -238 - -502. Factor -618*w**2 - r*w - 12 - 834*w**2 - 4 - 2662*w**3.
-2*(11*w + 2)**3
Factor -10227*g + 52*g**2 + 518*g**2 - 11433*g + g**3 + 274360 - 6*g**3.
-5*(g - 38)**3
Let z(h) be the third derivative of 5/18*h**3 + 1/72*h**6 - 1/36*h**5 + 0*h - 5/72*h**4 + 0 - h**2. What is f in z(f) = 0?
-1, 1
Let w(g) be the first derivative of -g**4/26 - 70*g**3/39 + 73*g**2/13 - 74*g/13 + 28. Solve w(x) = 0.
-37, 1
Let c(f) be the first derivative of -f**6/120 - f**5/60 + f**4/12 + 5*f**2/2 + 4. Let w(r) be the second derivative of c(r). Factor w(y).
-y*(y - 1)*(y + 2)
Let -24/5*w - 14/5*w**2 - 2/5*w**3 + 0 = 0. What is w?
-4, -3, 0
Let f(j) be the third derivative of -27*j**2 + 0 + 1/6*j**3 + 0*j + 1/120*j**5 + 1/16*j**4. Factor f(w).
(w + 1)*(w + 2)/2
Let x(l) be the second derivative of -5*l**7/42 + 59*l**6/6 - 899*l**5/4 + 4205*l**4/12 - 21*l. Find i, given that x(i) = 0.
0, 1, 29
Suppose -418*y = -421*y + 15. Factor -2/5*o + 0*o**3 + 2/5*o**y - 4/5*o**2 + 0 + 4/5*o**4.
2*o*(o - 1)*(o + 1)**3/5
Let s(m) be the first derivative of 9 - 2/39*m**3 - 5/13*m**2 - 8/13*m. Solve s(h) = 0.
-4, -1
Let r(h) be the second derivative of -h**8/504 + h**7/315 + h**6/180 - h**5/90 + 4*h**2 + 19*h. Let z(u) be the first derivative of r(u). Factor z(t).
-2*t**2*(t - 1)**2*(t + 1)/3
Let q(o) = -4*o**4 - 7*o**3 + 62*o**2 + 194*o - 476. Let k(c) = -c**4 + 2*c**3 + c**2 + c + 2. Let z(g) = 10*k(g) - 2*q(g). Factor z(f).
-2*(f - 9)**2*(f - 2)*(f + 3)
Let t = 30 + -254/9. Let u(d) be the first derivative of -7/3*d**2 + t*d**3 - 1 + 4/3*d - 1/2*d**4. Suppose u(v) = 0. Calculate v.
2/3, 1
Find n, given that -5120*n - 32*n**2 + 352*n**2 + 18 - 18 - 5*n**3 = 0.
0, 32
Let x be (-1 - 16/(-10))/(2/10). Factor 15 + 6*s**2 + 0*s**2 - 36*s + 93 - x*s**2.
3*(s - 6)**2
Let o = 7279 + -7274. Suppose 3 - 51/4*g**3 + 9/4*g**4 + 27/4*g**o + 6*g - 21/4*g**2 = 0. Calculate g.
-1, -2/3, 1
Solve 12*n**4 + 11*n**4 - 26*n**4 - 7*n**3 + 11*n**2 - 8 + 6*n + n**5 = 0 for n.
-2, -1, 1, 4
Factor -199*c + 2*c**4 - 259 - 96*c**2 - 34*c**3 + 276*c**2 - 173 - 17*c.
2*(c - 6)**3*(c + 1)
Let w = 2/11757 - -35263/47028. Suppose -3/4*r**2 + 0 - w*r**5 + 0*r - 9/4*r**3 - 9/4*r**4 = 0. Calculate r.
-1, 0
Let n(w) be the third derivative of w**5/75 - 8*w**4/15 + 13*w**2 - 2*w. Determine j, given that n(j) = 0.
0, 16
Let o(f) be the third derivative of -f**7/70 - 5*f**6/8 - 189*f**5/20 - 243*f**4/8 + 729*f**3 - 78*f**2. Suppose o(h) = 0. What is h?
-9, 2
Let q(n) = n**3 + 25*n**2 - 27*n + 27. Let x be q(-26). Suppose 14*i - 3 = x. Let -2/15*k**3 - 2/5*k**2 + 2/3*k + 2/15*k**i - 4/15 = 0. What is k?
-2, 1
Suppose 0 = -i - 1 + 4. Factor -3*t**3 - 2*t**4 + 6*t**2 - 2*t**2 + 2*t**2 - t**i.
-2*t**2*(t - 1)*(t + 3)
Suppose -525 = -55*o - 50*o. Determine w, given that -5/4 + 5/2*w**3 + o*w - 25/4*w**2 = 0.
1/2, 1
Let b(j) = -5*j**2 + 160*j - 1280. Let m(k) = -85*k**2 + 2720*k - 21760. Let g(f) = -35*b(f) + 2*m(f). Solve g(q) = 0.
16
Let f(z) be the first derivative of -z**5/30 + 19*z + 11. Let o(b) be the first derivative of f(b). Factor o(l).
-2*l**3/3
Determine m so that 216/5*m - 6/5*m**3 - 92/5*m**2 - 2/5*m**5 - 144/5 + 12/5*m**4 = 0.
-3, 2, 3
Let m(g) be the second derivative of -3*g**5/20 + 3*g**4/2 - 4*g**3 - 19*g + 3. Solve m(t) = 0.
0, 2, 4
Let a(v) be the first derivative of v**5/5 - v**4 + 2*v**3 - 2*v**2 - 9*v - 8. Let u(l) be the first derivative of a(l). Factor u(z).
4*(z - 1)**3
Let a(p) be the first derivative of 4/15*p + 18 - 1/5*p**2 + 2/45*p**3. Factor a(x).
2*(x - 2)*(x - 1)/15
Let y(p) be the first derivative of -7 + 0*p + 1/20*p**5 - 1/2*p**2 - 3/8*p**4 + p**3. Let q(j) be the second derivative of y(j). Factor q(g).
3*(g - 2)*(g - 1)
Let l(m) be the second derivative of -4/27*m**3 + 7/90*m**5 + 2/27*m**4 + 1/63*m**7 - 2/27*m**6 + 15*m + 0 + 0*m**2. What is x in l(x) = 0?
-2/3, 0, 1, 2
Let h(w) = -2*w + 8. Let j be 2/(-12) + 225/54. Let o be h(j). What is v in 0*v + 2/3*v**3 + o + 4/3*v**2 = 0?
-2, 0
Let x(t) be the first derivative of t**8/5460 + t**7/5460 - t**6/2340 - t**3/3 + 3. Let o(h) be the third derivative of x(h). Determine s, given that o(s) = 0.
-1, 0, 1/2
Let c = -730 - -1208. Find l such that c*l + 2*l**3 - 12*l**2 - 445*l - 5*l**3 - 18 = 0.
-6, 1
Suppose -5*v = -27 + 7. Suppose 0 = 3*w + v*u + 14, -3*w + 4*u = -7 - 19. Solve 1/2 + l + 1/2*l**w = 0.
-1
Let z(k) be the third derivative of -k**7/1680 + k**6/30 - 4*k**5/5 - 37*k**4/24 - 28*k**2. Let a(g) be the second derivative of z(g). Solve a(q) = 0.
8
Let -38/15*u + 2/15*u**2 - 44/5 = 0. Calculate u.
-3, 22
Let w be (-6)/(-9) + (-37)/(-3). Factor w*r**3 - 11*r**2 - 3*r**3 + 6*r**2 - 5*r**4.
-5*r**2*(r - 1)**2
Let t(f) be the first derivative