r) be the first derivative of -r**4/2 - 16*r**3/3 - 21*r**2 - 36*r - 71. Factor s(o).
-2*(o + 2)*(o + 3)**2
Let n(s) be the third derivative of -13*s**5/20 + 17*s**4/8 - 4*s**3 - 13*s**2. Let q(x) = -8*x**2 + 10*x - 5. Let w(m) = 5*n(m) - 24*q(m). Factor w(f).
-3*f*(f - 5)
Solve -2/3*v**3 + 8/3*v + 16/3 - 20/3*v**2 - 2/3*v**5 + 8/3*v**4 = 0 for v.
-1, 2
Let x(t) = -t**3 - 6*t**2 + 6*t + 3. Let b be x(-7). Let n = b - 6. Suppose -7/2*u + 1/2*u**n - 5/2*u**3 + 1 + 9/2*u**2 = 0. Calculate u.
1, 2
Let g(c) = 2*c**3 - 9*c**2 - 13. Let s be g(5). Let k be 3*(s/45)/((-14)/(-5)). Factor -4/7 + 2/7*a + k*a**2.
2*(a - 1)*(a + 2)/7
Let z(q) = -218*q + 7848. Let f be z(36). Suppose 0 + f*v**2 - 2/11*v**4 + 0*v - 2/11*v**3 = 0. Calculate v.
-1, 0
Factor -12*f**3 + 317*f - 5*f**4 - 30*f**2 - 297*f - 5 + 32*f**3.
-5*(f - 1)**4
Suppose 3*f - 4*p = 7, 0 = -3*f - 2*p - 2 - 15. Let s be (f/1)/((-3)/2). Determine j so that -2 + 5 - j**2 - s + j**3 - j = 0.
-1, 1
Let l(o) be the second derivative of -3*o**5/40 - o**4/4 + 2*o**3 - 3*o - 12. Factor l(j).
-3*j*(j - 2)*(j + 4)/2
Let i(x) be the second derivative of -x**5/10 + x**4/2 + 4*x**3/3 - 2*x - 113. Factor i(w).
-2*w*(w - 4)*(w + 1)
Let x be (17 - (-5572)/(-336))/((-5)/(-4)). Suppose 1/3 + 2/3*b + x*b**2 = 0. What is b?
-1
Let s(z) = z + 3 + 0*z - z - z. Let o be s(0). Factor -m + 0*m**o - 5*m**3 + 4*m**3 + 2*m**2.
-m*(m - 1)**2
Let k(d) be the second derivative of d**4/48 + d**3 - 76*d. Factor k(s).
s*(s + 24)/4
Solve -4*u**2 + 25 - 7*u - 38 + u**3 + 23 = 0.
-2, 1, 5
Let b(k) be the second derivative of -3*k**5/80 + 3*k**4/16 + 3*k**3/4 - 3*k**2 + 333*k. Factor b(r).
-3*(r - 4)*(r - 1)*(r + 2)/4
Factor -6/5 - 1/5*j**2 + 7/5*j.
-(j - 6)*(j - 1)/5
Suppose 3*x + 11*x - 28 = 0. Let m(r) be the first derivative of -r - 1/3*r**3 - r**x + 1. Factor m(a).
-(a + 1)**2
Let u(m) be the third derivative of m**8/168 - m**7/105 - m**6/60 + m**5/30 - 29*m**2 + 6. Find v such that u(v) = 0.
-1, 0, 1
Let a(y) = -y**4 + 2*y**3 + y**2 + y + 1. Let j(c) = -6*c**4 + 36*c**3 - 72*c**2 + 3*c + 3. Let o(i) = -3*a(i) + j(i). Factor o(s).
-3*s**2*(s - 5)**2
Suppose -5*h = 5*i - 10, 3*i - 7 + 1 = 4*h. Factor 2 + 6 + 80*g + 2*g**i - 72*g.
2*(g + 2)**2
Find h, given that 48*h + 52*h**4 - 108*h**2 + 2*h**5 - 79*h**4 + 84*h**3 + h**5 = 0.
0, 1, 2, 4
Let d be 1662/54 + (-2)/(-9). Suppose -5*f + 69 = -d. Suppose -23*n**5 + f*n**5 + n**4 - 3*n**4 = 0. What is n?
-2/3, 0
Let b be ((-9)/(-3))/((-1)/2*3). Let m be (-1)/((-4)/(-12)*3/b). Find k, given that -20/7*k + 4/7*k**3 - 4/7*k**m - 12/7 = 0.
-1, 3
Factor 55/3 + 1/3*g**2 + 16/3*g.
(g + 5)*(g + 11)/3
Let n(a) be the third derivative of -a**7/10080 - a**6/360 - a**5/30 + 13*a**4/24 + 32*a**2. Let p(s) be the second derivative of n(s). Factor p(w).
-(w + 4)**2/4
Suppose 6*g - 17 = 3*g + 4*c, c = -2. Let o be (-52)/(-20) - 4/(-10). Factor -3/2*h**4 - o*h**2 + 0*h + 9/2*h**g + 0.
-3*h**2*(h - 2)*(h - 1)/2
Solve 12/5*n + 54/5 - 2/5*n**2 = 0.
-3, 9
Factor -147/8*n - 75/4 + 3/8*n**2.
3*(n - 50)*(n + 1)/8
Let g(f) = 11*f**3 + 19*f**2 + 2*f - 19. Let u be ((6/2)/6)/(1/(-26)). Let p(j) = -5*j**3 - 9*j**2 - j + 9. Let z(h) = u*p(h) - 6*g(h). Factor z(d).
-(d - 3)*(d - 1)*(d + 1)
Let h(g) be the first derivative of 3/16*g**4 + 3/8*g**2 + 11 - 2/3*g**3 + 1/2*g. Let h(s) = 0. Calculate s.
-1/3, 1, 2
Find a such that -2 + 7/4*a + 1/4*a**2 = 0.
-8, 1
Let x be (1/(-4))/((-2)/8) - -3. Determine u, given that 12*u + x*u**3 - 4*u**2 - u**2 - 2*u**2 - 9*u**2 = 0.
0, 1, 3
Solve -8/19*h - 2/19*h**2 + 8/19*h**3 + 2/19*h**4 + 0 = 0.
-4, -1, 0, 1
Find v such that -9/4*v**3 + 0 - 5/4*v**2 - v**4 + 0*v = 0.
-5/4, -1, 0
Let h(l) = -l**2 + 79*l - 500. Let r be h(72). Let s(z) be the first derivative of -2/13*z**3 + 0*z - 10 - 2/13*z**2 - 1/26*z**r. Find n, given that s(n) = 0.
-2, -1, 0
Let z be 1 - 1 - 0 - 0. Let f = -437/16 - -4061/144. Factor z - f*t**2 + 2/9*t.
-2*t*(4*t - 1)/9
Suppose 0*c + 2/3*c**3 - 4/15*c**2 + 14/15*c**4 + 0 = 0. What is c?
-1, 0, 2/7
Let o be (-12)/(-90)*-6*(-1)/8. Let f(d) be the second derivative of 3*d**2 + 5/3*d**3 - o*d**5 - d + 1/6*d**4 + 0. Factor f(s).
-2*(s - 3)*(s + 1)**2
Let v(k) = -3*k**2 - 133*k - 110. Let i(m) = m**2 + 67*m + 54. Let h(t) = 5*i(t) + 3*v(t). Find u such that h(u) = 0.
-15, -1
Let h(j) be the first derivative of 5*j**8/336 - j**7/42 + 17*j**2 + 48. Let c(f) be the second derivative of h(f). Factor c(r).
5*r**4*(r - 1)
Let r be 4/12*(13 - -2). Let d be 3/2 - r/(-10). Solve 7*w - 5*w**2 + w**d - w**2 - 2 = 0 for w.
2/5, 1
Let l = 416 + -414. Let n(v) be the second derivative of 0 + 1/3*v**3 - 2*v - 1/12*v**4 - 1/2*v**l. Factor n(y).
-(y - 1)**2
Suppose 0 - 2*x**4 + 2*x**2 + 2/3*x**5 - 4/3*x + 2/3*x**3 = 0. What is x?
-1, 0, 1, 2
Let f = 247 - 247. Let s = -26605/13 - -2051. Suppose s*b**2 + f*b**3 + 0*b - 8/13 - 50/13*b**4 = 0. What is b?
-1, -2/5, 2/5, 1
Suppose -2 = 2*t - 3*t. Let u = 9111 - 100217/11. What is x in -2/11*x**3 - 2/11*x**t + 0 + u*x = 0?
-2, 0, 1
Factor -40 + 7*k + 0*k - 10*k + 5*k**2 - 7*k.
5*(k - 4)*(k + 2)
Suppose 4*j - 13 - 3 = 0. Factor -2*x**j + 4*x**3 + 4*x**4 + 98*x - 3 + 1 - 102*x.
2*(x - 1)*(x + 1)**3
Let f(y) be the first derivative of 12*y**5/5 + 111*y**4/4 + 9*y**3 - 648*y**2 - 324*y + 59. Factor f(v).
3*(v - 3)*(v + 6)**2*(4*v + 1)
Let m(i) = -3*i + 279. Let h be m(92). Factor 1/7*o**4 + 3/7*o**2 + 0 + 1/7*o + 3/7*o**h.
o*(o + 1)**3/7
Let f be 8/10*(-40)/(-112). Let y = -107 - -107. Let f*w**2 + y*w - 8/7 = 0. Calculate w.
-2, 2
Let f(z) = -z**3 - z + 1. Let m(k) = 3*k**2 - 3*k**2 + 6 - 6*k - 5*k**3. Suppose -5*o - 8*x + 30 = -3*x, 0 = -3*x. Let y(c) = o*f(c) - m(c). Factor y(j).
-j**3
Let j(k) = -3*k**2 + 23*k - 10. Let f be j(7). Let b(a) be the first derivative of 0*a**3 + 0*a - 1/14*a**4 + f + 0*a**2. Let b(c) = 0. Calculate c.
0
Let 26*z + 5*z**2 + 28 - 1/2*z**3 = 0. Calculate z.
-2, 14
Let a be -1*((-744)/(-40) + -18)/(3/(-2)). Find j such that a - 2/15*j**5 + 2/5*j**4 - 2/15*j + 4/15*j**3 - 4/5*j**2 = 0.
-1, 1, 3
Let s = 24 - 22. Let j(g) be the first derivative of 5/3*g**3 - g - 3/4*g**4 - 4/5*g**5 + 3/2*g**s + 4. Find f such that j(f) = 0.
-1, 1/4, 1
Let u be -4 - ((-12)/(-3) + -15). Suppose -31 = -12*o - u. Determine s so that -8/3*s - 2/3*s**o - 2 = 0.
-3, -1
Solve -16 - 5*l + 9*l**4 + l**5 + 4*l**5 + 16 - 10*l**2 + l**4 = 0 for l.
-1, 0, 1
Let i be 1/1*(16/(-4) - -27). Solve -24*x**3 + 12*x**4 - 1 + 12 + 8*x**5 - i + 32*x - 16*x**3 = 0.
-3, -1, 1/2, 1
Let p(a) be the second derivative of -1/220*a**5 + 0 + 5/66*a**3 + 1/132*a**4 + 3/22*a**2 - 17*a. Find j, given that p(j) = 0.
-1, 3
Let p(x) be the third derivative of x**7/1260 + x**6/120 - 11*x**4/72 + 5*x**3/12 + 61*x**2. What is s in p(s) = 0?
-5, -3, 1
Let q be 1/(75/(-20))*10/(-3). Let p(a) be the third derivative of q*a**3 - 9*a**2 + 0 - 4/9*a**4 - 1/9*a**5 + 0*a. Factor p(g).
-4*(g + 2)*(5*g - 2)/3
Let l(g) = -9*g**2 + 174*g + 39. Let d(p) = -10*p**2 + 172*p + 38. Let h(b) = 6*d(b) - 5*l(b). Determine y so that h(y) = 0.
-1/5, 11
Let z(u) = -6*u**3 - 4*u**2 - 10*u + 3. Let k(l) = 1 + l + 0 + 0 - l**3 - 2*l. Let a be (-15)/20 + (-74)/8. Let n(o) = a*k(o) + 2*z(o). Let n(y) = 0. What is y?
-2, -1
Let i(v) be the first derivative of 6/7*v - 2/21*v**3 + 13 + 1/7*v**4 - 4/7*v**2. Factor i(h).
2*(h - 1)**2*(2*h + 3)/7
Solve -265/8*b**2 - 109/8*b + 25/8*b**3 - 11/8 = 0.
-1/5, 11
Let m = -7265/3 + 2422. Determine f, given that 0 + 0*f + 1/2*f**3 + m*f**2 = 0.
-2/3, 0
Let z(m) be the first derivative of m**5/5 + m**4 + 5*m**3/3 + m**2 + 103. Factor z(i).
i*(i + 1)**2*(i + 2)
Let j = 1314 - 5253/4. Solve -1/4*d**2 + j*d + 0 = 0 for d.
0, 3
Let j(s) be the third derivative of -5*s**8/144 + 5*s**7/21 - 25*s**6/36 + 10*s**5/9 - 25*s**4/24 + 5*s**3/9 - 2*s**2 - 32*s. Factor j(r).
-5*(r - 1)**4*(7*r - 2)/3
Let g be 4/(-18) - 38/(-9). Suppose 3*c + 13 = 2*t, g*t = -7*c + 4*c + 17. Factor -6*s + 6*s + 6*s**2 - 3*s**t - 6*s**4 + 3*s + 0*s**5.
-3*s*(s - 1)*(s + 1)**3
Suppose -3*a = a - 0*a. Factor 3*l**2 + 10*l**3 - 9*l - 3*l**4 + a*l**2 - 5*l**3 + 4*l**4.
l*(l - 1)*(l + 3)**2
Let m(u) be the third derivative of u**7/105 - u**6/30 - 2*u**5/15 + 2*u**4/3 - 15*u**2 - 2. Find l such that m(l) = 0.
-2, 0, 2
Let a(d) be the third derivative of 17*d**2 - 1/16*d**4 - 7/24*d**3 + 0*d + 1/240*d*