 33*t(p). Suppose o(q) = 0. What is q?
-7/6, -1
Let f(p) be the third derivative of -p**5/120 + p**4/3 - 7*p**3/3 - 311*p**2. Factor f(n).
-(n - 14)*(n - 2)/2
Let h(l) be the third derivative of l**7/210 + 17*l**6/360 + 31*l**5/180 + 23*l**4/72 + l**3/3 - 5*l**2 - 15. Find b such that h(b) = 0.
-3, -1, -2/3
Let z be -10*(5 - 9/6 - 4). Let i(t) be the first derivative of 0*t + 3/2*t**4 + 4 - 4/3*t**3 - 2/5*t**z + 0*t**2. Factor i(x).
-2*x**2*(x - 2)*(x - 1)
Factor -481*v**3 - 489*v**3 + 12 - 22*v - 40*v**2 + 964*v**3.
-2*(v + 1)*(v + 6)*(3*v - 1)
Let u(c) be the third derivative of c**6/120 - 263*c**5/60 + 715*c**4 + 2904*c**3 + 45*c**2 + 5. Determine a so that u(a) = 0.
-1, 132
Let x(y) be the second derivative of -y**5/60 + 17*y**4/36 + y**3 + 20*y + 2. Determine s so that x(s) = 0.
-1, 0, 18
Let q(t) be the third derivative of 0*t + 0*t**3 + 3/20*t**5 - 1/120*t**6 + 0*t**4 + 17*t**2 + 0. Factor q(a).
-a**2*(a - 9)
Suppose -5*v + 32 = -4*h, -24*v + 19*v = 4*h - 48. Suppose 13*a - v*a = 3*a. Solve 0*k + 2/3*k**4 + a + 2/3*k**2 + 4/3*k**3 = 0 for k.
-1, 0
Let i be 46/88 - 12/44. Let p(d) be the first derivative of i*d**4 - 1/2*d**2 - 1/3*d**3 + d + 6. Factor p(w).
(w - 1)**2*(w + 1)
Let v(o) be the first derivative of -o**4/34 + 10*o**3/51 - 4*o**2/17 + 863. Factor v(n).
-2*n*(n - 4)*(n - 1)/17
Let h(r) = r**3 + 88*r**2 - 276*r - 270. Let k be h(-91). Factor 0 + 3/8*j**k - 3/8*j + 0*j**2.
3*j*(j - 1)*(j + 1)/8
Let p be (-9518)/22*(-5 + 6). Let h = 433 + p. Factor 0 - 2/11*j**3 - h*j**4 - 2/11*j**5 + 0*j**2 + 0*j.
-2*j**3*(j + 1)**2/11
Let y(p) be the first derivative of 2*p**6/3 - 3*p**4 - 8*p**3/3 - 66. Solve y(n) = 0 for n.
-1, 0, 2
Let z(i) = 4*i**2 - 17*i - 48. Suppose -2*t + 8 = 22. Let a = -7 - -9. Let n(v) = v**2 - 6*v - 16. Let s(y) = a*z(y) + t*n(y). Suppose s(m) = 0. What is m?
-4
Let x(h) = 3*h**3 + 248*h**2 + 2240*h + 4714. Let p(j) = 5*j**3 + 372*j**2 + 3360*j + 7070. Let r(t) = 5*p(t) - 7*x(t). Factor r(d).
4*(d + 3)*(d + 14)**2
Let z be (1 - 7/2)*(-2)/1. Let d = -6 + 8. Factor 4 + z - 4 + 12*m**3 - 16*m**d - 4*m + 3.
4*(m - 1)**2*(3*m + 2)
Let t(k) be the third derivative of k**8/1680 + k**7/1050 - k**6/40 + 23*k**5/300 - k**4/12 - 188*k**2. Find l, given that t(l) = 0.
-5, 0, 1, 2
Factor 0 - 7/3*u**2 + 20/3*u**3 - 11/3*u**4 - 2/3*u.
-u*(u - 1)**2*(11*u + 2)/3
Let b(x) = -x**3 - 4*x + 2. Let u(q) = -15*q**3 - 1264*q**2 - 28714*q - 8098. Let k(y) = -2*b(y) + 2*u(y). Find v, given that k(v) = 0.
-45, -2/7
Suppose 8 = 4*y - 0*y. Suppose 4*u - 24 = 5*x + 10, -u + 2 = 2*x. Determine n, given that n**2 + 12*n**3 + 0*n + u*n - 16*n**y - 3*n**4 + 0*n**4 = 0.
0, 1, 2
Suppose v - 3*v = -5*u - 25, 0 = 4*v + 3*u + 15. Suppose 12*b = -12*b - 30 + 78. What is d in -1/4*d**4 + 0 - 1/8*d + 1/8*d**5 + v*d**3 + 1/4*d**b = 0?
-1, 0, 1
Let y(q) be the first derivative of -3/2*q**4 - 2*q**2 - 16 + 8/5*q**5 - 6*q**3 + 0*q. Factor y(f).
2*f*(f - 2)*(f + 1)*(4*f + 1)
Let a(w) be the third derivative of -w**5/210 - 83*w**4/21 - 27556*w**3/21 - 13*w**2 - 11. Suppose a(y) = 0. Calculate y.
-166
Let d be (-2*3)/(1/3). Let r = -13 - d. Find o, given that 0*o**5 - 3*o**r + 9*o**2 + 4*o**2 - o**2 - 9*o**4 = 0.
-2, 0, 1
Let h be 4/(-10)*3*1/12*-5. Let -h*q**3 - 3/2*q**2 + 2 + 0*q = 0. What is q?
-2, 1
Let h(o) be the first derivative of 5*o**3/3 + 85*o**2 - 175*o + 90. Factor h(d).
5*(d - 1)*(d + 35)
Suppose 0 = 2*o - 1 + 5. Let i = 4 + o. Suppose -2*q**2 - 4*q**5 + 4*q**4 - 13*q**4 - 6*q**3 + q**i = 0. What is q?
-1, -1/4, 0
Let n(p) be the first derivative of 2*p**4 - 16/3*p**3 - 20 + 0*p + 16/5*p**5 - 6*p**2 + 2/3*p**6. What is z in n(z) = 0?
-3, -1, 0, 1
Let u be (-3)/((18/(-4))/3). Suppose 5*o = 5*a - 340, -25 = 3*a + u*o - 219. Determine n, given that 89*n + 4 - a*n**2 - 17*n - 3*n**4 - 31 + 24*n**3 = 0.
1, 3
Let s = -845 + 845. Let u(d) be the second derivative of -2*d + s + 1/18*d**4 + 0*d**2 + 0*d**3 - 1/45*d**6 + 0*d**5. Find y such that u(y) = 0.
-1, 0, 1
Let a(d) be the second derivative of d**5/4 + 2*d**4/3 - 7*d**3/6 - 3*d**2 - 23*d - 5. Factor a(z).
(z - 1)*(z + 2)*(5*z + 3)
Find d such that 15*d**3 - 23*d**4 - 16*d**4 + 5*d + 2*d + 34*d**4 - 15*d**2 - 2*d = 0.
0, 1
Let 30*r**2 - 5/2*r**5 - 10*r - 65/2*r**3 + 15*r**4 + 0 = 0. Calculate r.
0, 1, 2
Let p(a) be the first derivative of -a**6/39 - 22*a**5/65 - 9*a**4/13 + 4*a**3/39 + 19*a**2/13 + 18*a/13 + 41. Determine x so that p(x) = 0.
-9, -1, 1
Suppose 26 = -4*b - 18. Let p = b + 15. Factor -11*l**2 - 3*l**3 - p*l + 5*l + 9*l**2.
-l*(l + 1)*(3*l - 1)
Let i(y) = -9*y**3 - 3*y**2 + 6. Let n(f) = -8*f**3 - 3*f**2 + f + 5. Suppose -2*g - 2 - 8 = 0. Let x(z) = g*i(z) + 6*n(z). Find h, given that x(h) = 0.
-2, 0, 1
Suppose 3*m = 9, -4*n + 4*m = 5*m - 23. Suppose 5*q + a = q + 3, -5*q = a - n. Let -4*f**2 + 0*f**q + 4*f**4 - 4*f + 6*f**3 - 2*f**3 = 0. What is f?
-1, 0, 1
Let x(r) be the second derivative of -r**6/30 + 2*r**5/5 - 4*r**4/3 - 4*r - 2. Factor x(d).
-d**2*(d - 4)**2
Let m(t) = -2*t**2 - 20*t - 40. Let n be m(-3). Let i(y) be the first derivative of 1/6*y**3 - 1/4*y**n - 3 + 0*y. Factor i(j).
j*(j - 1)/2
Let y = -1231 - -1233. Let h(k) be the first derivative of 0*k + 2/9*k**3 - 2 + k**y. Factor h(c).
2*c*(c + 3)/3
Let u(m) be the third derivative of m**6/200 - m**5/25 + m**4/10 + 304*m**2. Let u(h) = 0. Calculate h.
0, 2
Let z(h) be the first derivative of -h**6/240 + 7*h**5/80 + h**4/2 + 14*h**3/3 + 2*h - 5. Let t(p) be the third derivative of z(p). Find d, given that t(d) = 0.
-1, 8
Let v(t) = -t**2 + 68*t - 372. Let l be v(6). Let m = 5 + -2. Solve 0 - 1/3*r**m + l*r**2 + 1/6*r**4 + 0*r = 0.
0, 2
Factor 0 + 12/7*r**2 + 15/7*r - 3/7*r**3.
-3*r*(r - 5)*(r + 1)/7
Let y(z) be the second derivative of -z**7/56 + 3*z**6/10 - 171*z**5/80 + 67*z**4/8 - 39*z**3/2 + 27*z**2 - 123*z. Solve y(i) = 0.
2, 3
Let d = 13906 - 13904. Suppose z + 2*h + 4 = 0, 8 = 2*h - 4*h. Factor 2/3*y**z + 2/3*y**3 + 0*y**d + 0*y + 0.
2*y**3*(y + 1)/3
Let c(b) = -9*b**3 - 26*b**2 - 24*b. Let v(q) = 4*q**3 + 12*q**2 + 11*q. Let n(o) = -3*c(o) - 7*v(o). Factor n(j).
-j*(j + 1)*(j + 5)
Let d be 6 - -272 - (2 - 0). Let j be d/30 + 4/(-20). Factor -12*o**2 + 2*o**4 + 6*o**4 + 16 - 41*o + j*o + 20*o**3.
4*(o - 1)*(o + 2)**2*(2*o - 1)
Let j(g) be the third derivative of g**5/140 + 15*g**4/56 + 18*g**3/7 - 440*g**2. Let j(a) = 0. Calculate a.
-12, -3
Let n(x) be the first derivative of x**5/135 + 23*x**2/2 + 19. Let j(o) be the second derivative of n(o). Factor j(v).
4*v**2/9
Let u(l) be the third derivative of 7*l**7/2 + 35*l**6/3 + 31*l**5/3 + 10*l**4/3 + 459*l**2. Factor u(t).
5*t*(3*t + 4)*(7*t + 2)**2
Let d(h) be the second derivative of -h**8/1680 + h**7/210 - 2*h**5/15 - 11*h**4/12 - 11*h. Let p(r) be the third derivative of d(r). Solve p(t) = 0 for t.
-1, 2
Let c = -180 - -185. Let d(l) be the third derivative of 0*l + 4/3*l**4 + 1/6*l**c + 0 + 4*l**2 + 4/3*l**3 - 5/12*l**6. Determine r so that d(r) = 0.
-2/5, 1
Let t(z) = -4*z**4 + 8*z**3 - 8*z**2 - 11*z - 9. Let l(y) = y**4 + y**2 + y + 1. Let g = 85 + -49. Let i(b) = g*l(b) + 4*t(b). Find v such that i(v) = 0.
-1, 0, 2/5
Let x(q) be the first derivative of -7*q**6/6 + 23*q**5/5 + 16*q**4 - 20*q**3/3 + 33. Find l, given that x(l) = 0.
-2, 0, 2/7, 5
Suppose -15 = -2*f + 1. Factor f*v - 58*v**2 - 9*v**3 + v - 6 + 64*v**2.
-3*(v - 1)*(v + 1)*(3*v - 2)
Let w be 16/(-80) + (-112)/(-35). Let z(u) be the second derivative of 5/2*u**w + 3/20*u**5 - 3*u**2 - u**4 - 3*u + 0. Factor z(h).
3*(h - 2)*(h - 1)**2
Let i(o) be the first derivative of o**3/3 - o**2/4 - 3*o + 846. Find x, given that i(x) = 0.
-3/2, 2
Let l(m) be the third derivative of 191/36*m**5 - 4*m**2 - 8/21*m**7 - 10/3*m**4 + 0 + 0*m + 20/63*m**8 - 61/18*m**6 + 10/9*m**3. Determine t so that l(t) = 0.
-2, 1/4, 2
Suppose -27914 = -63*w - 186*w - 1022. Factor w + 64/3*y**3 + 4/3*y**4 + 184/3*y**2 - 192*y.
4*(y - 1)**2*(y + 9)**2/3
Suppose -13*d - 2 = -15. Let p be (11/11 + d/(-1))/(-2). Let -20/3 + p*h + 5/3*h**2 = 0. What is h?
-2, 2
Factor 121 + 110 - 9*n + 3*n**2 - 225.
3*(n - 2)*(n - 1)
Let z(h) = 7*h - 12. Let k be z(2). Factor -24*u + 10*u**k + 3 + 5 - 4 + 4.
2*(u - 2)*(5*u - 2)
Factor 72 - 109*z**2 - 97*z**2 + 202*z**2 + 28*z.
-4*(z - 9)*(z + 2)
Let w(s) be the second derivative of -4*s**2 + 0 - 10/3*s**3 