Let d = -232/3 - -78. Let r(i) be the second derivative of 5/9*i**3 - 2/9*i**4 + 1/30*i**5 - d*i**2 + 0 - 3*i. Factor r(q).
2*(q - 2)*(q - 1)**2/3
Let j(c) be the second derivative of c**5/90 - 19*c**3/27 - 10*c**2/3 + 389*c. Factor j(b).
2*(b - 5)*(b + 2)*(b + 3)/9
Let o(t) be the first derivative of 2*t**6/3 - 8*t**5/5 - 7*t**4 + 32*t**3/3 + 24*t**2 + 145. Determine h so that o(h) = 0.
-2, -1, 0, 2, 3
Let j(p) = 31*p**4 - 79*p**3 - 273*p**2 - 209*p - 43. Let q(k) = 156*k**4 - 396*k**3 - 1364*k**2 - 1044*k - 216. Let f(n) = 16*j(n) - 3*q(n). Factor f(t).
4*(t - 5)*(t + 1)**2*(7*t + 2)
Factor 28/11 + 2/11*h**2 + 18/11*h.
2*(h + 2)*(h + 7)/11
Let o(q) be the third derivative of q**7/35 + q**6/30 + 5*q**2. Let a(i) = -i**3. Let t(y) = 6*a(y) + o(y). Suppose t(u) = 0. What is u?
0, 1/3
Let r = -33 + 201. Let h = -165 + r. Factor 0*u**h + 0*u - 1/3*u**4 - 1/3 + 2/3*u**2.
-(u - 1)**2*(u + 1)**2/3
Let h be ((-25)/30)/(1/3*-2). Suppose -5/2*v**2 + 0*v + h + 5/4*v**4 + 0*v**3 = 0. What is v?
-1, 1
Let y(v) be the second derivative of -3*v**5/140 + 11*v**4/28 - 5*v**3/7 - 261*v. Find a, given that y(a) = 0.
0, 1, 10
Suppose 142 = 4*g + 22. Let s be g/(-360) + (-50)/(-24). Factor 2/17*d**4 + 0 + 0*d + 2/17*d**3 + 0*d**s.
2*d**3*(d + 1)/17
Suppose 2*u + 4*v = -0*u + 2, -3*u + 2*v = -11. Factor 21 + 50*y**2 - 15*y**u - 15*y**3 + 105*y + 24 - 15*y**4 + 5*y**5.
5*(y - 3)**2*(y + 1)**3
Let l(p) = -p**2 - 4*p - 3. Let u(b) = -2*b**2 - 8*b - 6. Let j(q) = -10*l(q) + 6*u(q). Find m, given that j(m) = 0.
-3, -1
Let n(g) be the second derivative of g**6/50 + 47*g**5/100 + 59*g**4/15 + 58*g**3/5 - 72*g**2/5 + 28*g + 7. Let n(a) = 0. What is a?
-6, -4, 1/3
Factor -10*l + 2/7*l**2 - 72/7.
2*(l - 36)*(l + 1)/7
Let n(y) = y**4 + y**2. Let h(z) = -2*z**4 - 22*z**3 - 30*z**2 - 20*z - 4. Suppose 0 = 2*d - 17 - 11. Let j = d - 17. Let m(f) = j*n(f) + h(f). Factor m(o).
-(o + 1)**2*(o + 2)*(5*o + 2)
Suppose u = -w + 8, -4 = -4*u + 12. Let k(h) be the first derivative of 16/3*h**3 + 28/5*h**5 - 5 + 0*h**2 + 0*h + 16*h**w. Factor k(f).
4*f**2*(f + 2)*(7*f + 2)
Let d be (-2)/(-1) + (1 - 7)*-1. Factor d*g**3 + 3*g**3 - 10*g**3 + 2 - 3*g.
(g - 1)**2*(g + 2)
Let s(p) = -p**2 - p + 14. Let x be s(-4). Suppose t**2 + 3*t**x + 53*t**3 - 45*t**3 + 4*t**4 = 0. Calculate t.
-1, 0
Let s(q) be the first derivative of 8*q**6/15 + 56*q**5/25 + 57*q**4/20 + 19*q**3/15 + q**2/5 + 45. What is t in s(t) = 0?
-2, -1, -1/4, 0
Solve -5/2*k**2 + 185/2*k + 195 = 0 for k.
-2, 39
Let r(d) be the second derivative of d**5/20 - d**3/6 + d. Let c(a) = -2*a**4 - 9*a**3 - 6*a**2 + a. Let m(f) = c(f) + 3*r(f). Factor m(q).
-2*q*(q + 1)**3
Find c, given that 44/3 + 16/3*c**2 - 60*c = 0.
1/4, 11
Let n(a) be the second derivative of -a**4/36 - 2*a**3/9 + 7*a**2/2 - 292*a. Suppose n(m) = 0. What is m?
-7, 3
Let a(t) be the third derivative of 25*t**8/1512 + 16*t**7/189 + 2*t**6/45 - 32*t**5/135 + 4*t**4/27 + 35*t**2 + t. Factor a(w).
2*w*(w + 2)**2*(5*w - 2)**2/9
Determine x so that 8/5*x**2 - 6/5*x**3 + 0*x**4 + 1/5*x**5 - 3/5*x + 0 = 0.
-3, 0, 1
Let t be (-46)/(-6) + 9/(-54)*42. Factor -t*f**4 + 0 + 0*f + 2/3*f**2 - 2/3*f**3 + 2/3*f**5.
2*f**2*(f - 1)**2*(f + 1)/3
Factor 0 + 0*x**2 - 1/3*x**3 + 4/3*x.
-x*(x - 2)*(x + 2)/3
Let l be 5/(10/(-24)) - (111 + -125). Solve -50*t - 250 - 5/2*t**l = 0 for t.
-10
Let w(o) = 1. Let a(j) = 45*j**2 + 32*j - 33. Let m be a(1). Let d(k) = 20 - k**2 + 2*k + 6*k**2 - 3*k**2 - 2*k**3. Let v(b) = m*w(b) - 2*d(b). Factor v(q).
4*(q - 1)**2*(q + 1)
Let f(j) = 2*j**2 - 2*j + 1. Let b be f(2). Suppose 6*z = b*z + 15. Factor -5*u**4 - 3*u - 15*u**3 + 0*u - 2*u - z*u**2 + 0*u**4.
-5*u*(u + 1)**3
Let k(w) be the first derivative of 161*w**5/15 - 193*w**4/12 + 28*w**3/9 + 2*w**2/3 - 63. Solve k(o) = 0.
-2/23, 0, 2/7, 1
Let y(d) be the third derivative of d**6/200 - 3*d**5/50 + 9*d**4/40 - 2*d**3/5 + 46*d**2. Factor y(c).
3*(c - 4)*(c - 1)**2/5
Let u(k) be the first derivative of -k**6/120 + k**5/20 - 2*k**3/3 - 5*k**2/2 + 7. Let d(y) be the second derivative of u(y). Determine o so that d(o) = 0.
-1, 2
Let 90 - 3*p**4 - 135*p**2 + 33*p**3 - 145*p - 59*p + 447*p - 252 = 0. What is p?
2, 3
Let l(h) be the third derivative of 0*h + 1/20*h**5 - 3/8*h**4 + 0 - 9*h**2 + h**3. Determine k, given that l(k) = 0.
1, 2
Let p = 88/3 + -22. Let c(i) be the first derivative of 0*i + 272/5*i**5 - 5 - p*i**3 + 2*i**2 - 112/3*i**6 - 15/2*i**4. Determine r so that c(r) = 0.
-2/7, 0, 1/4, 1
Let t(v) be the second derivative of 4*v**7/189 - v**6/135 - 2*v**5/15 - 5*v**4/54 + 2*v**3/27 + 47*v. Solve t(p) = 0.
-1, 0, 1/4, 2
Let r(d) be the first derivative of -d**4/66 - d**3/11 + 12*d + 12. Let z(j) be the first derivative of r(j). Factor z(t).
-2*t*(t + 3)/11
Let j(d) be the second derivative of d**5/8 + 10*d**4/3 + 65*d**3/3 + 60*d**2 - 76*d - 2. Factor j(o).
5*(o + 2)**2*(o + 12)/2
Let m = 58 - 56. Factor -5*w**3 - 7*w**3 + 6*w**2 - 4*w - 14*w**2 - 4*w**4 - 4*w**m.
-4*w*(w + 1)**3
Let y be -4 + (1 + 1)*(-6)/(-3). Suppose -15*r + y - 12 + 0 - 3*r**2 = 0. What is r?
-4, -1
Factor 0 + 2/11*c**5 + 0*c**2 + 0*c - 8/11*c**4 - 10/11*c**3.
2*c**3*(c - 5)*(c + 1)/11
Suppose -12 = -4*l - 0. Suppose -3*f - 94 = -103. Factor 0*c**2 - 3*c**4 - 25*c**5 + 3*c**l + 22*c**5 + f*c**2.
-3*c**2*(c - 1)*(c + 1)**2
Let -75*l**2 + 23*l - 3*l**4 + 3*l**3 - 71 + 137*l + 8*l**4 - 13*l**3 - 9 = 0. What is l?
-4, 1, 4
Let z(i) be the first derivative of i**5 + 38 + 0*i - 5/2*i**4 + 5/6*i**6 + 0*i**2 + 0*i**3. What is l in z(l) = 0?
-2, 0, 1
Let o(l) be the second derivative of -9/4*l**4 + 10*l + 27/2*l**3 + 0 - 81/2*l**2 + 3/20*l**5. Factor o(s).
3*(s - 3)**3
Factor 144/5 - 4/5*r**3 - 144/5*r + 44/5*r**2.
-4*(r - 6)*(r - 3)*(r - 2)/5
Let q be 80/126 + 14/63. Let c(l) = l**3 + 13*l**2 + 24*l + 24. Let m be c(-11). Factor 0*j - 6/7*j**3 + 2/7*j**m - 2/7*j**5 + q*j**4 + 0.
-2*j**2*(j - 1)**3/7
Let t(b) be the first derivative of 0*b**5 + 1/3*b**6 - 4/3*b**3 + 18 + 0*b - 3/2*b**4 + 0*b**2. Find m such that t(m) = 0.
-1, 0, 2
Solve -36/7*z**4 + 8*z**3 - 60/7*z - 100/7 + 136/7*z**2 + 4/7*z**5 = 0 for z.
-1, 1, 5
Let w(d) = -3*d**2 + 3*d - 5. Let r(j) = -4*j**2 + 4*j - 6. Let u(p) = 5*r(p) - 6*w(p). Factor u(i).
-2*i*(i - 1)
Factor 852*l**2 + 854*l**2 - 1709*l**2 - 10*l + 8.
-(l + 4)*(3*l - 2)
Let i(n) be the second derivative of 33*n**6/50 - 39*n**5/100 - 97*n**4/60 + 13*n**3/10 - n**2/5 + n + 5. Solve i(l) = 0 for l.
-1, 2/33, 1/3, 1
Let z be (-1)/(16*8/36 + -2). Let w = -1/7 - z. Find j such that -3/2*j**3 + 2*j + 2*j**4 - 2*j**2 - w*j**5 + 0 = 0.
-1, 0, 1, 2
Suppose -3*m - 23 = 2*v, -m - 6*v = -5*v + 7. Let s be (-6)/27 - 29/m. Factor -2*k**2 - 2*k**s + 3*k**3 + k**2 + 0*k**2.
k**2*(k - 1)
Let p(c) be the first derivative of 4/9*c**2 - 35 - 8/9*c - 2/27*c**3. Factor p(t).
-2*(t - 2)**2/9
Let t be (-18)/4*33/(-297). Solve t + 3/4*o + 1/4*o**2 = 0 for o.
-2, -1
Let q(t) be the first derivative of -t**6/54 - t**5/5 - 3*t**4/4 - t**3 - 48. Factor q(m).
-m**2*(m + 3)**3/9
Let l(h) be the second derivative of -6*h - 4/27*h**4 + 4/27*h**3 + 0 + 0*h**2 + 1/30*h**5. Let l(m) = 0. Calculate m.
0, 2/3, 2
Let i = 111 + -554/5. Let a(q) be the second derivative of i*q**5 + 0*q**2 - 6*q + 0 + 0*q**3 + 0*q**4 - 2/15*q**6 + 1/42*q**7. Let a(c) = 0. What is c?
0, 2
Let z(o) be the third derivative of o**8/3024 - o**7/315 + o**6/270 + o**5/90 - 5*o**4/216 - 168*o**2. Determine k so that z(k) = 0.
-1, 0, 1, 5
Suppose -8*c - 6*c = 14. Let a be -5*c*(-60)/(-275). Find w, given that -10/11*w - 4/11 + 16/11*w**3 - 6/11*w**5 + a*w**2 - 8/11*w**4 = 0.
-2, -1, -1/3, 1
Let q be -11 + (-36846)/(-3132) - 2/(-29). What is f in -5/3*f**3 + q*f**5 - 10*f**2 + 5/2*f**4 - 20/3*f + 0 = 0?
-2, -1, 0, 2
Factor 1/2*a + 1/2*a**3 + a**2 + 0.
a*(a + 1)**2/2
Let x(y) be the second derivative of y**7/2016 - y**5/24 + 13*y**4/12 - 7*y. Let u(c) be the third derivative of x(c). Solve u(n) = 0 for n.
-2, 2
Suppose 0 = -k - 4 + 7. Factor -3*g**k + 7*g**3 - 3*g**2 - g**3.
3*g**2*(g - 1)
Suppose 10 = 3*y + 4*x - 12, 4*y = 5*x - 12. Factor 120*l + 61*l**3 + 4 + 160*l**3 - 351*l**y - 16 + 22*l**3.
3*(l - 1)*(9*l - 2)**2
Suppose -a - 3*y = 10, -55*a + 2*y = -59*a. Factor -3/2*o**2 - 4*o + 3/2*o**5 + 17/2*o**3 + a - 13/2*o**4.
(o - 2)*(o - 1)**3*(3*o + 2)/2
Let r = -1977 + 444826/