. Let g(k) be the second derivative of 1/3*k**3 + 0 + u*k**2 - 1/6*k**4 - 15*k. Determine v, given that g(v) = 0.
-1, 2
Let f(d) be the first derivative of d**4/20 + 19*d**3/15 + 59*d**2/5 + 48*d + 2077. Solve f(w) = 0.
-8, -6, -5
Let w be (-1)/3 - ((17 - 227)/(-10) + (-79)/3). Let 4/9*d**w + 0*d - 44/9*d**3 + 16/3*d**2 + 0 - 8/9*d**4 = 0. What is d?
-3, 0, 1, 4
Let z be 60/((1/12)/(2/9)). Factor 736 - 161*k - z + 4*k**2 + 65*k.
4*(k - 12)**2
Let u = -404 - -698. Let r be (u/63)/((-2)/(-9)). Factor -6*l**4 - 274*l**2 + 274*l**2 + r*l**5.
3*l**4*(7*l - 2)
Suppose -3*o + 9 = -0. Solve 5*i**3 + 2*i**o + 13*i**2 - 10*i**2 - i**3 = 0 for i.
-1/2, 0
Let q(l) be the first derivative of -16*l**6/27 - 16*l**5/45 + 5*l**4/6 + 16*l**3/27 + l**2/9 - 4100. Determine d, given that q(d) = 0.
-1, -1/4, 0, 1
Let g(h) be the third derivative of -25*h**8/168 - 27*h**7/2 - 8771*h**6/24 - 6977*h**5/4 - 28485*h**4/8 - 3645*h**3 + 2*h**2 - h + 25. Let g(v) = 0. What is v?
-27, -6/5, -1, -1/2
Let c = -573 - -1278. Solve -804*j**2 + c*j**2 + 2*j**4 + 336*j - 42*j**3 - 192 - 5*j**4 = 0 for j.
-8, 1
Let n(a) be the third derivative of -4/2415*a**7 - 2/345*a**5 + 0*a**3 + 1/276*a**4 + 1/230*a**6 - 89*a**2 + 0 + 0*a + 1/3864*a**8. Factor n(d).
2*d*(d - 1)**4/23
Let n(x) be the first derivative of -5*x**6/6 + 21*x**5 - 245*x**4/2 - 710*x**3/3 + 495*x**2/2 + 605*x - 1079. Find a such that n(a) = 0.
-1, 1, 11
Let b(y) be the first derivative of 2/15*y**5 + 65 - 2/3*y**3 + 1/6*y**4 + 4/3*y - 1/3*y**2. Solve b(o) = 0.
-2, -1, 1
Let v(n) = 4*n**2 + 19*n - 33. Suppose 59 = 12*b - 13. Let i(m) = 9*m**2 + 40*m - 67. Let s(d) = b*i(d) - 14*v(d). Factor s(j).
-2*(j - 2)*(j + 15)
Factor 0 - 2956*u - 57560*u - 984*u**2 + 0 - 4*u**3.
-4*u*(u + 123)**2
Suppose -5*v + 37 = 3*s - 8, -5*v - 5*s = -45. Solve 7 + 25 - 12*c**2 + 17 + 5 + v*c - 3*c**3 = 0.
-3, 2
Let 125 - 55/6*h + 1/6*h**2 = 0. What is h?
25, 30
Let r(s) be the third derivative of -2*s**7/105 - 29*s**6/30 - 69*s**5/5 + 29*s**4/6 + 416*s**3/3 - s**2 - 2*s + 474. Determine c so that r(c) = 0.
-16, -13, -1, 1
Let c(b) be the third derivative of b**7/105 - 31*b**6/60 - 38*b**5/15 + 1441*b**4/3 + 1936*b**3 + 4324*b**2. Factor c(l).
2*(l - 22)**2*(l + 1)*(l + 12)
Suppose c = -3*v - 113, v + 442 = -4*c - v. Let k = c + 160. Let -55*h**2 + 111*h**2 - k*h**2 - 20*h - 16 = 0. What is h?
-2/3, 4
Factor 180 - 24*h + 3/4*h**2.
3*(h - 20)*(h - 12)/4
Find j, given that 13708*j - 532824/7 - 1216/7*j**2 + 4/7*j**3 = 0.
6, 149
Let z(h) be the second derivative of -5*h**4/48 - 5*h**3/24 + 165*h**2/2 - 2*h - 1243. Suppose z(u) = 0. Calculate u.
-12, 11
Let 26/7*p**3 - 96/7*p + 0 - 68/7*p**2 - 2/7*p**4 = 0. What is p?
-1, 0, 6, 8
Let x(j) be the second derivative of j**6/540 + j**5/36 + j**4/6 + 17*j**3/6 + 47*j - 1. Let z(q) be the second derivative of x(q). Factor z(r).
2*(r + 2)*(r + 3)/3
Let o(l) be the second derivative of l**5/100 + 2*l**4/15 - 59*l**3/30 + 39*l**2/5 - 550*l. Factor o(r).
(r - 3)*(r - 2)*(r + 13)/5
Suppose 0 = 3*r + 2*z - 23, 4*r + 7 - 23 = z. Find d, given that 55*d**4 - d**2 + 72*d**r + 3*d**3 - 223*d**4 + 47*d**3 - 3*d**2 = 0.
0, 1/6, 2
Let u(b) be the third derivative of -b**7/840 + b**6/15 + b**5/80 - 49*b**4/48 + 8*b**3/3 + 2*b**2 + 11*b - 5. Find q, given that u(q) = 0.
-2, 1, 32
Suppose -13*r = -39, -u + 783*r - 784*r = -3. Solve u*l - 11*l**3 + 0 + 0*l**2 - 21/2*l**4 + 1/2*l**5 = 0.
-1, 0, 22
Let j = -767 + 52. Let g be 5*33/j - -1. Factor -g*t**2 - 2/13 + 12/13*t.
-2*(t - 1)*(5*t - 1)/13
Let p be (-4)/14 - (-1025)/35. Suppose -a + 32 = p. Find b such that a*b**3 + 3*b**3 - 3*b - b**3 - 2*b = 0.
-1, 0, 1
Suppose -d + 8 = 1291*a - 1289*a, -2*a = -4. Let x(s) be the second derivative of 0*s**2 - 1/190*s**5 - 13*s + 0 + 4/57*s**3 + 1/38*s**d. What is y in x(y) = 0?
-1, 0, 4
Let y(h) be the second derivative of h**5/20 + 7*h**4/3 - 31*h**3/6 - 29*h**2 - 1088*h. Factor y(s).
(s - 2)*(s + 1)*(s + 29)
Let d = 124 + -126. Let t be (-12)/(-3) - (d - 9/(-3)). Suppose 14*l**t - 19*l**2 - 16*l**3 + l**4 + 19*l**2 = 0. What is l?
0, 2
Let n = -12380 + 99057/8. Let y(j) be the third derivative of -4/5*j**5 + 0*j + 10*j**2 + 0 + n*j**4 + 3/40*j**6 - 2*j**3. Factor y(v).
3*(v - 4)*(v - 1)*(3*v - 1)
Let g be (8/10)/(350/(-4125)) - 0. Let i = 153/14 + g. What is u in 3/2*u - 3/2*u**2 - i*u**3 + 3/2 = 0?
-1, 1
Let q be 208/936 + 1/(-18). Let i(j) be the third derivative of 0 + 1/24*j**4 - 1/240*j**5 - 29*j**2 - q*j**3 + 0*j. Let i(z) = 0. Calculate z.
2
Factor -36*o**4 - 46*o**3 + 22*o**3 + 16*o**3.
-4*o**3*(9*o + 2)
Let s be ((-11359)/(-333) + -34)*27/6*6/15. Find i, given that s*i - 1/5*i**3 - 13/5*i**2 + 13/5 = 0.
-13, -1, 1
Let q(t) be the second derivative of -5/9*t**3 + 2/3*t**2 - 1/45*t**6 + 1/6*t**4 + 2*t + 19 + 1/30*t**5. Factor q(g).
-2*(g - 1)**3*(g + 2)/3
Suppose 2*p - 5*i = 13, 3*i - 8*i - 5 = 0. Suppose 5*s + 6 = -p*l + 29, 4*l - 17 = -3*s. Factor 9*m - 10*m + 11*m - 5*m**2 - 7*m**s + 2*m**3.
-5*m*(m - 1)*(m + 2)
Let -112/3 + 94/15*i - 2/15*i**2 = 0. What is i?
7, 40
Suppose 4*x - 21 = -3*n, -21 = -3*x - 0*n + 3*n. Let v be 3/x*48/21. Factor v*c - 4/7*c**2 + 12/7.
-4*(c - 3)*(c + 1)/7
Suppose -11*j + 14*j = 2*k + 6, -8 = 3*k - 4*j. Let i(w) be the third derivative of 3/40*w**6 + w**3 - 15*w**2 - 2/5*w**5 + k + 0*w + 3/8*w**4. Factor i(x).
3*(x - 2)*(x - 1)*(3*x + 1)
Suppose -26*a = 22*a - 164 - 76. Let p(q) be the first derivative of -8 + 7/2*q**6 + 14*q**3 - 9/2*q**2 - 36/5*q**a - 6*q - 3*q**4. Factor p(t).
3*(t - 1)**3*(t + 1)*(7*t + 2)
Let y(x) be the second derivative of 1/70*x**5 + 3/7*x**2 + 62*x + 0 - 5/21*x**3 + 1/42*x**4. Solve y(b) = 0 for b.
-3, 1
Let q(r) = r**2 + 297*r + 5181. Let v(i) = 8*i**2 + 2676*i + 46628. Suppose -28*c = 87 - 3. Let a(p) = c*v(p) + 28*q(p). Factor a(n).
4*(n + 36)**2
Let h be (-2 - -2) + -1 - (-24 + 19). Find k such that -5*k - 9 - k**3 + 4*k + 6*k + h*k + k**2 = 0.
-3, 1, 3
Let v(h) be the second derivative of -h**6/6 + 19*h**5/2 - 535*h**4/4 - 1900*h**3/3 - 1000*h**2 - 73*h - 1. Factor v(x).
-5*(x - 20)**2*(x + 1)**2
Let c(x) be the third derivative of x**8/168 - 2*x**7/105 - x**6/20 - 2*x**2 - 1041*x. Determine q so that c(q) = 0.
-1, 0, 3
Let u be ((-11)/(110/12) - -1)*-25. Suppose 25 = 5*r + 5*g, 3*r + u*g = -0*g + 25. Let -2/5*n**2 + r + 0*n = 0. What is n?
0
Let w be 30/1680*24*4/6. Suppose 8/7 - 8/7*g + w*g**2 = 0. What is g?
2
Suppose 3*r + 4*x = -14, -4*r + 2*r = -3*x - 19. Factor -32*n + 11 + 24 - 9 + 4*n**2 + r.
4*(n - 7)*(n - 1)
Let m(o) be the first derivative of 178 - 27/7*o**2 + 0*o + 2/21*o**3. Factor m(y).
2*y*(y - 27)/7
Let l(f) be the second derivative of -f**8/2240 - 11*f**7/840 - f**4 + 144*f. Let v(k) be the third derivative of l(k). Determine s, given that v(s) = 0.
-11, 0
Determine o, given that -322212*o + 0*o**2 + o**3 + 322252*o + 11*o**2 + 48 = 0.
-4, -3
Let t = 82 - 78. Let z = 164 + -490/3. Factor -4/3*g**t + 2*g**2 + 0 + z*g**3 + 0*g.
-2*g**2*(g + 1)*(2*g - 3)/3
Let f(x) = -78*x + 80. Let u be f(1). Factor 393*q**2 + 5 - 402*q**u + 7 + 5*q**3 - 8*q.
(q - 2)*(q - 1)*(5*q + 6)
Let d(i) = -6*i**4 + 45*i**3 - 48*i**2 - 111*i + 3. Let j(k) = k**4 - k**3 - 5*k**2 + k - 1. Let c(u) = -d(u) - 3*j(u). Let c(g) = 0. What is g?
-1, 0, 3, 12
Suppose -285*f**3 - 286*f**3 + 231*f - 281*f**3 + 849*f**3 + 153*f**2 + 87*f = 0. Calculate f.
-2, 0, 53
Let y(x) = -8*x**5 + 8*x**4 + 102*x**3 + 94*x**2 - 18*x - 30. Let q(n) = 2*n**5 + n**4 - n**2 - n. Let j(t) = 4*q(t) - y(t). Solve j(h) = 0 for h.
-5/4, -1, 1/2, 3
Suppose -266 = 3*k + q - 288, 0 = -k + q + 2. Let i(j) be the first derivative of k*j**2 - 22 + 14*j - 2/3*j**3. Factor i(z).
-2*(z - 7)*(z + 1)
Suppose -2*d + 2*c + 4 = 0, 10*d - 65*c + 63*c = 36. Suppose -1/4*v + 0 + 9/4*v**3 + 3/4*v**2 + 5/4*v**d = 0. What is v?
-1, 0, 1/5
Let n(x) be the second derivative of -x**7/21 - 38*x**6/15 + 123*x**5/2 - 402*x**4 + 612*x**3 + 59*x - 17. Let n(p) = 0. What is p?
-51, 0, 1, 6
Let u(a) be the first derivative of -a**6/216 + a**5/18 - 5*a**4/18 - 2*a**3 + 2*a + 80. Let v(l) be the third derivative of u(l). Factor v(o).
-5*(o - 2)**2/3
Let w = -54134/21 - -2578. Let v(r) be the second derivative of -1/42*r**4 - 4/7*r**2 + w*r**3 + 0 + 3*r. Let v(i) = 0. What is i?
2
Let b(r) be the second derivative of -1/24*r**4 - 30*r