
Let h(n) be the third derivative of n**6/900 + n**5/300 - 2*n**3 - 10*n**2. Let p(u) be the first derivative of h(u). Suppose p(w) = 0. What is w?
-1, 0
Factor -2/3*a**2 + 4*a + 2/3*a**4 - 4*a**3 + 0.
2*a*(a - 6)*(a - 1)*(a + 1)/3
Let m(c) be the first derivative of c**6/36 - c**5/5 + c**4/3 + c**3/3 - 3*c**2/4 + 173. Factor m(y).
y*(y - 3)**2*(y - 1)*(y + 1)/6
Let i be 0 + -7*(0 - 1). Let c(n) be the third derivative of -1/21*n**i + 0*n**3 - 1/6*n**4 - 1/30*n**5 + 0 + 2/15*n**6 + 2*n**2 + 0*n. Factor c(p).
-2*p*(p - 1)**2*(5*p + 2)
Let l(x) be the second derivative of 12*x + 0 + 0*x**4 + 2*x**3 - 4/5*x**5 + 2*x**2. Factor l(z).
-4*(z - 1)*(2*z + 1)**2
Let u = 50/21 - 12/7. Let v = 3682 - 3680. Find c, given that -u*c**v - 2/3 + 4/3*c = 0.
1
Let g(i) be the first derivative of 0*i**3 - 1/960*i**6 - 1/240*i**5 + 0*i**4 + 0*i - 1 + 2*i**2. Let t(c) be the second derivative of g(c). Factor t(y).
-y**2*(y + 2)/8
Let y(i) = -837*i + 2513. Let n be y(3). Solve -1/8*p**n - 1/8 - 1/4*p = 0 for p.
-1
Let a = 36 - 43. Let p(h) = 3*h + 24. Let k be p(a). Factor 2/3*u**4 + 2*u**2 - 8/3 + 8/3*u**k - 8/3*u.
2*(u - 1)*(u + 1)*(u + 2)**2/3
Let m be 1 + -2 - (0 - 1). Suppose m = 2*n - 5*n + 21. Factor -4*v + 2*v - n*v**2 + 4*v.
-v*(7*v - 2)
Factor -2/11*f**3 - 10/11*f - 8/11*f**2 - 4/11.
-2*(f + 1)**2*(f + 2)/11
Factor 22*d**4 - 164*d**3 + 2*d**4 + 195*d**2 + 242*d**2 - 224*d - 81*d**2 - 48.
4*(d - 3)*(d - 2)**2*(6*d + 1)
Let c = 1479 + -1474. Determine v, given that 2/5*v + 0 + 3/5*v**4 - 4/5*v**3 + 2/5*v**c - 3/5*v**2 = 0.
-2, -1, 0, 1/2, 1
Let s(g) be the first derivative of 3/25*g**5 + 1/75*g**6 + 4/5*g**2 + 6 - 5*g + 13/30*g**4 + 4/5*g**3. Let i(l) be the first derivative of s(l). Factor i(b).
2*(b + 1)**2*(b + 2)**2/5
Suppose 0 = -56*q + 64*q + 216. Let n = q - -55/2. What is h in -1/4*h + n*h**2 - 1/4*h**3 + 0 = 0?
0, 1
Determine c, given that -1/5*c**2 + 0 + 51/5*c = 0.
0, 51
Let g be (3/(-5))/((-1)/10). Suppose -r + 2 = -y - g, -2*r + y = -11. Factor -k**5 - 8*k**r + k**4 + 8*k**3.
-k**4*(k - 1)
Let p(j) = 25*j**2 - 30*j - 75. Let w(z) = z**2 - 1. Let l(t) = -p(t) + 30*w(t). Find i such that l(i) = 0.
-3
Let v be 3*2/9 + 412/2163. Suppose -15/7*k + 9/7*k**3 + 12/7*k**2 - v = 0. Calculate k.
-2, -1/3, 1
Let l(m) be the third derivative of -7*m**5/60 - 97*m**4/168 + m**3/21 + 1085*m**2. Let l(j) = 0. Calculate j.
-2, 1/49
Let r(a) be the second derivative of 0*a**2 + 13/10*a**5 + 28*a + 0 + 4/15*a**6 + 11/6*a**4 + 2/3*a**3. Determine d so that r(d) = 0.
-2, -1, -1/4, 0
Let c = 6 + -5. Suppose 4*s = -0*s - r - c, 0 = 5*s - 5*r - 5. Factor -4/5*k**2 - 2*k**3 - 6/5*k**4 + 0*k + s.
-2*k**2*(k + 1)*(3*k + 2)/5
Let x = -1001 + 12017/12. Let b(c) be the second derivative of -5/3*c**3 + x*c**4 + 0*c**2 + 12*c + 0. Suppose b(r) = 0. Calculate r.
0, 2
Suppose 2*r + 2 = 322*d - 318*d, 5*d = 10. Factor 8/3*k - 2/3*k**r + 0 + 2*k**2.
-2*k*(k - 4)*(k + 1)/3
Let x(y) be the first derivative of y**7/560 - 7*y**6/240 + y**5/10 + y**4 - 4*y**3/3 - 13. Let m(h) be the third derivative of x(h). What is k in m(k) = 0?
-1, 4
Suppose 0*n - 70 = 5*n. Let c = -12 - n. Factor 2*v + 1 - 6*v**c + 0*v**2 + 7*v**2.
(v + 1)**2
Solve -4*f**4 - 2/9*f**5 + 104/9*f**2 + 0 + 2/3*f**3 - 8*f = 0.
-18, -2, 0, 1
Factor -4*t**2 + 13*t**2 + 55 - 5*t**2 + 69 + 52*t - 4.
4*(t + 3)*(t + 10)
Let z(j) be the first derivative of 0*j**2 + 1/2*j**3 + 13 + 0*j + 33/16*j**4 + 27/20*j**5. Factor z(y).
3*y**2*(y + 1)*(9*y + 2)/4
Solve 49/3*t**2 + 0*t - 55/3*t**4 - 182/3*t**3 - 4/3*t**5 + 0 = 0.
-7, 0, 1/4
Let p(z) = -z**2 + 12*z - 12. Suppose 3*r - 12 = -6. Let d(j) = 2*j**2 + 0*j**r - 3*j**2. Let w(m) = -2*d(m) - p(m). Find n such that w(n) = 0.
2
Let i(d) be the second derivative of -2*d - 1/21*d**7 + 0*d**2 - 1/3*d**3 - 3/5*d**5 - 2/3*d**4 + 0 - 4/15*d**6. Factor i(u).
-2*u*(u + 1)**4
Let g be (-11 - -22) + (-1 - 0). Let t = g - 8. Factor 23*c**3 - 3*c**4 + 1 - 17*c**3 - 3*c**t - 1.
-3*c**2*(c - 1)**2
Suppose -v + 0*v - 5 = -5*y, -3*v = 3*y - 3. Let f(w) be the third derivative of 1/12*w**4 + 0 - 4*w**2 + 1/120*w**6 - 1/20*w**5 + 0*w**3 + v*w. Factor f(j).
j*(j - 2)*(j - 1)
Let d(k) be the second derivative of 3*k**5/20 + 2*k**4 - 74*k. Factor d(s).
3*s**2*(s + 8)
Factor 2*h**3 - 19*h**2 - 12 + 22*h + 3*h**2 + 4*h**2.
2*(h - 3)*(h - 2)*(h - 1)
Let w = 64 + -60. Let c(d) be the first derivative of 3/5*d - 1/25*d**5 + 0*d**w - 12 - 4/5*d**2 + 2/5*d**3. Factor c(g).
-(g - 1)**3*(g + 3)/5
Let d(n) be the first derivative of 5*n**6/3 + 51*n**5/10 + 17*n**4/4 - 2*n**3/3 - 3*n**2/2 + n/2 - 2. Find m such that d(m) = 0.
-1, 1/5, 1/4
Let f(p) = -p**2 - 10*p + 26. Let n be f(-12). Let r(w) be the second derivative of -1/9*w**3 + 1/2*w**n + 2*w - 1/36*w**4 + 0. Factor r(v).
-(v - 1)*(v + 3)/3
Let z(g) be the second derivative of 1/8*g**3 + 0 - 3*g - 1/48*g**4 - 1/4*g**2. Let z(u) = 0. What is u?
1, 2
Let a be 2/8 - 176/(-64). Factor -64*d**4 + 0*d**3 + 3*d**2 + 65*d**4 - a*d**3 + d + 6*d**3.
d*(d + 1)**3
Suppose 62*f - 6*f = 18*f. Factor f + 8/5*c - 8/5*c**2 + 2/5*c**3.
2*c*(c - 2)**2/5
Let z(m) be the second derivative of -5*m**6/6 + 33*m**5/4 - 70*m**4/3 + 10*m**3 + 40*m**2 + 811*m. What is w in z(w) = 0?
-2/5, 1, 2, 4
Let z(v) be the third derivative of 11*v**6/480 + 13*v**5/160 + v**4/16 - 3*v**3 + 7*v**2. Let m(k) be the first derivative of z(k). What is n in m(n) = 0?
-1, -2/11
Let z be (-52 - -64)*(-1 + 140/128). Determine t so that 3/4*t + 0 + 3/8*t**3 - z*t**2 = 0.
0, 1, 2
Let a be 3/(-7) + (426/(-1491))/(4/(-62)). Factor 0 + 1/4*u**a + 0*u**3 + 1/2*u - 3/4*u**2.
u*(u - 1)**2*(u + 2)/4
Let u(o) be the second derivative of 7*o**5/5 - 11*o**4 - 20*o**3/3 + 4*o - 19. Factor u(w).
4*w*(w - 5)*(7*w + 2)
Find w, given that 2553*w**2 + 0 + 12*w - 21*w**4 - 2532*w**2 + 0 - 18*w**3 + 6*w**5 = 0.
-1, -1/2, 0, 1, 4
Suppose 3 + 67 = 35*m. Determine o, given that 16/3*o**m + 8/3 + 20/3*o + 4/3*o**3 = 0.
-2, -1
Let c = -1 - -10. Suppose -c + 34 = 5*t. Determine h so that 4*h**2 - 6*h - 2*h**2 + t - 5 = 0.
0, 3
Let p = 196/29 + -530/87. Let p*n - 2*n**2 + 0 - 2/3*n**4 + 2*n**3 = 0. What is n?
0, 1
Let j = 2/1217 - -1213/2434. What is s in s + j*s**2 + 1/2 = 0?
-1
Let h(t) = 16*t**3 + 79*t**2 + 110*t + 54. Let s(m) = 5*m**3 + 26*m**2 + 37*m + 18. Let z = -75 - -68. Let d(b) = z*s(b) + 2*h(b). Factor d(v).
-3*(v + 1)**2*(v + 6)
Let i(c) be the second derivative of c**5/140 - 47*c**4/84 + 575*c**3/42 - 529*c**2/14 - 42*c. Factor i(o).
(o - 23)**2*(o - 1)/7
Suppose 0 = 2*o + g - 4, 5*g + 13 = o - 0. Let 3*q - 15*q**4 + 13*q**4 - o*q**3 + 10*q**4 - 8*q**2 = 0. Calculate q.
-1, 0, 3/8, 1
Factor 12/5*u**2 + 0 + 2/5*u**3 - 2/5*u**4 + 0*u.
-2*u**2*(u - 3)*(u + 2)/5
Let m = 5100 - 5098. What is d in -1/2*d**4 + 0 + 0*d - 2*d**m + 2*d**3 = 0?
0, 2
Let m be (4/22)/((-60)/(-110)). Let o(h) be the second derivative of 1/15*h**4 + 3*h - m*h**3 + 3/5*h**2 + 0. Factor o(d).
2*(d - 1)*(2*d - 3)/5
Let r(w) be the first derivative of 2/21*w**3 + 4/7*w - 3/7*w**2 + 20. Find i such that r(i) = 0.
1, 2
Suppose -22*w**2 - 9*w**3 - 6*w**3 - 10*w**3 + 27*w**3 - 96*w + 6*w**2 = 0. What is w?
-4, 0, 12
Let z(b) = b**2 + 6*b - 11. Let h be z(-8). Suppose 55 = h*q - 3*y, q = -4*y - y - 17. Find w such that -3*w**2 - q - 19*w + w + 3 - 10 = 0.
-5, -1
Let h(t) be the third derivative of 3/32*t**4 + 1/480*t**6 + 0*t - 1/40*t**5 + 0 + 0*t**3 - 30*t**2. Determine v so that h(v) = 0.
0, 3
Let q be (-1 + 22)/((-6)/(-6) - 2). Let s be q/(-60) + (-5 - 81/(-15)). Factor s*r + 1/4*r**2 + 1/2.
(r + 1)*(r + 2)/4
Suppose 0 = -t - 5*j - 33, 4*t = 31*j - 36*j - 27. Factor 0 + 12/17*v + 2/17*v**t.
2*v*(v + 6)/17
Let u be 12 + (-14 + 3 - -6 - (-6)/(-3)). What is d in -d**2 + d**4 - 1/2*d + 0*d**3 + 1/2*d**u + 0 = 0?
-1, 0, 1
Determine c, given that -2*c**3 + 2*c**2 + 40 + 0*c**2 + 5*c + 21*c + 6*c = 0.
-2, 5
Determine f, given that 4/9*f**3 + 2/9*f**4 + 28/9*f - 8/3*f**2 - 10/9 = 0.
-5, 1
Let u(l) be the first derivative of -25*l**3/6 - 65*l**2/2 + 99. Solve u(z) = 0 for z.
-26/5, 0
Let s(o) = 15*o**3 + 63*o**2 + 309*o - 357. Let q(k) = 28*k**3 + 126*k**2 + 616*k - 715. Let h(r) = 6*q(r) - 11*s(r). Factor h(x).
3*(x - 1)*(x + 11)**2
Suppose -12*f + 36 = -10*f. Suppose -3*p - 18 = -f. Suppose 0*d - 2/7*d**4 - 2/7*d**5 + p*d**3 + 0 + 0*d**2 = 0. Calculate d.
-1, 