 1739. Let n(g) be the second derivative of 10/3*g**3 + 0 + 0*g**2 + 1/5*g**5 + 2*g**a + 15*g. What is s in n(s) = 0?
-5, -1, 0
Determine j so that 125/6 - 1/6*j**2 + 10/3*j = 0.
-5, 25
Suppose -5*w + 0 + 5 = 0. Let t(p) = 5*p - 1. Let x be t(w). Find c, given that 69*c**4 - 8 - 2*c**2 - 40*c - 26*c**3 + 10*c**5 - 55*c**x - 60*c**2 = 0.
-1, -2/5, 2
Let a be (-2)/((-2)/25) + (-2 - -4). Suppose 3*x = v + a - 2, 4*x - 4*v = 20. Determine o so that 3*o - x*o**3 - 8*o**2 + 8 + 6*o**3 + o = 0.
-2, -1, 1
Let s be -1*((-1260)/27 + 16 + 20). Factor -16/3 + 8/3*f**2 - 3*f**4 + 8*f**3 - s*f.
-(f - 2)**2*(3*f + 2)**2/3
Let d(b) = -2*b**4 - b**2 - 2*b - 8. Let n(o) = 3*o**5 - 27*o**4 + 18*o**3 + 3*o**2 - 10*o - 40. Let x(q) = -5*d(q) + n(q). Solve x(i) = 0 for i.
-1/3, 0, 2, 4
Solve -84/5*l**2 + 32*l + 0*l**3 + 1/5*l**4 + 0 = 0 for l.
-10, 0, 2, 8
Let i(j) = -4*j**4 + 42*j**3 + 113*j**2 + 63. Let m(s) = s**4 - 14*s**3 - 38*s**2 - 18. Let v(c) = 4*i(c) + 14*m(c). Suppose v(h) = 0. Calculate h.
-10, -4, 0
Let k(t) be the first derivative of 3*t**5/5 - 27*t**4/4 - 360*t**3 - 3425. Factor k(i).
3*i**2*(i - 24)*(i + 15)
Let u(x) = 218*x - 22. Let a be u(-1). Let f = a - -1212/5. Factor -f*m - 13/5*m**2 - 1/5*m**4 - 4/5 - 6/5*m**3.
-(m + 1)**2*(m + 2)**2/5
Suppose 22 = 3*v + 2*x, -v + 18 = 3*x - 5*x. Let h(b) be the first derivative of -b**5 + 0*b - v*b**2 + 20/3*b**3 + 5/4*b**4 - 7. Find c such that h(c) = 0.
-2, 0, 1, 2
Let s be (4/6)/(4/6). Let u(m) = 4*m**2 + 3. Let v(n) = -118*n**2 - 90. Let y(h) = -60*u(h) - 2*v(h). Let r(q) = 1. Let i(x) = s*y(x) + 16*r(x). Factor i(b).
-4*(b - 2)*(b + 2)
Let w(q) = 61*q**2 + 2169*q - 2185. Let v(k) = 34*k**2 + 1084*k - 1093. Let o(p) = 9*v(p) - 5*w(p). Find u, given that o(u) = 0.
1, 1088
Find h such that 66 - 1/5*h**2 + 107/5*h = 0.
-3, 110
Suppose 5*z = 4*z + 5, 0 = 5*w + 4*z - 40. Factor 16*x + 12*x**2 + 11 + 7 - 2*x**w - 12.
-2*(x - 3)*(x + 1)**3
Find w such that 8*w**3 + 57/2*w**2 - 7/2*w**4 + 18*w + 0 - w**5 = 0.
-4, -3/2, -1, 0, 3
Let x(d) be the third derivative of -d**8/1680 + 2*d**7/525 + 7*d**6/600 - 17*d**5/150 + d**4/5 - d**2 + 180*d - 1. Suppose x(n) = 0. Calculate n.
-3, 0, 1, 2, 4
Let d be (((-42)/(-70))/(4/70))/(108/117) - 8. Factor -21/8*u - d + 1/8*u**3 + 7/8*u**2.
(u - 3)*(u + 1)*(u + 9)/8
Let l(w) = 6*w**2 - 5*w + 4. Let v be l(1). Solve 8*g**2 - 71 + 71 + 8*g**4 - 2*g - 2*g**v - 3*g**3 - 9*g**3 = 0.
0, 1
Let u(m) be the second derivative of 1/42*m**4 + 0 - 1/3*m**3 + 12/7*m**2 + 15*m. Suppose u(n) = 0. Calculate n.
3, 4
Suppose 4*h - 3*p - 60 = 0, -3*p = -714*h + 721*h + 27. Factor -6/7*k**2 + 6/7*k - 2/7 + 2/7*k**h.
2*(k - 1)**3/7
Let g(j) be the third derivative of -j**5/360 + 29*j**4/24 + 59*j**3/4 - j**2 - 197. Solve g(z) = 0 for z.
-3, 177
Let i(n) be the first derivative of -2*n**3/39 - 3272*n**2/13 - 5352992*n/13 - 576. Factor i(k).
-2*(k + 1636)**2/13
Let g be (6/(-351))/((-247)/26676). Factor g + 8/13*m - 2/13*m**2.
-2*(m - 6)*(m + 2)/13
Let v = -73 - -73. Suppose 3*w**3 - 63*w**2 + 2*w**3 + 73*w**2 + v*w**3 = 0. Calculate w.
-2, 0
Let z(x) be the third derivative of x**6/480 - 1467*x**5/80 + 2152089*x**4/32 - 1052371521*x**3/8 + 1826*x**2 + 4*x. Factor z(a).
(a - 1467)**3/4
Let j = 57197 + -285937/5. Suppose 36/5*z**4 - 28/5*z**5 + 0*z + 0 + j*z**3 - 16/5*z**2 = 0. What is z?
-1, 0, 2/7, 2
Let q(r) be the second derivative of r**6/60 + 4*r**5/5 + 295*r**4/24 + 79*r**3 + 171*r**2 - 372*r + 2. Let q(s) = 0. What is s?
-19, -6, -1
Let n = -904105 - -904105. What is q in n*q - 1/2*q**2 + 0 - 1/2*q**3 = 0?
-1, 0
Let l(d) = d**2 + 22*d + 43. Let z be l(-20). Solve -3*u**2 + 39*u - 45*u + 5 + 4*u**2 + z = 0.
2, 4
Suppose -19536/5*h + 484/5*h**2 + 197136/5 = 0. What is h?
222/11
Let p be 7/56*24 - 1. Let x(f) be the second derivative of 1/10*f**3 - 1/20*f**4 - 1/10*f**p + 15*f + 0 + 1/100*f**5. Solve x(h) = 0 for h.
1
Let h(l) be the second derivative of -l**6/15 + 29*l**5/10 - 40*l**4/3 + 52*l**3/3 - 618*l + 2. Factor h(k).
-2*k*(k - 26)*(k - 2)*(k - 1)
Let z = 58757 - 58755. Let -8 - 44/3*q + 8/3*q**3 + 4*q**z = 0. What is q?
-3, -1/2, 2
Let i(z) be the first derivative of z**3/12 + 11*z**2/4 + 105*z/4 + 885. Factor i(x).
(x + 7)*(x + 15)/4
Let o(a) be the third derivative of a**6/3420 - a**5/190 + 2*a**4/57 + 58*a**3/3 - 23*a**2. Let z(g) be the first derivative of o(g). Let z(v) = 0. What is v?
2, 4
Factor 166/9*b**2 - 112/3*b + 1/9*b**3 + 0.
b*(b - 2)*(b + 168)/9
Let d = -85938 - -85938. Find x such that 4/9*x + 2/3*x**3 + d + 14/9*x**2 - 14/9*x**4 - 10/9*x**5 = 0.
-1, -2/5, 0, 1
Let q = 69604/52185 - 8/17395. Factor 1/3*d**2 + q - 5/3*d.
(d - 4)*(d - 1)/3
Let c(v) be the third derivative of -v**8/1512 + 2*v**7/45 - 7*v**6/20 + 74*v**5/135 + 720*v**2. Solve c(x) = 0 for x.
0, 1, 4, 37
Find j such that -48*j**3 + 31 + 5 + 57*j + 126*j**2 + 51*j**3 - 102*j**2 = 0.
-4, -3, -1
Let m(w) = 29*w**3 - 858*w**2 + 1725*w - 860. Let a(j) = 64*j**3 - 1713*j**2 + 3450*j - 1720. Let h(s) = -4*a(s) + 9*m(s). Determine y, given that h(y) = 0.
1, 172
Let r(n) = -8*n**2 - 40*n. Let h = 12 - 20. Let x(s) = -18*s**2 - 33*s + 6*s**2 - 38*s + 11*s. Let b(v) = h*r(v) + 5*x(v). Factor b(t).
4*t*(t + 5)
Let t = -3591/5 + 474013/660. Let j(v) be the third derivative of t*v**6 + 0*v**3 + 0*v - 1/165*v**5 - 1/44*v**4 + 0 - 8*v**2. Factor j(c).
2*c*(c - 3)*(c + 1)/11
Let j = 27350 + -27350. Let r(y) be the second derivative of 0*y**3 - 5*y + 1/20*y**5 - 1/18*y**4 + 0 + j*y**2 + 1/45*y**6. Solve r(n) = 0.
-2, 0, 1/2
Let a(l) be the third derivative of l**8/30240 - l**7/1512 - l**6/180 - l**5/12 - 8*l**2 + 1. Let r(m) be the third derivative of a(m). Solve r(c) = 0.
-1, 6
Let a(q) be the first derivative of -3*q**4/16 - 5*q**3/2 - 21*q**2/2 - 18*q - 437. Solve a(v) = 0.
-6, -2
Let h(l) = 2*l**5 + l**2 - 1. Let s(g) = 11*g**5 + 570*g**4 + 8833*g**3 - 6079*g**2 + 1024*g - 1. Let a(w) = -4*h(w) + 4*s(w). Find f, given that a(f) = 0.
-32, 0, 1/3
Let f be (-7)/(714/85) + ((-93)/18 - -6). Find v, given that f*v + 0 + 1/2*v**4 - 3/2*v**3 + v**2 = 0.
0, 1, 2
Suppose -32 = -2*v + 2*z, 5*v - 7*z + 4*z = 78. Let o(g) be the first derivative of 0*g + 33 - 5*g**2 + 25/4*g**4 - v*g**3. Factor o(j).
5*j*(j - 2)*(5*j + 1)
Let a = -564 + 569. Factor -191*m**3 + 196*m**3 + 6*m**2 + 2 + m**4 - a + 3.
m**2*(m + 2)*(m + 3)
Let o(j) = -14*j**3 + 14*j**2 + 254*j - 206. Let a(k) = 10*k**3 - 9*k**2 - 168*k + 137. Let s(q) = 8*a(q) + 5*o(q). Let s(m) = 0. Calculate m.
-3, 1, 11/5
Let s(c) be the first derivative of 2*c**3/39 + 737*c**2/13 + 1472*c/13 + 10624. Let s(p) = 0. Calculate p.
-736, -1
Let l = 2099 - 2096. Factor 16/5 - 4*h**2 - 12/5*h**l + 4/5*h**4 + 12/5*h.
4*(h - 4)*(h - 1)*(h + 1)**2/5
Let o(u) = -15*u**2 - 1055*u - 3165. Let c(t) = 37*t**2 + 2641*t + 7914. Let h(r) = 5*c(r) + 12*o(r). Determine s, given that h(s) = 0.
-106, -3
Let a be -477*8/(-12) - (-2 + -2). Let f = a - 319. Find t, given that 2*t**4 - 6*t**5 + 28/3*t**f - 10/3*t - 2/3 - 4/3*t**2 = 0.
-1, -1/3, 1
Let c be 5 + 6/((-8)/4). Factor -24*g**3 + 5*g + 12*g**4 + g - 3*g**2 + 0*g**c - 27*g**4.
-3*g*(g + 1)**2*(5*g - 2)
Let p = 28636 - 28632. Factor -42/11*g + p - 2/11*g**2.
-2*(g - 1)*(g + 22)/11
Let z be ((-6)/8)/(3927/(-10472)). Factor -61/4*v + 15/2 + 8*v**z - 1/4*v**3.
-(v - 30)*(v - 1)**2/4
Let q(f) be the second derivative of -f**5/90 + f**4/54 + 2*f + 207. Suppose q(a) = 0. Calculate a.
0, 1
Let m = -170 - -205. Factor 25*v**3 - 72*v - m*v**2 - 2*v**2 + 4 - 5 - 19 - 28*v**3.
-(v + 2)*(v + 10)*(3*v + 1)
Let h(i) = 9*i**3 + 154*i**2 - 656*i + 692. Let r(s) = 190*s**3 + 3235*s**2 - 13775*s + 14535. Let m(u) = 85*h(u) - 4*r(u). Factor m(w).
5*(w - 2)**2*(w + 34)
Factor -1/3*n**2 + 9*n - 140/3.
-(n - 20)*(n - 7)/3
Suppose -34*o + 78 = -36*o. Let k = -16 - o. Solve 4*n**2 + n**2 + 2 + k*n + 8 - 8*n = 0 for n.
-2, -1
Let o(y) be the third derivative of -y**6/160 + y**5/80 + 3*y**4/4 + 9*y**3/2 + 18*y**2 - 54*y. Determine r so that o(r) = 0.
-3, -2, 6
Let u(y) be the first derivative of 3*y**4/16 - 261*y**3/4 + 68121*y**2/8 - 1975509*y/4 + 661. Determine d so that u(d) = 0.
87
Let x = 16 + -14. Factor -6*l**3 + 2*l**4 + 2*l + 6 - 2*l**3 + 6*l**3 - 2 - 6*l**x.
2*(l - 2)*(l - 1)*(l + 1)**2
Let g = -20 + 4. Let m = -11 - g. Factor -m*i + 2*i + 2*i**3 + 6*i - 1 - i**3 - 3*i