 Find f, given that c(f) = 0.
15
Let x be 10*11/(-66) + 8 + (-330)/54. Factor -10/9 + x*p + 10/9*p**2 - 2/9*p**3.
-2*(p - 5)*(p - 1)*(p + 1)/9
Let -54 + 2557*f - 20*f**3 - 5361*f - 72*f**2 - 2*f**4 + 2696*f = 0. What is f?
-3, -1
Factor -2/3*t**2 + 5944/3*t - 4416392/3.
-2*(t - 1486)**2/3
Let b(n) be the first derivative of n**3 - 1998*n**2 + 1330668*n + 8226. Factor b(a).
3*(a - 666)**2
Let c(k) be the first derivative of -k**6/45 + k**5/6 - 7*k**4/18 + k**3/3 + 66*k + 87. Let u(p) be the first derivative of c(p). Find b such that u(b) = 0.
0, 1, 3
Let i(l) = 13*l - 10. Let q be i(2). Let d = 19 - q. Factor -3*a**2 - 63*a**d + 3*a**4 + 117*a**3 + 3*a**5 - 57*a**3.
3*a**2*(a - 1)*(a + 1)**2
Let l(c) be the first derivative of -c**3/2 + 111*c**2/4 - 54*c - 2850. Let l(d) = 0. What is d?
1, 36
Let b(t) = 2*t**2 - 49*t + 237. Let f be b(18). Let s(o) = -o**3 - 6*o**2 + 8*o + 9. Let h be s(-7). Factor -f - 69*l**2 + 19 + 16*l + 73*l**h.
4*(l + 2)**2
Suppose -2*x = -168 - 82. Let r = x - -106. Determine c, given that -239 - 36*c + r - 2*c**2 + 36*c**3 + 10*c**2 = 0.
-1, -2/9, 1
Let a(k) = -12*k**2 + 3 + 29*k**2 - 19*k**2 - 13*k. Let b(q) = 7*q**2 + 40*q - 9. Let g(c) = 11*a(c) + 4*b(c). What is v in g(v) = 0?
-3, 1/6
Let i(k) be the first derivative of 5*k**4/4 - 85*k**3 + 120*k**2 + 500*k + 4128. Factor i(p).
5*(p - 50)*(p - 2)*(p + 1)
Let 3/4*y**4 + 0 + 135/4*y**2 + 9*y**3 + 81/2*y = 0. Calculate y.
-6, -3, 0
Let p be 32/((-40)/5) + 507. Let i = 2529/5 - p. Determine o so that -2/5 - 6*o**2 - i*o - 8/5*o**4 - 26/5*o**3 = 0.
-1, -1/4
Let u = -107 + 107. Let d be (-21)/6*(-16)/14 - u. Solve 6*s**3 + 1364*s + 16*s**4 - 1364*s + 6*s**5 - d*s**2 = 0.
-2, -1, 0, 1/3
Let o(k) be the second derivative of -k**4/3 + 20*k**3/3 + 1518*k**2 - k - 2463. Determine x, given that o(x) = 0.
-23, 33
Let t(w) = w**3 + 8*w**2 + 4*w. Let n be (-14)/6*(1 + 10/5). Let g be t(n). Find y, given that 16*y**2 + 5*y - 17 + 47 - g*y**2 = 0.
-2, 3
Let j(i) = i**2 + 13*i - 317. Let n be j(13). Suppose -l = k, 5*l = 83*k - 81*k - n. Factor 0*b - 1/2*b**k + 1/2*b**4 - 1/2*b**2 + 1/2*b**5 + 0.
b**2*(b - 1)*(b + 1)**2/2
Let r be (-24960)/704 + (36 - 0). Let -6*q**2 + 0 + 6/11*q**3 + 34/11*q**4 + r*q**5 + 20/11*q = 0. What is q?
-5, -2, 0, 1/3, 1
Let f(l) = 2*l**2 + 50*l - 106. Let i be f(2). Suppose i*x - 3*x = -8*x. Let x + 1/4*o**2 + 0*o = 0. What is o?
0
Let n(t) be the first derivative of -t**4/7 - 2236*t**3/21 - 22240*t**2 + 44800*t + 4039. Solve n(r) = 0 for r.
-280, 1
Let m(q) = 10*q**3 + 17*q**2 + 13. Let f(l) = 4362*l - 5*l**3 - 6 - 4362*l - 9*l**2. Let r(b) = 13*f(b) + 6*m(b). Solve r(p) = 0.
-3, 0
Let t(n) be the first derivative of n**4/72 - 5*n**3/36 - n**2/2 - 135*n + 134. Let v(o) be the first derivative of t(o). Suppose v(p) = 0. What is p?
-1, 6
Let j = -1079588 + 22671350/21. Factor -2/21*i - 16/21*i**2 + 16/21 + j*i**3.
2*(i - 8)*(i - 1)*(i + 1)/21
Let q(k) be the second derivative of -k**6/1440 - 7*k**5/240 + k**3/6 - 45*k**2/2 - 41*k. Let g(y) be the second derivative of q(y). Factor g(o).
-o*(o + 14)/4
Let p(f) be the third derivative of -f**7/105 - 17*f**6/20 + 26*f**5/15 - 125*f**2 + 4. Factor p(h).
-2*h**2*(h - 1)*(h + 52)
Let r(q) be the second derivative of 11/50*q**6 - 5 + 31/60*q**4 - 2/5*q**2 - 53/100*q**5 + 0*q**3 - 1/30*q**7 - 28*q. Solve r(j) = 0 for j.
-2/7, 1, 2
Suppose -62*t - 5 = -63*t. Determine k so that -29*k**2 + 1337*k**t - 1342*k**5 - k**2 - 30*k**4 - 55*k**3 = 0.
-3, -2, -1, 0
Factor -115/4*d + 5/4*d**2 + 255/2.
5*(d - 17)*(d - 6)/4
Let v(h) = h + 7. Let f be v(-7). Let j be (666/24 + 10560/(-384))*(-8)/(-3). What is o in 0*o**3 + f*o**2 - 4/3*o**4 + j*o**5 + 0*o + 0 = 0?
0, 2
Suppose -6*g - 2*z = -g, 4*g = z + z. Let y(r) be the second derivative of 0*r**5 - 1/27*r**4 + 1/9*r**2 + 0 + g*r**3 - 22*r + 1/135*r**6. Factor y(l).
2*(l - 1)**2*(l + 1)**2/9
Let j(k) be the third derivative of 1/7*k**7 - 1/8*k**6 + 5/336*k**8 - 14/3*k**5 - 10*k**4 + 0*k + 0*k**3 + 0 - 49*k**2. Let j(m) = 0. Calculate m.
-4, -1, 0, 3
Let u = -969 - -969. Suppose 2*d + 2 = 4*t - u*t, -3 = t + 3*d. Factor t*m + 0 - 1/5*m**3 + 1/5*m**2.
-m**2*(m - 1)/5
Let j(d) be the third derivative of -d**7/2415 + 7*d**6/345 - 61*d**5/345 + 41*d**4/69 - d**3 + 139*d**2 - 7*d. Determine b, given that j(b) = 0.
1, 3, 23
Factor -94/3*k - 44/3*k**2 + 2/3*k**3 - 16.
2*(k - 24)*(k + 1)**2/3
Let a be (21/(-9) - -2)/(3/(-27)). What is m in 2*m**3 - 20 - 18*m + 20*m**2 + 8*m - 6*m**a + 14*m = 0?
-1, 1, 5
Suppose 874 = -38*u + 950. Factor -6 + 1/2*m**2 - u*m.
(m - 6)*(m + 2)/2
Find t such that 845/3*t**5 + 305/3*t**3 - 10982/3*t**2 + 9412/3*t**4 - 1780/3*t + 2200/3 = 0.
-11, -10/13, 2/5, 1
Let q(g) = 4*g + 59. Let r be q(-14). Let -5*l**4 + 75*l**r + 25*l**2 + 11*l**2 + 45*l**2 - l**2 = 0. Calculate l.
-1, 0, 16
Suppose -3*p + 18 = -n, 9*p - 4*p = n + 28. Let h be 3 + -1 - (-11 - (n - 8)). Solve 6*i**3 + 18*i**h + 18*i + 2/3*i**4 + 0 = 0 for i.
-3, 0
Factor 70/3*f - 2/3*f**4 + 0 + 2/3*f**3 + 74/3*f**2.
-2*f*(f - 7)*(f + 1)*(f + 5)/3
Let c(y) = 5*y**2 + y + 2. Let m(g) = 27*g**2 + 375*g - 354. Let r(b) = 6*c(b) - m(b). Factor r(j).
3*(j - 122)*(j - 1)
Let a(k) be the first derivative of -25*k**4 + 39680*k**3/3 - 15848*k**2 + 6336*k + 4492. Factor a(z).
-4*(z - 396)*(5*z - 2)**2
Suppose -10 + 1 = -3*j. Suppose 15 = 2*g + j*l, 5*g + 4*l = 19 + 8. Factor 0 + 12/5*i + 46/5*i**2 + 14/5*i**g.
2*i*(i + 3)*(7*i + 2)/5
Let k(n) be the third derivative of -n**5/60 + 67*n**4/24 - 613*n**3/6 - 24*n**2. Let t be k(56). Factor 0*a + 2/11*a**t + 6/11*a**2 - 8/11.
2*(a - 1)*(a + 2)**2/11
Factor 56/5*b**3 + 0*b - 8/5*b**4 + 0 - 64/5*b**2 - 2/5*b**5.
-2*b**2*(b - 2)**2*(b + 8)/5
Let h(v) = v**3 - 2*v. Let b(p) = -10*p**3 - 25*p**2 - 20*p. Suppose 14*m - 47 - 23 = 0. Let k(o) = m*h(o) + b(o). Factor k(t).
-5*t*(t + 2)*(t + 3)
Let i(l) = l**3 + 2*l**2 - 26*l + 8. Let v = -511 - -515. Let w be i(v). Factor 4/15*b**3 + w*b + 0*b**2 + 2/5*b**4 + 0 + 2/15*b**5.
2*b**3*(b + 1)*(b + 2)/15
Suppose 10058*x + 60*x**3 - 10046*x + 3*x**4 + 24*x**2 - 45*x**3 = 0. What is x?
-2, -1, 0
Let m = 88261/30 + -2942. Let d(v) be the third derivative of -1/20*v**4 - 1/60*v**5 - 17*v**2 - m*v**3 + 0*v + 0. Factor d(f).
-(f + 1)*(5*f + 1)/5
Let o(g) be the second derivative of 0 + 8/3*g**3 - 6*g**2 - 67*g - 1/3*g**4. Let o(z) = 0. What is z?
1, 3
Let o(l) be the second derivative of 1/39*l**3 - 2 - 1/39*l**4 + 9*l - 1/130*l**5 + 2/13*l**2. Factor o(q).
-2*(q - 1)*(q + 1)*(q + 2)/13
Suppose 96875/4*k - 78125/2 - 10125/4*k**2 + 385/4*k**3 - 5/4*k**4 = 0. Calculate k.
2, 25
Suppose 513591*q - 515111/2*q**2 - 1026169/4 + 507*q**3 - 1/4*q**4 = 0. Calculate q.
1, 1013
Suppose 0*r + 0 + 4*r**4 + 2*r**2 - 7/3*r**5 + 25/3*r**3 = 0. Calculate r.
-1, -2/7, 0, 3
Let y(n) be the first derivative of n**4/20 - 29*n**3/15 + 39*n**2/2 + 45*n - 1628. Factor y(f).
(f - 15)**2*(f + 1)/5
Let y be (-79)/474*10*(3/(-10) - 0). Factor 0 + 6*h + y*h**2.
h*(h + 12)/2
Determine c so that -40 + 36*c + 144/5*c**4 + 3552/5*c**2 - 1436/5*c**3 = 0.
-1/4, 2/9, 5
Let y = -247241/5 - -49457. Solve 2/5*d**2 - y + 18/5*d = 0 for d.
-11, 2
Let m be (4 - 5 - -1) + 5. Let 2*b**2 - m*b**2 - 23*b**2 - 20*b**2 + 180 + 20*b + b**2 - 5*b**3 = 0. What is b?
-9, -2, 2
Let x(c) be the third derivative of c**5/20 + 93*c**4/4 - 380*c**3 - 1198*c**2. Solve x(h) = 0 for h.
-190, 4
Suppose 3*z - 2*p = 2, -8 = -6*p + 2*p. Determine y so that 14*y**5 + 35*y**3 + 11*y**5 - 19*y**5 + 59*y**3 + 20*y + 46*y**4 + 74*y**z = 0.
-5, -1, -2/3, 0
Let a(v) = v**2 + 267*v - 266. Let g be a(1). Suppose 1 = -m + 4. Let -16*x**2 + 14*x**4 + g*x**2 - x**m + 4*x - 3*x**3 = 0. Calculate x.
-1, 0, 2/7, 1
Let s be (-1)/(-6)*1*4. Let j be (34 - (-7322)/(-231)) + (-18)/11. Factor j - 2/9*f + 2/9*f**3 - s*f**2.
2*(f - 3)*(f - 1)*(f + 1)/9
Find d such that 2*d**4 - 7*d**4 + 970*d**2 + 1920*d - 106*d**3 - 609*d**3 - 240*d**3 = 0.
-192, -1, 0, 2
Let m(b) = -2501*b - 27509. Let c be m(-11). Factor 9/8*u**c + 3/4*u + 0.
3*u*(3*u + 2)/8
Let w be (1120/(-20) - -30)/(-11). Factor -2/11*u + 2/11*u**3 + 26/11*u**2 - w.
2*(u - 1)*(u + 1)*(u + 13)/11
Suppose 5*i - 2*k - 25 = 0, 2 - 12 = 2*k. Solve -132*d + 40 - i*d**4 + 24*d**2 + 15*d**2 + 5 + 87*d**2 + 2*d**3 - 38*d**3 = 0 for d.
-15, 1
Let t(k) be the first derivat