1/63*n**7 - 1/18*n**4 + 1/30*n**5 + 0 + 0*n**3. Factor f(k).
-2*k**2*(k - 1)**2*(k + 1)/3
Let t(b) be the second derivative of 0*b**2 - 12*b - 3/80*b**5 + 1/16*b**4 + 1/120*b**6 + 0 - 1/24*b**3. Factor t(m).
m*(m - 1)**3/4
Let j(c) be the first derivative of -2*c**3/21 + 186*c**2/7 - 17298*c/7 + 110. Determine p so that j(p) = 0.
93
Let q be (8 + -3 + 0)*1. Factor -20*h**5 + 27*h**4 + q*h**2 - 11*h**3 - 34*h**3 + 5*h + 28*h**4.
-5*h*(h - 1)**3*(4*h + 1)
Let a(h) be the third derivative of 0*h + 1/3*h**3 - 10*h**2 + 0 + 1/8*h**4 + 0*h**5 - 1/120*h**6. Factor a(t).
-(t - 2)*(t + 1)**2
Let p be (-22)/(-10) - (-2)/(-10). Let u(b) = b**3 - 2*b - 1. Let x be u(p). Let -t**2 + 11*t**x + 6*t**5 - t**4 - 10*t**4 - 3*t**5 - 2*t = 0. Calculate t.
-1/3, 0, 1, 2
Let x = -1/8493 + 50969/93423. Factor 0 + 12/11*o - 6/11*o**3 + x*o**2.
-6*o*(o - 2)*(o + 1)/11
Let g(b) be the first derivative of b**8/840 - b**7/210 + b**6/180 - 20*b**3/3 - 12. Let q(a) be the third derivative of g(a). Solve q(l) = 0.
0, 1
Let n(g) = -g**3 + 5 - g**4 - g + g**2 - 16 + 11. Let j(d) = -3*d**4 - 4*d**3 + 3*d**2. Let r(q) = -j(q) + 2*n(q). Find z such that r(z) = 0.
-2, -1, 0, 1
Let c = 56 + 5. Let n be 256/14 + (-2)/7. Solve -32*x**4 + 20*x - 30*x**4 - n*x**2 + c*x**4 - 8 + 7*x**3 = 0.
1, 2
Let z = 6978 - 27909/4. Factor 0 + 1/2*f**2 + z*f**4 - 7/4*f**3 + 0*f.
f**2*(f - 2)*(3*f - 1)/4
Let 3*a**3 + 237*a + 67 - 33 + 123*a**2 + 83 = 0. Calculate a.
-39, -1
Let t = 18527/1122 - 7/561. Determine h so that 21/2*h**2 + 15/2 - t*h - 3/2*h**3 = 0.
1, 5
Suppose 0 = 2*h - 2, 4*h = m + 6*h + 33. Let k = m - -145/4. Let 1/4*v**2 - 3*v**4 - 1/4 + k*v - 17/4*v**3 = 0. Calculate v.
-1, 1/4, 1/3
Let r(i) = i**3 + 2*i**2 - 6*i - 9. Let u be r(-2). Factor -j**5 - 13*j - 6 - 4*j**2 - j**u + 7*j**3 - 81*j**4 + 83*j**4 + 0*j**2.
-(j - 3)*(j - 2)*(j + 1)**3
Let s(a) be the third derivative of -a**6/720 + 19*a**5/120 + 13*a**4/16 + 59*a**3/36 + 14*a**2. Let s(x) = 0. Calculate x.
-1, 59
Solve -8/9*k**3 + 2/9*k**4 + 8/3 + 8/9*k - 26/9*k**2 = 0 for k.
-2, -1, 1, 6
Let c(z) be the third derivative of -z**11/2494800 + z**9/453600 - 4*z**5/15 + 6*z**2. Let u(q) be the third derivative of c(q). Find g such that u(g) = 0.
-1, 0, 1
Let m = 4 - 0. Suppose -5*z + 8 = v, -5*v = -4*z - 3*v + 12. Factor -g**3 + 6*g**3 - 3*g**2 + 3*g**m - 3*g - z*g**3.
3*g*(g - 1)*(g + 1)**2
Factor 36*v - 39*v**2 + 3*v**3 - 12*v**2 + 27*v**2.
3*v*(v - 6)*(v - 2)
Suppose -3*d + 27 = 15. Let z(u) be the third derivative of 1/1155*u**7 + 1/22*u**5 + 7/660*u**6 + 3/44*u**d + 0*u**3 + 0*u + 0 - 6*u**2. Factor z(r).
2*r*(r + 1)*(r + 3)**2/11
Let m = -2502 - -450361/180. Let t(x) be the third derivative of m*x**6 + 1/90*x**5 - 1/9*x**3 + x**2 - 1/36*x**4 + 0 + 0*x. Factor t(i).
2*(i - 1)*(i + 1)**2/3
Let p be (-7774)/(-644) + (2/(-16))/((-1)/4). Let 52/7*x**2 + p*x + 8/7*x**3 + 32/7 = 0. Calculate x.
-4, -2, -1/2
Let h(s) be the second derivative of s**4/30 + 19*s**3/15 + 12*s**2 + 2*s + 55. Factor h(q).
2*(q + 4)*(q + 15)/5
Let u = -51 - -55. Factor -612 - 45*w - 75*w**2 + 612 - 35*w**3 - 5*w**u.
-5*w*(w + 1)*(w + 3)**2
Let x = 1323 - 2645/2. Let w(a) = a**2 + 5*a - 4. Let s be w(-6). Find k such that 1/4*k**s + 3/4*k + x = 0.
-2, -1
Let a(t) be the second derivative of t**6/15 - 2*t**4/3 - 388*t. Factor a(b).
2*b**2*(b - 2)*(b + 2)
Let a(b) be the second derivative of 0 - 1/8*b**3 + 1/96*b**4 + 4*b + 9/16*b**2. Suppose a(r) = 0. What is r?
3
Suppose n - 10 = -4*n. Solve -3*a + 9*a**2 + a - 12*a**n - a = 0 for a.
-1, 0
Suppose 695 = -6*f + 713. Factor -f*t + 9/2 + 1/2*t**2.
(t - 3)**2/2
Let p(d) = -1. Suppose -5*i + 92 = -4*x, 4*x - 17 = -2*i - x. Let o = i - 18. Let b(y) = y**2 - 2*y - 12. Let a(c) = o*b(c) + 18*p(c). Factor a(z).
-2*(z - 3)*(z + 1)
Let a(l) = -2*l**2 + 2*l + 52. Let v(p) = -p**2 + 2*p + 18. Let y(j) = -3*a(j) + 8*v(j). Factor y(o).
-2*(o - 3)*(o - 2)
Let w = 187 - 187. Let h(u) be the second derivative of 1/8*u**3 + u + w - 1/4*u**2 - 1/48*u**4. Factor h(v).
-(v - 2)*(v - 1)/4
Factor 13*f**3 - 1/4*f**5 + 5/2*f**4 + 0 + 14*f**2 + 0*f.
-f**2*(f - 14)*(f + 2)**2/4
Let u(j) = 2*j**3 + 4*j - 16. Let r be u(4). Let s be (-4)/30 - (r/30)/(-2). Factor 27*q**s - 21/2*q**3 + 3/2*q**4 - 30*q + 12.
3*(q - 2)**3*(q - 1)/2
Let o(x) = -13728*x**4 - 4327*x**3 - 456*x**2 - 21*x - 10. Let m(f) = -20593*f**4 - 6490*f**3 - 684*f**2 - 32*f - 16. Let q(s) = -5*m(s) + 8*o(s). Factor q(d).
-d*(19*d + 2)**3
Let b = -66805/9 - -7423. What is g in 0*g - b*g**3 + 2/9*g**2 + 0 = 0?
0, 1
Let u(a) = 2*a + 25. Let y be u(-9). Factor -19 - 4*l**2 + 5 + 11 + y.
-4*(l - 1)*(l + 1)
Suppose -16 = -3*g + g - 2*x, g - 5*x - 32 = 0. Let m be (-9)/g + 44/16. Find q such that q - 2 + m*q + 0*q**2 + 2*q + 3*q**2 = 0.
-2, 1/3
Suppose x + 17 = 4*a, -x + a + 1 = 12. Let h be 32/8 + 30/x. Suppose 4/3*g**2 + 0*g**3 - h*g**4 + 0*g - 2/3 = 0. Calculate g.
-1, 1
Let a(f) = 3*f**3 - 10 + 18*f**4 + 0*f**4 - 9*f**3 + 2*f + 8. Let w(b) = 36*b**4 - 13*b**3 + 5*b - 5. Let g(d) = -5*a(d) + 2*w(d). Solve g(q) = 0 for q.
0, 2/9
Let g(p) be the third derivative of 0*p**5 - 1/1008*p**8 + 0*p + 0 + 2/315*p**7 + 0*p**4 - 1/90*p**6 + 0*p**3 - 26*p**2. Factor g(i).
-i**3*(i - 2)**2/3
Let z be -27*(-3 - 22/(-6)). Let d be (z/(-5))/(4/10). Find y such that 5*y + 3*y**2 - d*y**5 - 3*y**3 - 3*y - 15*y**4 - 2*y = 0.
-1, 0, 1/3
Let t = -171 + 152. Let b = t + 19. Factor 4/9*u**3 - 2/9*u**2 - 2/9*u**4 + b + 0*u.
-2*u**2*(u - 1)**2/9
Suppose 9*a**3 + 54*a**2 - 972*a - 10*a**3 + 6043 + 1066 - 1277 = 0. Calculate a.
18
Let y(h) be the first derivative of -3*h**3 - 49*h**2/2 - 20*h - 937. Let y(f) = 0. What is f?
-5, -4/9
Let x = 72 - 68. Let h be x/8*(-6)/(-5). Let 0 - h*s + 1/5*s**2 = 0. Calculate s.
0, 3
Find y such that 3*y**3 - 64*y**2 + 58*y**2 - 5*y**3 + 8 = 0.
-2, 1
Suppose 7 - 41 = -17*u. Let g(c) be the first derivative of 0*c + 3*c**u + 3/4*c**4 - 3*c**3 - 2. Factor g(k).
3*k*(k - 2)*(k - 1)
Let z(f) be the third derivative of f**6/300 + f**5/15 + 9*f**4/20 + 6*f**3/5 - f**2 + 16*f. Let z(j) = 0. What is j?
-6, -3, -1
Let t(j) be the third derivative of -j**7/210 + 3*j**6/160 - j**5/120 - 85*j**2. Let t(d) = 0. What is d?
0, 1/4, 2
Let f(c) be the second derivative of 1/6*c**4 + 0 + 9/2*c**2 + 0*c**3 - 5*c + 1/30*c**5. Let g(y) be the first derivative of f(y). Suppose g(u) = 0. What is u?
-2, 0
Let p(b) = -b**4 - 59*b**3 - 90*b**2 - 42*b + 5. Let d(g) = -3*g**4 - 147*g**3 - 225*g**2 - 105*g + 12. Let l(y) = 5*d(y) - 12*p(y). What is h in l(h) = 0?
-7, -1, 0
Let m(q) be the first derivative of -q**6/11 - 14*q**5/55 + 9*q**4/22 + 14*q**3/33 - 6*q**2/11 + 34. Find u, given that m(u) = 0.
-3, -1, 0, 2/3, 1
Let t be (-12)/(-5)*((-46)/(-6) + -1). Solve 56*m + t + 14*m**2 + 3*m**3 + 2*m**2 + 9*m**2 = 0.
-4, -1/3
Let y(x) be the third derivative of 0 + 5/2*x**4 + 50/3*x**3 + 0*x - 3/5*x**5 + 24*x**2 + 1/30*x**6. Factor y(q).
4*(q - 5)**2*(q + 1)
Let u = -2/3731 + 7472/18655. Determine g so that 0*g - 4/5*g**3 + u*g**4 + 0 + 2/5*g**2 = 0.
0, 1
Let x(r) be the first derivative of -5/4*r**4 + 5*r - 15/2*r**2 - 12 + 5*r**3. Factor x(a).
-5*(a - 1)**3
Let b(g) be the third derivative of g**8/1008 - 13*g**7/105 + 2027*g**6/360 - 8749*g**5/90 - 169*g**4/6 + 8788*g**3/9 + 125*g**2. Solve b(u) = 0.
-1, 1, 26
Let t(m) = -m**3 + 4*m**2 + 6*m - 5. Suppose 9 = 3*j, -h + 3*j + 0 = 4. Let i be t(h). Solve i*c**2 + 3*c**2 - 3*c**2 + 3*c**2 + 27 - 18*c = 0 for c.
3
Suppose -164*l - 21 = -171*l. Let p(a) be the third derivative of 0*a - 5*a**2 + 1/20*a**4 + 0 - 1/100*a**5 + 0*a**l. Factor p(x).
-3*x*(x - 2)/5
Let j(i) = -i**5 - 23*i**4 - 11*i**3 + 13*i**2 + 17*i + 5. Let n(w) = -12*w**4 - 6*w**3 + 6*w**2 + 9*w + 3. Let x(p) = -3*j(p) + 5*n(p). Solve x(m) = 0.
-2, -1, 0, 1
Let t = 11/56 + 3/56. Let m(l) be the third derivative of 1/10*l**5 + 0*l + 1/3*l**3 + t*l**4 + 1/60*l**6 - 5*l**2 + 0. What is i in m(i) = 0?
-1
Suppose 4*t + 7 = -5*r, -4*t - r + 1 = -2*t. Factor 13*p**t - 2*p + 11*p**2 - 25*p**2.
-p*(p + 2)
Let c = 917 + -913. Let h(y) be the first derivative of -1/2*y**2 - 1/15*y**3 + 1/20*y**c + 5 - 3/5*y. Factor h(d).
(d - 3)*(d + 1)**2/5
Let n(h) = -190*h**2 - 122*h - 7. Let g(v) = 571*v**2 + 369*v + 24. Let r(b) = -6*g(b) - 17*n(b). Let r(o) = 0. What is o?
-5/14
Find b, given that -100*b**3 - 9*b