 1)/9
Solve 8/3 - k**5 - 16/3*k**4 + 4*k - 9*k**3 - 10/3*k**2 = 0 for k.
-2, -1, 2/3
Let t = 347 - 321. Suppose t*i - 16*i**2 + 38 - 2*i**3 + 12*i - 31 - 27 = 0. Calculate i.
-10, 1
Determine f so that 3840*f + 2139656*f**5 - 2232*f**2 - 18871 - 2139659*f**5 + 47671 + 54*f**4 - 84*f**3 = 0.
-4, 6, 10
Let w(p) = 346*p + 6230. Let n be w(-18). Factor 2/5*r**n + 4/5*r - 16/5.
2*(r - 2)*(r + 4)/5
Let q(w) = -3*w**2 + 2*w - 1. Let f be q(4). Let t = -36 - f. Factor 4 + t*y - 3*y - 5*y**2 + 6*y.
-(y - 2)*(5*y + 2)
Let o(p) be the first derivative of -p**4/20 - 4*p**3 - 333*p**2/10 - 486*p/5 + 378. Factor o(i).
-(i + 3)**2*(i + 54)/5
Let c(v) be the second derivative of -57*v - 1/165*v**6 + 2/11*v**4 + 0*v**2 + 0*v**5 + 16/33*v**3 + 0. Determine g so that c(g) = 0.
-2, 0, 4
Suppose -5 = -3*m - b, 0 = -5*m + 2*b - 13 + 3. Let o(r) = 53*r + 3. Let z be o(m). Factor 0*h - 2/9*h**4 + 2/9*h**z + 0 + 0*h**2.
-2*h**3*(h - 1)/9
Let o be (8 - 5) + -1 + 16. Suppose 0 = 5*j + 2*f - 18, -4*j - 2*f + o - 2 = 0. Find w such that -10/11*w - 2/11*w**j + 12/11 = 0.
-6, 1
Let d(q) = -27*q + 21. Let j be d(4). Let k = j - -108. What is w in -3*w + 5*w**2 - 2*w**2 + k*w**3 - 15*w**3 = 0?
-1, 0, 1/2
Let y(k) be the first derivative of k**4/4 + 19*k**3/3 + 32*k**2 + 60*k - 158. Find m such that y(m) = 0.
-15, -2
Let z be (-48)/(-26) + (48279/741 - 65). Factor 9/4*d**z + 12*d + 15/4.
3*(d + 5)*(3*d + 1)/4
Let c(b) = -1422*b - 113758. Let n be c(-80). Solve 486/11*v**n + 2/11*v**4 + 54/11*v**3 + 0 + 1458/11*v = 0.
-9, 0
Let a(x) be the second derivative of x**8/896 - x**7/280 + x**6/320 + 3*x**2 - 25*x + 1. Let y(q) be the first derivative of a(q). Factor y(u).
3*u**3*(u - 1)**2/8
Let n = -134749 - -404261/3. Factor 3*d - 1/3*d**2 - n.
-(d - 7)*(d - 2)/3
Let p = 3354/187 - 448357/27302. Let m = -1/73 + p. Determine f so that -m*f - 9/4 + 3/4*f**2 = 0.
-1, 3
Let f(b) be the second derivative of 2*b**4/3 - b**3 - b**2 + 2*b - 2973. Find d such that f(d) = 0.
-1/4, 1
Suppose 0 = -72*k + 78*k - 36. Let h(t) = -3*t - 6. Let u be h(-3). Factor 3 + 3*w - 4*w**2 - 3*w**u - 8*w**2 + 3 + k*w**2.
-3*(w - 1)*(w + 1)*(w + 2)
Let k(r) be the second derivative of 3*r**7/14 - 19*r**6/30 - 5*r**5/4 + 13*r**4/4 + 16*r**3/3 - 2*r**2 + 8283*r. Let k(u) = 0. What is u?
-1, 1/9, 2
Suppose -4*r = 5*x - r - 32, 0 = -3*r + 12. Let k be (21*3/297)/(x/24). What is j in -4/11*j**3 + 0 - k*j**2 + 14/11*j**4 + 4/11*j = 0?
-1, 0, 2/7, 1
Solve 1/2*n**2 + 43/2*n + 140 = 0.
-35, -8
Let u(k) = k**4 + 27*k**3 + 81*k**2 + 111*k + 24. Let h(b) = b**4 + 24*b**3 + 81*b**2 + 110*b + 16. Let o(g) = 3*h(g) - 2*u(g). Factor o(t).
t*(t + 3)**2*(t + 12)
Let -18*d**3 - 25*d**3 - 27*d**3 + 14*d**3 + 61*d**3 + 200 - 35*d**2 - 170*d = 0. Calculate d.
-4, 1, 10
Factor -99/2 - 197/4*m + 1/4*m**2.
(m - 198)*(m + 1)/4
Let x(s) be the third derivative of -s**6/96 - 217*s**5/48 + 2185*s**4/96 - 365*s**3/8 + 419*s**2 - 3*s. Factor x(v).
-5*(v - 1)**2*(v + 219)/4
Suppose 5*j + l - 8 = 0, -3*j - 4*l = -l. Solve -223*t**2 - 201*t**j + 162*t**4 - 47*t**3 - 853*t**3 - 48*t = 0 for t.
-2/9, 0, 6
Let v be (-3)/11*(-1040)/780. Let g(s) be the first derivative of -13 + v*s + 0*s**3 - 3/11*s**2 + 1/22*s**4. Find p such that g(p) = 0.
-2, 1
Factor 16/3 + 17/3*a**2 + 24*a.
(a + 4)*(17*a + 4)/3
Let l(y) = -15*y**2 - 153*y - 543. Let p(f) = 7*f**2 + 77*f + 272. Let g(c) = -4*l(c) - 9*p(c). Find o, given that g(o) = 0.
-23, -4
Suppose 3*m - 5*m - w = -35, 3*w = -3. Factor t - 2 + 15*t - t**2 + 5*t**2 + m.
4*(t + 2)**2
Let o(r) = 29*r**2 + 553*r + 1122. Let s(m) = -4*m**2 + 2*m - 2. Let n(v) = o(v) + 6*s(v). Factor n(t).
5*(t + 2)*(t + 111)
Let f(d) be the second derivative of 1/3*d**3 - 1/10*d**5 - 4/5*d**2 + 1/10*d**4 - 4*d + 0 + 1/75*d**6. Factor f(j).
2*(j - 4)*(j - 1)**2*(j + 1)/5
Let v(n) be the first derivative of -5*n**6/9 + 13*n**5/3 + 205*n**4/3 - 1955*n**3/9 - 4260*n**2 - 15120*n + 7165. Solve v(p) = 0 for p.
-4, -7/2, 9
Let h(b) be the first derivative of -b**3/3 + 587*b**2 - 344569*b + 445. Determine i so that h(i) = 0.
587
Let w(f) be the first derivative of 220 + 0*f**2 + 1/3*f - 1/9*f**3. Factor w(v).
-(v - 1)*(v + 1)/3
Suppose -3*x = l - 3, -5*l + 16 = -2*x + 52. Let a(b) be the third derivative of 0*b**x + 29*b**2 + 0 + 0*b + 1/135*b**5 + 1/540*b**6 + 1/108*b**4. Factor a(r).
2*r*(r + 1)**2/9
Let t be 208/(-84)*(-102)/221. Let y be 4 - -2*48/(-28). Let -y*x**2 - t*x + 12/7 = 0. What is x?
-3, 1
Let p(z) be the third derivative of z**8/168 - 13*z**7/105 + 59*z**6/60 - 119*z**5/30 + 9*z**4 - 12*z**3 - 34*z**2 - 3. Suppose p(w) = 0. What is w?
1, 2, 3, 6
Let q(h) be the third derivative of h**9/3780 + h**8/700 + h**7/525 + 13*h**3 + 22*h**2 + h. Let o(u) be the first derivative of q(u). Factor o(x).
4*x**3*(x + 1)*(x + 2)/5
Let r(m) be the first derivative of 0*m + 0*m**2 - 25/2*m**6 - 21*m**5 - 33/4*m**4 - m**3 - 4. Factor r(o).
-3*o**2*(o + 1)*(5*o + 1)**2
Let a(n) be the second derivative of -n**4/12 + 125*n**3/3 + 729*n. Determine l so that a(l) = 0.
0, 250
Let -8/21*a**5 + 130/21*a + 226/21*a**2 - 26/3*a**4 - 44/21 - 122/21*a**3 = 0. Calculate a.
-22, -1, 1/4, 1
Let u(n) be the second derivative of -5*n**7/42 - 17*n**6/6 + 45*n**5/4 + 685*n**4/12 + 190*n**3/3 - 3*n + 1359. Let u(m) = 0. What is m?
-19, -1, 0, 4
Let n(y) be the second derivative of y**7/14 + 31*y**6/10 + 417*y**5/20 + 241*y**4/4 + 92*y**3 + 78*y**2 + 2244*y. Suppose n(w) = 0. Calculate w.
-26, -2, -1
Let o(t) = 348*t**3 + 1032*t**2 + 684*t. Let n(p) = p**4 - 347*p**3 - 1032*p**2 - 684*p. Let q(h) = -3*n(h) - 4*o(h). Solve q(j) = 0.
-114, -2, -1, 0
Let p(x) be the second derivative of -x**6/900 - 7*x**5/300 + 3*x**4/10 + 79*x**3/2 + 92*x - 2. Let s(t) be the second derivative of p(t). Factor s(f).
-2*(f - 2)*(f + 9)/5
Suppose -2143296/25*j + 1077504/25*j**2 + 0 + 2/25*j**4 - 2932/25*j**3 = 0. What is j?
0, 2, 732
Suppose 870*r - 485*r = 770. Solve 0*s + 4/5 + 1/5*s**5 - 1/5*s**3 + 3/5*s**4 - 7/5*s**r = 0.
-2, -1, 1
Let p(t) = t**2 + 88*t + 6. Let a be p(15). Let i = a + -1551. Factor -2/7*h - 1/7*h**2 + i.
-h*(h + 2)/7
Let g(u) = -u**2 + 383*u - 1504. Let r(s) = -380*s + 1510. Let h(a) = 5*g(a) + 6*r(a). Factor h(c).
-5*(c - 4)*(c + 77)
Let b be (10269/(-12) - 5) + (-3)/12. Let k = -857 - b. Factor 0*h + 0*h**3 - 4/9*h**2 + 2/9 + 2/9*h**k.
2*(h - 1)**2*(h + 1)**2/9
Let c(g) = -302*g**3 + 15962*g**2 - 48416*g + 36428. Let p(a) = -69*a**3 + 3547*a**2 - 10759*a + 8095. Let h(d) = -10*c(d) + 44*p(d). Let h(o) = 0. Calculate o.
-225, 3/2
Factor 32*m**2 - 4/5*m**3 + 704/5*m + 0.
-4*m*(m - 44)*(m + 4)/5
Let a(o) = 91*o**3 + 11817*o**2 - 23703*o + 11846. Let x(i) = 11*i**3 + 1477*i**2 - 2963*i + 1481. Let m(s) = 2*a(s) - 17*x(s). Let m(y) = 0. Calculate y.
-297, 1
Factor -4/3*t**4 + 608/3*t + 616/3*t**3 + 0 - 1220/3*t**2.
-4*t*(t - 152)*(t - 1)**2/3
Let j(y) = 4*y**2 - y + 1. Let r(p) = -28*p**2 + 260*p + 240. Let g(u) = -8*j(u) - r(u). Let g(k) = 0. Calculate k.
-62, -1
Factor -257*o**2 - 256 - 128*o - 238*o**2 - o**3 - 252*o**2 + 727*o**2.
-(o + 4)*(o + 8)**2
Let y(s) be the first derivative of -s**5/20 + 19*s**4/16 + 11*s**3/2 + s**2/2 - 22*s + 1019. Factor y(d).
-(d - 22)*(d - 1)*(d + 2)**2/4
Let j(q) be the first derivative of -432*q + 17/2*q**4 + 2/5*q**5 - 45 + 108*q**2 + 60*q**3. Factor j(o).
2*(o - 1)*(o + 6)**3
Let h(n) be the third derivative of n**7/315 + 23*n**6/45 + 1103*n**5/45 + 115*n**4 + 225*n**3 - 296*n**2. Suppose h(t) = 0. Calculate t.
-45, -1
Let a = -1630/3 - -550. Let m(g) be the first derivative of -15/4*g**4 + 5/6*g**6 + 0*g - 2*g**5 - 7 + a*g**3 + 10*g**2. Factor m(t).
5*t*(t - 2)**2*(t + 1)**2
Let -55539/7*o - 15*o**3 - 1/7*o**4 - 3861/7*o**2 - 215622/7 = 0. Calculate o.
-33, -6
Factor -36/5 + 2/15*b**2 - 2*b.
2*(b - 18)*(b + 3)/15
Let s(d) be the second derivative of -1/30*d**5 + 0*d**2 + 1 - 1/6*d**4 - 22*d + 0*d**3. Factor s(f).
-2*f**2*(f + 3)/3
Find a, given that 58/15*a - 64/5 + 2/15*a**2 = 0.
-32, 3
Suppose 3*v + 30 = -9. Let m = -11 - v. Suppose 6*k**2 - 3*k**4 - 15*k**m + 4*k**3 + 3*k**2 + 10*k**2 = 0. Calculate k.
-2/3, 0, 2
Let n(q) be the third derivative of -q**5/12 + 1015*q**4/12 - 10025*q**3/6 + 612*q**2 - 4. Factor n(u).
-5*(u - 401)*(u - 5)
Suppose -3*x - 8*f + 10 = -12*f, -4*f - 30 = -5*x. Let u be (2/x)/(594/540). Sup