p(f) be the third derivative of 0 - 1/24*f**i + 0*f**3 - 5/8*f**4 + 1/3*f**5 + 0*f - 3*f**2. Suppose p(j) = 0. What is j?
0, 1, 3
Let d(k) be the second derivative of -5*k**7/21 - 4*k**6/5 - 2*k**5/5 + 5*k**4/3 + 3*k**3 + 2*k**2 - 60*k. Suppose d(i) = 0. What is i?
-1, -2/5, 1
Let c(u) be the second derivative of -14*u + 0*u**4 + 0*u**2 + 1/100*u**5 - 1/30*u**3 + 0. Factor c(r).
r*(r - 1)*(r + 1)/5
Suppose 1500 = 4*k - 344. Let z = 1397/3 - k. Suppose 4*r**2 - 4/3 - z*r - 28/3*r**4 + 34/3*r**3 = 0. What is r?
-1/2, -2/7, 1
Let g(c) = -c**3 - 1. Let m(f) = -8*f**3 - 25*f**2 + 12*f - 1. Let p(t) = -4*g(t) + 4*m(t). Factor p(j).
-4*j*(j + 4)*(7*j - 3)
Let w(a) be the first derivative of 1/22*a**4 - 2/33*a**3 + 0*a**2 + 3 + 0*a + 2/55*a**5 - 1/33*a**6. Factor w(f).
-2*f**2*(f - 1)**2*(f + 1)/11
Suppose -568 - 493 = -142*m + 217. Factor -15/2*x - m + 3/2*x**2.
3*(x - 6)*(x + 1)/2
Factor 5*k**3 - 5*k + 212 - 212.
5*k*(k - 1)*(k + 1)
Let b(i) be the third derivative of -3/14*i**4 + 1/140*i**5 + 0 + 0*i + 18/7*i**3 + 10*i**2. Solve b(l) = 0.
6
Let i = 7 - 2. Suppose -522 = 15*d - 1302. Factor i*k**5 + d*k**4 - 31*k**3 + 28*k**2 - 21*k**5 + 10*k**3 - 4*k - 39*k**3.
-4*k*(k - 1)**3*(4*k - 1)
Let u(n) be the second derivative of -n**5/20 + 7*n**4/2 - 66*n**3 - 484*n**2 - 1033*n. Factor u(z).
-(z - 22)**2*(z + 2)
Let t(a) be the second derivative of -3*a**5/20 - 5*a**4/2 - 9*a**3/2 + 6*a - 4. Factor t(u).
-3*u*(u + 1)*(u + 9)
Let l be (-182)/2730*18/((-12)/4). Solve l*a + a**3 - 7/5*a**2 + 0 = 0.
0, 2/5, 1
Let l(r) = 13*r**2 - 35*r + 42. Let g(h) = -2*h**2 + h. Let v(k) = 20*g(k) + 5*l(k). Find z such that v(z) = 0.
2, 21/5
Let z(y) be the third derivative of -1/12*y**4 - 6*y**2 + 1/60*y**5 + 0*y**3 + 0*y + 0. Solve z(p) = 0 for p.
0, 2
Let l be 11/(-3) - (-2 + 1). Let m = l + 4. Solve m*u**2 - 4/3*u**3 - 2/3 - 2/3*u**4 + 2/3*u + 2/3*u**5 = 0.
-1, 1
Let r be (-1348)/(-3033) - ((-100)/18 + 1). Let -6/5*y**3 + 0*y - 6/5*y**4 - 2/5*y**r - 2/5*y**2 + 0 = 0. Calculate y.
-1, 0
Let k(a) = 5*a + 23. Let p be k(12). Let l = -413/5 + p. Factor -1/5*n - 4/5*n**2 + 3/5*n**3 + l.
(n - 1)**2*(3*n + 2)/5
Let t be (-4)/(-6) - (-5 + 5/1). Let o(m) be the first derivative of t*m**3 + 1/2*m**4 + 0*m**2 + 3 + 0*m. Suppose o(f) = 0. Calculate f.
-1, 0
Suppose -35*u = -57*u - 7*u - 68*u. Let -1/9 + 1/9*g**2 + u*g = 0. Calculate g.
-1, 1
Let c = 317/40 - 57/8. Suppose -n = n. Factor c*m + n - 2/5*m**2.
-2*m*(m - 2)/5
Let k(d) = -d**2 - 105*d - 2726. Let c be k(-58). Let -t**4 + 0 + 1/3*t**5 + c*t + 0*t**2 + 0*t**3 = 0. Calculate t.
0, 3
Solve 27648*w + 1/2*w**4 + 1728*w**2 + 48*w**3 + 165888 = 0 for w.
-24
Let w(y) be the first derivative of y**7/210 + y**6/90 - y**5/30 - y**4/6 + y**3 - 1. Let g(f) be the third derivative of w(f). Find x such that g(x) = 0.
-1, 1
Let q(g) be the second derivative of g**6/25 - 7*g**5/50 + g**4/6 - g**3/15 + 204*g. Find c such that q(c) = 0.
0, 1/3, 1
Let j(h) = -3*h**4 - 15*h**3 + 9*h**2 + 15*h - 33. Let u(t) = t**2 - 1 + 0 - 892*t**3 - t + 893*t**3. Let w(b) = j(b) + 15*u(b). Factor w(i).
-3*(i - 2)**2*(i + 2)**2
Let t(v) be the third derivative of -v**7/1050 + v**6/150 - v**5/50 + v**4/30 - v**3/30 - 137*v**2. Factor t(o).
-(o - 1)**4/5
Let x(k) be the third derivative of -10*k**2 + 4/27*k**3 - 1/108*k**6 + 1/9*k**4 + 1/90*k**5 + 0*k + 0. Find o such that x(o) = 0.
-1, -2/5, 2
Let r(m) be the second derivative of -m**5/5 + 46*m**4/3 + 190*m**3/3 + 96*m**2 - 175*m. Factor r(x).
-4*(x - 48)*(x + 1)**2
Let f = -1/6083 - -97331/18249. Find q such that -f*q**3 - 16/3 + 12*q + 14*q**2 - 2*q**4 = 0.
-4, -1, 1/3, 2
Let l = 29558/9 - 3284. Let y = 34/315 - -4/35. Factor -l + 4/9*m**2 + 4/9*m**3 - 2/9*m - y*m**5 - 2/9*m**4.
-2*(m - 1)**2*(m + 1)**3/9
Factor -4/7*g - 12/7 + 1/7*g**2.
(g - 6)*(g + 2)/7
Let o(g) be the first derivative of 0*g + 0*g**2 - 32 - 1/6*g**6 - 2/3*g**3 + 3/4*g**4 + 0*g**5. Solve o(l) = 0.
-2, 0, 1
Let n = -6/7 + 58/35. Factor -n*u**4 - 4/5*u**3 + 0*u + 0 + 0*u**2.
-4*u**3*(u + 1)/5
Let z(s) be the second derivative of 0 + 5/6*s**3 + 0*s**2 - 18*s + 3/4*s**5 - 5/4*s**4 - 1/6*s**6. Factor z(f).
-5*f*(f - 1)**3
Let r(w) be the first derivative of 0*w**2 + 7/4*w**4 + 3 + 1/2*w**6 + w - w**3 - 27/20*w**5 - 1/14*w**7. Let i(m) be the first derivative of r(m). Factor i(c).
-3*c*(c - 2)*(c - 1)**3
Let -648*r**4 + r - r + 647*r**4 + 12*r**3 = 0. Calculate r.
0, 12
Let m(i) be the second derivative of -11*i**7/12600 + 13*i**6/3600 - i**5/300 + i**4/4 - 40*i. Let s(t) be the third derivative of m(t). What is g in s(g) = 0?
2/11, 1
Let a = 47869/12540 + 1/1140. Find m such that a*m - 36/11 + 2/11*m**3 - 16/11*m**2 = 0.
2, 3
Suppose -170 = -2*y + 122. Find j, given that -2*j**2 + 146 - j**3 - y - j = 0.
-1, 0
Let z(w) be the first derivative of -14*w**2 + 1 + 1 - w**3 + 20*w**2. Factor z(g).
-3*g*(g - 4)
Let a be (-10 - -14)*1/9. Factor -2/9*b - a + 2/9*b**2.
2*(b - 2)*(b + 1)/9
Find d, given that -7*d**4 - 828*d**3 + 7*d + 821*d**3 + 8*d**4 - d**2 = 0.
-1, 0, 1, 7
Let q(f) be the first derivative of -3*f**5/10 + 39*f**4/8 + 7*f**3 - 458. Let q(z) = 0. Calculate z.
-1, 0, 14
Suppose 2*u - 8 = -4. Let m be (1 - u)/2*(-8 - -2). Factor -2*k - 1/4*k**m + 5/4*k**2 + 1.
-(k - 2)**2*(k - 1)/4
Let y = -9 + 14. Suppose -4*p = -3 - 5. Suppose t**p + y*t - 2*t - 4*t = 0. What is t?
0, 1
Let s(g) be the first derivative of g**3/15 - 83*g**2/10 + 82*g/5 - 277. Factor s(h).
(h - 82)*(h - 1)/5
Factor 2/5*d**2 + 92/5 - 94/5*d.
2*(d - 46)*(d - 1)/5
Let d(z) be the third derivative of z**7/20160 - z**5/960 - 11*z**4/24 - 17*z**2. Let q(u) be the second derivative of d(u). Factor q(t).
(t - 1)*(t + 1)/8
Factor 2/7*w**2 - 4/7*w - 6/7.
2*(w - 3)*(w + 1)/7
Let o = 12893 + -38678/3. Find c, given that 4/3*c**2 - o*c + 4/3*c**4 - 2*c**3 - 1/3*c**5 + 0 = 0.
0, 1
Let h = -17 + 20. Suppose 0 = -4*j + 13 + 3. Suppose j + 7*l**2 - 4 - 2*l + 5*l**h - 4*l**2 = 0. What is l?
-1, 0, 2/5
Suppose -9*u = 8*u - 56 + 22. Suppose 0 + 5*m + 5/2*m**3 - 15/2*m**u = 0. What is m?
0, 1, 2
Let p(l) be the second derivative of -l**7/105 + l**6/75 + l**5/10 - l**4/30 - 8*l**3/15 - 4*l**2/5 - 3*l - 16. What is y in p(y) = 0?
-1, 2
Let v be ((-8)/20)/((-42)/20 + 2). Let n(o) = -5*o**2 + 20*o + 7. Let h(r) = -5*r**2 + 19*r + 6. Let i(d) = v*n(d) - 3*h(d). Factor i(a).
-(a - 5)*(5*a + 2)
Suppose 275*f = 293*f. Factor -2/3 + 2/3*b**2 - b + 4/3*b**3 + f*b**4 - 1/3*b**5.
-(b - 2)*(b - 1)*(b + 1)**3/3
Let s(u) = -6*u**2 - 311*u. Let y(v) = 9*v**2 + 467*v. Let q(w) = -8*s(w) - 5*y(w). Factor q(c).
3*c*(c + 51)
Suppose 12*w - 216 = -47*w - 13*w. Factor 2/11*r**5 - 4/11*r**w + 4/11*r**2 + 2/11*r - 2/11*r**4 - 2/11.
2*(r - 1)**3*(r + 1)**2/11
Suppose -24/19*g**4 + 42/19*g + 20/19 - 2/19*g**5 - 40/19*g**3 + 4/19*g**2 = 0. What is g?
-10, -1, 1
Let x = 925/266 - -3/133. Suppose x*s**2 - 9/2*s + 1 = 0. What is s?
2/7, 1
What is i in 18*i - 11*i + 60 + 13*i - 5*i**2 = 0?
-2, 6
Suppose 7*r - 4*r = 36. Suppose -5*m - 4*a + 17 = 6, 3*m - 3*a = r. Factor 6*d + 2*d**4 + m + d**4 - 6*d**3 - 6.
3*(d - 1)**3*(d + 1)
Let n(c) = -c**2 + c + 1. Let t(b) = -2*b**4 + 10*b**3 - 14*b**2 + 10*b - 8. Let j = 54 - 58. Let f(k) = j*n(k) - t(k). What is z in f(z) = 0?
1, 2
Suppose 11*h = -6*h. Let w(t) be the second derivative of 1/2*t**3 + 1/14*t**7 + 1/10*t**6 - 1/2*t**4 + h - 3/10*t**5 + 3/2*t**2 - 7*t. Factor w(d).
3*(d - 1)**2*(d + 1)**3
Let i(k) = k**3 - 7*k**2 + 5*k + 8. Let y be i(6). Let q = -16 + 20. Determine f so that 9*f**3 - q*f - 5*f**4 + f**4 + 7*f - 9*f**y + f**4 = 0.
0, 1
Suppose -5*s + 15 = 5*c, 2*s = c + 7*s + 13. Suppose -4*f = -c*f + 12. Solve 7*o**4 - f*o**2 + o**4 - 9*o**4 + 4*o**3 = 0.
0, 2
Let m(h) be the third derivative of -2*h**7/105 + h**6/6 - 7*h**5/15 + h**4/2 + 178*h**2. Suppose m(z) = 0. Calculate z.
0, 1, 3
Let r(f) be the first derivative of f**4/2 - 178*f**3 + 23763*f**2 - 1409938*f + 179. Determine l, given that r(l) = 0.
89
Let v(f) be the first derivative of 2/3*f**3 + 9 + 8/5*f**2 + 8/5*f + 1/10*f**4. Factor v(h).
2*(h + 1)*(h + 2)**2/5
Let n(a) be the second derivative of -2*a**6/15 + 24*a**5/5 - 214*a**4/3 + 560*a**3 - 2450*a**2 + 40*a. Determine k, given that n(k) = 0.
5, 7
Let z(y) = y**4 - y**2 + 2. Let m(d) = -5*d**5 - 14*d**4 - 16*d**3 - d**2 + 10. Let l(c) = m(c) - 5*z(