2*(59*c - 3)**2
Let d(p) be the first derivative of 8*p + 2/3*p**3 + 4*p**2 - 6. Factor d(s).
2*(s + 2)**2
Solve -25*q - 111*q - 2*q**3 - 2*q**3 - 32 - q**4 - 4*q**3 - 124*q**2 + 13*q**4 = 0.
-2, -1, -1/3, 4
Suppose 0 = -3*o + 34 - 1. Suppose -8 = 9*b - o*b. Factor 1/2*v**b + 27/2 + 5*v**3 + 27*v + 18*v**2.
(v + 1)*(v + 3)**3/2
Factor -13/12*a**2 + 0 + 1/12*a**4 - 5/12*a**3 - 7/12*a.
a*(a - 7)*(a + 1)**2/12
Let c(g) be the third derivative of g**10/37800 - g**8/5040 + 3*g**5/20 + 8*g**2. Let v(t) be the third derivative of c(t). Suppose v(u) = 0. What is u?
-1, 0, 1
Let m = 66928 - 66923. Let y(u) = u**2 + 2*u + 1. Let t be y(-1). Suppose t + 4/5*h**2 + 0*h**3 + 2/5*h**m - 2/5*h - 4/5*h**4 = 0. What is h?
-1, 0, 1
Let j(w) = -6*w**4 + 348*w**3 + 5*w**2. Let g(r) = -3*r**4 + 174*r**3 + 3*r**2. Let c(s) = -5*g(s) + 3*j(s). Factor c(b).
-3*b**3*(b - 58)
Let n be 18/(-6) + (-104)/(-32). Let c(k) be the third derivative of 0 - n*k**4 + 0*k**3 + 0*k + 1/20*k**5 - 3*k**2. Suppose c(o) = 0. What is o?
0, 2
Let b(a) = a**3 + 3*a**2 - 4*a - 3. Let y be b(-4). Let g = 0 - y. Factor 0*u**2 - 4*u**3 + 3*u**g + 2*u**2 - 3*u**4.
-u**2*(u + 1)*(3*u - 2)
Suppose 0 = 3*s + l - 74, -3*s = l + 2*l - 78. Let a = s - 16. Factor 3 - w**2 + a*w**2 - w**2 - 9*w.
3*(w - 1)*(2*w - 1)
Factor -1 - 3/2*j - 1/2*j**2.
-(j + 1)*(j + 2)/2
Let j(s) = 3. Let o(b) = -13. Let q(c) = 9*j(c) + 2*o(c). Let r(x) = 4*x**2 + 8*x + 4. Let y(g) = -4*q(g) + r(g). Factor y(p).
4*p*(p + 2)
Let m be (-13 - -14)*((-1)/(-1) - 1). Let c(l) be the second derivative of -5*l - 3/4*l**2 - 1/8*l**4 + m - 1/2*l**3. Factor c(t).
-3*(t + 1)**2/2
Let w(h) be the first derivative of -h**6/315 + h**5/105 - 2*h**3/63 + h**2/21 - 6*h + 6. Let d(u) be the first derivative of w(u). Find o, given that d(o) = 0.
-1, 1
Let p = -8 + 11. Suppose -5*d = p*f - 65, 5*f = -2*d + f + 26. Factor d*r**2 + 3 + r - 4*r - 12*r**2 - 7.
(r - 4)*(r + 1)
Let a be (40/24)/((-75)/(-324)). Solve 98/5*i**4 - a*i**5 - 4/5 - 74/5*i**3 + 22/5*i - 6/5*i**2 = 0 for i.
-1/2, 2/9, 1
Let s be 8/(-10)*(-15)/(-2). Let f be 11/2 - 3/s. Factor f - m + 4*m**2 + 4*m**2 - 2*m**2 - 14*m.
3*(m - 2)*(2*m - 1)
Let q(a) = -10*a + 83. Let w be q(8). Let t(g) be the second derivative of -1/20*g**5 + 0*g**2 - 1/3*g**w - 2*g + 1/4*g**4 + 0. Solve t(v) = 0.
0, 1, 2
Let d(m) be the first derivative of -m**5/25 - m**4/5 - m**3/5 + 2*m**2/5 + 4*m/5 + 50. Factor d(z).
-(z - 1)*(z + 1)*(z + 2)**2/5
Let t(h) be the second derivative of h**6/30 + 9*h**5/20 - 29*h + 2. Determine i so that t(i) = 0.
-9, 0
Suppose x - 3 = 3*c, 0*c = 2*c. Let l(b) = -21*b**2 + 24*b - 12. Let o(h) = -h**3 + 19*h**2 - 24*h + 12. Let n(m) = x*o(m) + 2*l(m). Solve n(k) = 0.
1, 2
Let u be (-27)/(-12) + (-1)/4. Suppose c = -u*c. Factor -24/5*m**3 + 0 - 18/5*m**4 + c*m - 8/5*m**2.
-2*m**2*(3*m + 2)**2/5
Let f(x) be the second derivative of x**5/270 + x**4/54 - 5*x**2 + 13*x. Let p(q) be the first derivative of f(q). Determine v, given that p(v) = 0.
-2, 0
Let d be (-1432)/(-40) - 2/(-10). Let x be -4 - -38*4/d. What is z in -x*z - 4/9 + 2/9*z**2 = 0?
-1, 2
Let u be (3 + 0 - 0) + -1 + 1. Let n = 0 + u. Let -1/2*b**n + 2 - 3/2*b**2 + 0*b = 0. What is b?
-2, 1
Suppose -10*u + 6*u + 14 = -3*a, -3*u = 4*a - 23. Let q(l) = -l + 10. Let c be q(10). Find w such that 1/2*w**a + c - 1/2*w**3 + w = 0.
-1, 0, 2
Let r be 0 - -13 - (5 - 3). Suppose 5 = 3*d - 2*t, -4*t = -0*d + d - r. Factor -4/9 - 2/3*j**d + 2/3*j + 2/9*j**2 + 2/9*j**4.
2*(j - 2)*(j - 1)**2*(j + 1)/9
Suppose 2*k + 6 - 2 = 0. Let s be -2*(1/k - 1). What is r in 82*r**3 - 56*r**2 + 16*r**s + 8*r + 39 - 39 = 0?
0, 2/7
Let -2/13*r**3 - 170/13*r - 172/13*r**2 + 0 = 0. Calculate r.
-85, -1, 0
Suppose -3*f = -3*d + 9, -3*d + 121 - 112 = -f. Suppose -6/17*p**4 + 0 + 2/17*p**5 - 16/17*p + 24/17*p**2 - 4/17*p**d = 0. Calculate p.
-2, 0, 1, 2
Let v(z) = -z**3 - 6*z**2 - z - 6. Let p be v(-6). Suppose -10*i**2 + p*i - 10*i**2 - 10*i - 5*i**3 - 5*i = 0. Calculate i.
-3, -1, 0
Let r = 36717 - 36715. Factor -3/2*x**2 - 1/2*x**4 + 2*x - r*x**3 + 2.
-(x - 1)*(x + 1)*(x + 2)**2/2
Let w(o) = -18*o**4 - 9*o**3 + 108*o**2 - 36*o - 15. Let b(q) = q**4 - 4*q**2 + 1. Let a(m) = -15*b(m) - w(m). Factor a(s).
3*s*(s - 2)*(s - 1)*(s + 6)
Let u(q) be the first derivative of q**7/840 + q**6/30 + 2*q**5/5 + 8*q**4/3 - 14*q**3/3 - 12. Let t(p) be the third derivative of u(p). Factor t(n).
(n + 4)**3
Let b(g) be the third derivative of 0 + 0*g - 19/60*g**5 + 7/60*g**6 + 2/3*g**3 + 1/6*g**4 - 1/70*g**7 + 8*g**2. What is j in b(j) = 0?
-1/3, 1, 2
Let 24*h + 9/2*h**2 - 24 - 3/4*h**4 - 15/4*h**3 = 0. What is h?
-4, 1, 2
Let f(r) be the second derivative of -r**5/10 - 73*r**4/4 - 990*r**3 + 3025*r**2/2 + r - 56. Factor f(k).
-(k + 55)**2*(2*k - 1)
Let k(h) = -13*h**3 + 81*h**2 - 173*h + 63. Let b(t) = 77*t**3 - 487*t**2 + 1041*t - 377. Let m(i) = 6*b(i) + 34*k(i). Solve m(c) = 0.
2/5, 3, 5
Factor 6*h**2 - 4/3*h**3 - 64/3 + 40*h.
-2*(h - 8)*(h + 4)*(2*h - 1)/3
Find d, given that 0 + 0 + 526*d - 526*d - 3*d**2 = 0.
0
Factor -2*d**2 - 21*d + 7 + 24*d + 3 - 11.
-(d - 1)*(2*d - 1)
Determine n so that -38/7*n**3 + 88/7*n - 6/7*n**4 - 48/7 + 4/7*n**2 = 0.
-6, -2, 2/3, 1
Suppose 4*c - c - 48 = 0. Let f = 20 - c. Let -2*x**f + 12*x**3 + 2*x**4 - 4 + 4*x**5 - 12*x + 12*x**4 - 8*x**2 - 4*x**3 = 0. Calculate x.
-1, 1
Suppose 23648 = 58*k + 23474. Suppose 0*d + 0 - 1/3*d**4 + 4*d**2 + 8/3*d**k - 1/3*d**5 = 0. Calculate d.
-2, 0, 3
Let g be (8/(-266))/(1074/(-236817)). Determine r so that g*r**5 + 8/19 - 142/19*r**2 + 0*r + 134/19*r**4 - 126/19*r**3 = 0.
-1, -2/7, 2/9, 1
Let y(s) be the second derivative of -s**4/24 - 3*s**3/4 - 2*s**2 - 143*s. Solve y(n) = 0 for n.
-8, -1
Factor 3/2*r**2 + 0 + 1/2*r**3 + r.
r*(r + 1)*(r + 2)/2
Let i(h) be the first derivative of 4*h**3 - 75*h**2/2 + 18*h - 53. What is m in i(m) = 0?
1/4, 6
Let p(c) be the third derivative of c**6/120 - c**5/30 - c**4/12 + c**3/3 + c**2 - 3. Let b be p(0). Factor -1/5*h**b - 3/5 - 4/5*h.
-(h + 1)*(h + 3)/5
Let s = -2 - -19. Suppose -4 + 4 - s*j**3 + 22*j**3 + 5*j**4 = 0. What is j?
-1, 0
Find c, given that 4/3*c**3 + 1/3*c**4 - 14/3*c - c**2 - 8/3 = 0.
-4, -1, 2
Let o(k) be the second derivative of -2/45*k**5 + 4*k + 1/9*k**3 + 0*k**2 - 4 - 11/54*k**4. Find r such that o(r) = 0.
-3, 0, 1/4
Let y(z) be the second derivative of 1/5*z**2 - 1/50*z**5 + 0 - 9*z - 1/30*z**4 + 1/15*z**3. Factor y(j).
-2*(j - 1)*(j + 1)**2/5
Suppose 0 = -9*b + b + 16. Factor b - 3*g**3 + 6*g**2 + 3*g - 2 + g**4 - 7*g**2.
g*(g - 3)*(g - 1)*(g + 1)
Let o(y) be the third derivative of -2*y**7/35 + 79*y**6/30 - 26*y**5/15 + 835*y**2. What is r in o(r) = 0?
0, 1/3, 26
Let n(y) be the third derivative of y**5/135 + y**4/36 - 2*y**3/27 - 22*y**2 - 5. Determine i, given that n(i) = 0.
-2, 1/2
Let x(s) = 25*s - 17. Let p be x(1). Let w(c) be the first derivative of 6 + 8*c**2 + 1/10*c**5 + p*c + c**4 + 4*c**3. Suppose w(z) = 0. What is z?
-2
Factor 219*b + 12*b + 30 - 96*b**2 + 141*b**2.
3*(b + 5)*(15*b + 2)
Let o(n) = -21*n**2 + 50*n + 71. Let h(r) = 4*r**2 - 10*r - 14. Let u(t) = 11*h(t) + 2*o(t). Solve u(v) = 0.
-1, 6
Let t = 66 + -67. Let x be (t - 1/(-10))/((-21)/35). Factor -x*g**2 - 9*g - 27/2.
-3*(g + 3)**2/2
Let o(x) be the second derivative of -x + 75/2*x**2 + 0 - 5*x**3 + 1/4*x**4. Suppose o(n) = 0. What is n?
5
Suppose -2*q = -3*d + 9, 3*q - 2 + 11 = 3*d. Let t(l) be the first derivative of 9/2*l + 7 + 3/2*l**2 - 1/2*l**d. Factor t(z).
-3*(z - 3)*(z + 1)/2
Let r be 2/(-1575)*9/(-6). Let b(s) be the third derivative of 0 + 1/25*s**6 + r*s**7 + 0*s + 27/5*s**3 + 9/5*s**4 + 2*s**2 + 9/25*s**5. What is m in b(m) = 0?
-3
Let j(z) = -3*z**2. Let o(v) = 2*v**2 + v. Let k(t) = -j(t) - 3*o(t). Factor k(s).
-3*s*(s + 1)
Let u(g) = -g**2 - 5*g + 16. Let w be u(-8). Let z be (2/5)/(w/(-270)). Factor 6*k**2 + z*k + 3.
3*(k + 2)*(4*k + 1)/2
Let z(c) be the first derivative of -13/12*c**2 - 15 + c - 5/18*c**3. Suppose z(d) = 0. Calculate d.
-3, 2/5
Let d(f) = -2*f. Let b(l) = -l**3 + 4*l**2 + 2. Let k be b(4). Let h(o) = 4*o**2 + 8*o - 2. Let p(s) = k*h(s) + 10*d(s). Suppose p(u) = 0. What is u?
-1/2, 1
Let j = 5720 - 62902/11. Factor 0 - 4/11*o + 14/11*o**2 - 2/11*o**5 + 10/11*o**4 - j*o**3.
-2*o*(o - 2)*(o - 1)**3/11
Let o be ((-208)/(-105) - 2)*(-266