0*f + 36969*f**2 + 468*f**3 + 3/2*f**4 + 72075/2 = 0.
-155, -1
Solve -3 - 9/4*f**4 - 69/4*f**3 - 79/4*f - 151/4*f**2 = 0.
-4, -3, -1/3
Let n(r) be the second derivative of -154*r + 25/14*r**2 + 1/84*r**4 + 5/21*r**3 + 0. Let n(s) = 0. What is s?
-5
Find t, given that 20*t**3 + 881*t + 145*t**2 - 192*t**2 - 310*t - 19*t**3 - 525 = 0.
1, 21, 25
Let d(l) = -37*l**2 - 835*l + 16512. Let t(x) = -22*x**2 - 505*x + 9907. Let j(s) = -7*d(s) + 12*t(s). Determine p, given that j(p) = 0.
-55, 12
Let p(f) be the third derivative of -1235/24*f**4 + 205*f**2 + 245/3*f**3 + 0 + 0*f + 5/12*f**5. Find l, given that p(l) = 0.
2/5, 49
Let t be 1/(-7) + (-15)/(156975/(-1460)). Let r = t - -904/2093. Determine a, given that 3/7*a**2 + 6/7*a**3 + r*a**4 + 0 + 0*a = 0.
-1, 0
Let p(a) be the third derivative of -a**8/2352 + a**7/210 + a**6/168 - 71*a**5/420 - 5*a**4/21 + 50*a**3/21 - 1382*a**2. Suppose p(r) = 0. What is r?
-2, 1, 5
Let z be ((-232)/60 - -4)/(6/480). Let t = 443/132 + -1/44. Determine y so that 50/3*y**3 - t*y**2 - z*y - 8/3 = 0.
-2/5, 1
Let o be (1/(-2))/(9/2 + -4). Let n be (-3)/1*-1 - o. Let -31*z**2 + 6*z**n - 4*z + 3*z**5 + z + 6*z**2 + 19*z**2 = 0. What is z?
-1, 0, 1
Let i be 165/(-605) + 1671/198. Let g(u) be the first derivative of -20 + 1/18*u**3 + i*u + 7/6*u**2. Factor g(h).
(h + 7)**2/6
Let d(m) be the second derivative of 4/5*m**3 - 8 + 1/15*m**4 - 2*m + 0*m**2. Factor d(y).
4*y*(y + 6)/5
Suppose 32*n + 2*n - 34 = 0. Let m be n + 6 + -5 + 1. Factor -3*w - 2 - 1/4*w**m - 3/2*w**2.
-(w + 2)**3/4
Suppose -12 + 7*r - 1/4*r**3 + 0*r**2 = 0. What is r?
-6, 2, 4
Let p(u) = -11*u**4 + 43*u**3 + 762*u**2 + 2307*u + 3. Let s(t) = -4*t**4 - 3*t**3 - 2*t**2 + t + 1. Let d(h) = 2*p(h) - 6*s(h). Solve d(l) = 0.
-24, -4, 0
Let t(b) be the first derivative of b**5/60 - 11*b**4/24 - 47*b**3/36 - b**2 - 5711. Factor t(v).
v*(v - 24)*(v + 1)**2/12
Let x(t) = -t**2 + 7*t - 5. Let d be 2/(-15) + (-385)/(-75). Let p be x(d). Suppose -45*m**2 - 84*m - 21*m + 167 - 222 + p*m**3 = 0. What is m?
-1, 11
Suppose 3*w + 8/3*w**2 + 0 - 1/3*w**3 = 0. Calculate w.
-1, 0, 9
Determine b so that -303279*b + 303867*b + 2*b**2 - 144 - 1638 = 0.
-297, 3
Solve 1/2*m**4 + 0 - 15*m**2 + 0*m - 1/2*m**3 = 0.
-5, 0, 6
Let o(h) be the second derivative of -h**8/1680 + h**7/63 + 7*h**4/12 - 3*h**2/2 - 51*h. Let w(q) be the third derivative of o(q). Let w(r) = 0. Calculate r.
0, 10
Suppose 307/4*f + 305/4*f**2 + 1/2 = 0. What is f?
-1, -2/305
Let d(t) be the second derivative of -t**4/96 + 121*t**3/6 + 6305*t. Suppose d(y) = 0. Calculate y.
0, 968
Let f = 21 + -9. Let u(b) be the first derivative of -f*b - 13*b**3 - 3/5*b**5 + 18*b**2 + 6 + 9/2*b**4. Factor u(l).
-3*(l - 2)**2*(l - 1)**2
Let k be ((-49)/245)/(((-10)/75)/2). Determine c, given that 44/7*c - 86/7*c**2 + 24/7*c**k - 6/7 = 0.
1/4, 1/3, 3
Let y(f) be the first derivative of f**5/30 - f**4/12 - f**3/6 + 3277. Factor y(n).
n**2*(n - 3)*(n + 1)/6
Let y(c) be the second derivative of c**3/6 + 3*c**2 - 7*c. Let d be y(-4). Determine l, given that 2*l**3 + d*l**2 - l**2 + 2*l**2 + 2*l + l**2 = 0.
-1, 0
Let h(x) be the third derivative of x**6/180 + 517*x**5/10 + 451244*x**4/3 + 5410276*x**3/9 + x**2 - 8*x + 117. Factor h(g).
2*(g + 1)*(g + 2326)**2/3
Let z be 2 + 9/2 + 16/32. Suppose -2*q + z = 1, -v - 4*q = -16. Factor -2*w**4 - 3*w**4 + w**2 + v + 9*w**4 - 9*w**2.
4*(w - 1)**2*(w + 1)**2
Let m(f) be the second derivative of f**7/147 - 31*f**6/105 + 249*f**5/70 - 15*f**4/14 - 450*f**3/7 + 1831*f. Solve m(h) = 0.
-2, 0, 3, 15
Let d(v) = -53061 - v**3 + 53061 - 2*v. Let u(x) = 68*x**3 - 160*x**2 + 76*x - 8. Let o(y) = 4*d(y) + u(y). Let o(h) = 0. Calculate h.
1/4, 2
Let t = -4551/5 - -915. Suppose 4*f - 3 = -h, -450*f + 20 = -450*f - 4*h. Factor -t*u + 16/5 + 12/5*u**f - 2/5*u**3.
-2*(u - 2)**3/5
Let a(q) = -10*q**3 - 50*q**2 - 129*q - 68. Let m(p) = -10*p**3 - 48*p**2 - 128*p - 64. Let j(v) = 8*a(v) - 7*m(v). Factor j(g).
-2*(g + 2)**2*(5*g + 12)
Suppose -n = -2*k + 103 - 99, 2*k - 2*n - 4 = 0. Let i(s) be the third derivative of 0*s + 1/28*s**4 + 0 - 1/210*s**5 - 2/21*s**3 - 10*s**k. Factor i(z).
-2*(z - 2)*(z - 1)/7
Let m(f) be the second derivative of -33/7*f**2 - 6/7*f**4 - 3/140*f**5 - 50 - 45/14*f**3 + 2*f. Find a, given that m(a) = 0.
-22, -1
Let q be (-2)/36*87/(-116). Let l(d) be the third derivative of 0*d + 0 + 1/6*d**5 + 0*d**3 - q*d**6 + 0*d**4 + 16*d**2. Factor l(g).
-5*g**2*(g - 2)
Let x(p) be the third derivative of p**5/60 + 5*p**4/12 - 125*p**3/2 - 5*p**2 - 709. Determine z so that x(z) = 0.
-25, 15
Let j(m) = 27*m**2 + 58*m + 8. Let o be j(-2). Suppose o - 1/4*f + 1/2*f**4 + 0*f**2 + 3/4*f**3 = 0. What is f?
-1, 0, 1/2
Let p be (-4)/(-21) + (-92872)/(-9870). Let d(r) be the second derivative of -1/50*r**5 + 2 - p*r**2 + 1/6*r**4 + 2*r + 8/15*r**3. Factor d(l).
-2*(l - 4)**2*(l + 3)/5
Suppose -17926 + 17944 = 6*o. Factor 0 + 6/11*x**4 - 6/11*x**o + 2/11*x**2 + 0*x - 2/11*x**5.
-2*x**2*(x - 1)**3/11
Find d such that 1/3*d**3 - 14/3*d**2 + 14/3 - 1/3*d = 0.
-1, 1, 14
Find z, given that -315/2 + 2829/4*z + 27/4*z**2 = 0.
-105, 2/9
Let p be 464/40 + -11 - (-7 + 171/30). Factor 1/10*j**3 + 21/10 + p*j**2 - 41/10*j.
(j - 1)**2*(j + 21)/10
Suppose 192*w - 210*w = -1710. Suppose w*o = 81*o. Factor 2/11*r**2 + 2/11*r**3 - 4/11*r + o.
2*r*(r - 1)*(r + 2)/11
Let v(w) be the first derivative of 4/63*w**3 - 2/7*w + 22 - 1/21*w**2. Let v(z) = 0. Calculate z.
-1, 3/2
Let p(y) = 2*y**3 + 65*y**2 - 17*y + 2894. Let a be p(-34). Suppose 0*z**2 - 3/7*z**5 + 0*z**a - 3/7*z + 0 + 6/7*z**3 = 0. Calculate z.
-1, 0, 1
Suppose 0 = -19*a - 21 + 55 + 42. Let i(z) be the first derivative of 1/10*z**2 + 0*z**3 + 22 - 1/20*z**a + 0*z. Find k such that i(k) = 0.
-1, 0, 1
Let a(o) = -6*o**2 - 10*o - 16. Let h(v) = -5*v**2 - 10*v - 17. Let k(t) = 4*a(t) - 5*h(t). Let k(j) = 0. Calculate j.
-7, -3
Suppose r + 13 = 57. Factor -10*l - l**2 - 64 + 36 + r - 5*l.
-(l - 1)*(l + 16)
Let r = -433/6 + 1303/18. Let i(d) be the second derivative of -r*d**3 + 0 - 1/36*d**4 + 0*d**2 - 9*d. Determine l, given that i(l) = 0.
-4, 0
Let c = 9433 - 9398. Let f(y) be the third derivative of c*y**2 + 40/3*y**3 + 0*y + 1/12*y**5 + 5/3*y**4 + 0. Let f(o) = 0. Calculate o.
-4
Factor -211250 + 1300/3*s - 2/9*s**2.
-2*(s - 975)**2/9
Let n(b) = 12*b**3 + 453*b**2 + 1143*b + 54. Let u(r) = -r**3 - 35*r**2 - 88*r - 4. Let d(h) = 2*n(h) + 27*u(h). Find x such that d(x) = 0.
-10, -3, 0
Let l(u) = -838*u - 16756. Let y be l(-20). Factor 27/7*j**2 + 15/7*j**y - 36/7*j**3 + 0 - 6/7*j.
3*j*(j - 1)**2*(5*j - 2)/7
Let f(z) = -z**3 + 4*z**2 + 2*z - 5. Let y(h) = -3*h + 1. Let v be y(-1). Let a be f(v). Factor 35*k**3 - 9*k**2 - 13*k**a + 12 - 19*k**3.
3*(k - 2)**2*(k + 1)
Let a(y) = 29*y**3 + 333*y**2 - 2268*y. Let r(g) = 8*g**3 + 95*g**2 - 648*g. Let f(i) = 5*a(i) - 18*r(i). Factor f(p).
p*(p - 36)*(p - 9)
Suppose 5 = -19*f + 81. Suppose g - 3 = -d, -4*g - 16 + 4 = -f*d. Factor -y**3 + y + 3/2*y**4 - 3/2*y**2 + g.
y*(y - 1)*(y + 1)*(3*y - 2)/2
Let d(r) = 4*r - 20. Let s be d(5). Let z be -2 + (-4 - -8) - (-4 + 4). Suppose -3/7*l**3 + 18/7*l**z - 27/7*l + s = 0. What is l?
0, 3
Let k = 1822 - 1817. Let i(a) be the third derivative of -39*a**2 + 1/120*a**k + 0*a**3 + 0 + 0*a + 1/16*a**4. Suppose i(p) = 0. Calculate p.
-3, 0
Let s = 1614 + -1614. Let i(n) be the third derivative of s*n + 0*n**3 + 12*n**2 + 0 + 1/30*n**5 + 1/6*n**4. Factor i(f).
2*f*(f + 2)
Suppose -64/17 - 1628/17*l + 6*l**2 = 0. Calculate l.
-2/51, 16
Suppose -231*d = 114*d - 11*d - 1336. Factor 8 + 1/2*f**2 + d*f.
(f + 4)**2/2
Suppose -l - 2*c = -22, 64 = 121*l - 117*l + 4*c. Determine r so that -31/5*r**2 - l*r + 2/5*r**3 - 17/5 = 0.
-1, -1/2, 17
Let s(l) be the third derivative of l**6/420 + 11*l**5/210 - l**4/7 - 2*l**2 - 270. Factor s(v).
2*v*(v - 1)*(v + 12)/7
Let z = -15/77023 + 308137/231069. Solve 0 + 8/3*p - 4*p**3 + z*p**2 = 0 for p.
-2/3, 0, 1
Let i(u) be the first derivative of u**5 + 75*u**4/4 + 10*u**3 - 950*u**2 + 3000*u + 2565. Factor i(r).
5*(r - 3)*(r - 2)*(r + 10)**2
Let l = -204479/30 - -6816. Let k(q) be the second derivative of 1/150*q**6 + 0 - 1/100*q**5 + 2*q - l*q**4 + 0*q**2 + 0*q**3. Find g such that k(g) = 0.
-1, 0, 2
Let q = -34372 - -34375. Let s(g) be the second derivative of 1/