 the third derivative of 5*m**6/84 + m**5/7 - 3*m**4/7 + 8*m**3/21 + 51*m**2. Determine f, given that p(f) = 0.
-2, 2/5
Let t(q) = -q + 3. Let z be t(5). Let x = z + 4. Factor -2*w**x - 8 + 13*w - 2*w**2 + 2*w**2 - 5*w.
-2*(w - 2)**2
Let b(o) be the first derivative of -6*o**5/65 + 71*o**4/26 - 212*o**3/39 - 92*o**2/13 + 176*o/13 - 930. Solve b(v) = 0.
-1, 2/3, 2, 22
Factor -36/7 + 1/7*i**2 - 16/7*i.
(i - 18)*(i + 2)/7
Suppose -4*p = -3*p - 8. Let x(n) = 11*n**2 + 3*n - 7 + 10*n + 14 + p. Let r(l) = -5*l**2 - 6*l - 7. Let i(b) = -13*r(b) - 6*x(b). Let i(q) = 0. Calculate q.
-1, 1
Factor -30258/7 - 2/7*r**2 - 492/7*r.
-2*(r + 123)**2/7
Let h(g) be the first derivative of -g**3 - 117*g - 121*g + 24*g**2 + 3 + 46*g. Determine a, given that h(a) = 0.
8
Let u(s) = -s**3 - 2*s**2 + 7*s - 1. Let a be u(-4). Solve -1335 - 12*g**a - 20*g - 64*g**2 + 1335 = 0.
-5, -1/3, 0
Let y(c) be the second derivative of -c**7/280 + c**6/60 + c**5/40 - c**4/4 - c**3/3 + 12*c. Let u(g) be the second derivative of y(g). Factor u(m).
-3*(m - 2)*(m - 1)*(m + 1)
Suppose 8 - 11 = -x. Let m be (-8)/70 - x/((-15)/2). Factor -m*f**2 + 2/7*f + 0.
-2*f*(f - 1)/7
Factor 6*l - 1/2*l**2 + 14.
-(l - 14)*(l + 2)/2
Find r such that -6*r**3 - 9*r**3 - 322*r + 102*r**2 + 13*r**3 - 1412*r + 9826 = 0.
17
Let p(u) be the third derivative of -5/48*u**4 + 1/6*u**3 + 0*u - 26*u**2 + 0 + 1/40*u**5. Factor p(t).
(t - 1)*(3*t - 2)/2
Suppose -5*o - 5*i - 90 = 0, o + 8 = -4*i + 8*i. Let r = -9 - o. Factor 1 + 6 + r*x**2 - 3 - 2 + 9*x.
(x + 1)*(7*x + 2)
Suppose -5*q = -9*p + 35, 5*q - 3*q + 14 = -p. Suppose p + 1/5*a**4 - 4/5*a**3 - 11/5*a**2 - 6/5*a = 0. Calculate a.
-1, 0, 6
Let x(o) = 2*o**4 - o**3 - 17*o**2 + 13*o + 24. Let z(y) = 6*y**4 - 2*y**3 - 52*y**2 + 38*y + 72. Let d(f) = 20*x(f) - 6*z(f). Let d(h) = 0. Calculate h.
-2, -1, 2, 3
Let l(m) be the third derivative of m**5/12 - 145*m**4/12 + 4205*m**3/6 - 149*m**2. Let l(c) = 0. Calculate c.
29
Let w(t) = -4*t**4 + 40*t**3 + 92*t**2 + 104*t + 49. Let b(x) = -x**4 + 13*x**3 + 31*x**2 + 35*x + 16. Let o(s) = 14*b(s) - 4*w(s). Find g, given that o(g) = 0.
-7, -2, -1
Find u such that -61*u + 3*u**2 - 3*u**5 + 0*u**5 - 3*u**4 + 37*u + 15*u**3 + 12 = 0.
-2, 1
Solve -58*x**2 + 676*x**4 + 48*x**2 - 884*x**3 - 16*x + 234*x**2 = 0 for x.
0, 2/13, 1
Let a be (-1 - 4)/((-595)/476). Factor -1/5*y**5 + 4/5*y**2 - 6/5*y**3 - 1/5*y + 0 + 4/5*y**a.
-y*(y - 1)**4/5
Suppose 0 = -3*j + 2*r + 15, -4*j + 5*r + 25 = j. Suppose 3*q - j = 1. Factor -z**3 + 2 - 1 + 0*z**q - 3*z - z**2 + 4*z**2.
-(z - 1)**3
Let l(h) be the first derivative of h**9/2352 + h**8/784 + h**7/1960 - h**6/840 + 19*h**3/3 + 11. Let x(b) be the third derivative of l(b). Factor x(n).
3*n**2*(n + 1)**2*(3*n - 1)/7
Let d = 6062/3 - 2020. Solve -d - 22/9*i - 20/9*i**2 = 0 for i.
-3/5, -1/2
Let w(j) be the first derivative of -j**3/9 - 5*j**2/3 - 3*j + 109. Find p, given that w(p) = 0.
-9, -1
Let l(b) be the second derivative of -b**8/224 - b**7/140 + b**6/80 + b**5/40 - 17*b**2/2 - 6*b. Let u(x) be the first derivative of l(x). Factor u(w).
-3*w**2*(w - 1)*(w + 1)**2/2
Suppose -5*h + m - 12 = -0*h, 0 = -5*h + 2*m - 14. Let u be -1*(-8)/(2 - h). Determine c so that -5*c - 4*c**2 + c**2 - c**3 - c**2 - u = 0.
-2, -1
Let p(s) be the second derivative of 91/5*s**6 + 57/20*s**5 + 21/2*s**7 - 2*s**3 - 18*s + 0 - 5*s**4 + 0*s**2. Suppose p(d) = 0. Calculate d.
-1, -2/7, 0, 1/3
Let b(g) = 50*g**3 - 260*g**2 - 35*g + 230. Let p(n) = -7*n**3 + 37*n**2 + 5*n - 33. Suppose -6 = -2*r - 10. Let q(w) = r*b(w) - 15*p(w). Factor q(f).
5*(f - 7)*(f - 1)*(f + 1)
Let w = 78 - 47. Let f = w - 29. Find j, given that -4/7 - 2/7*j + 2/7*j**f = 0.
-1, 2
Find u such that 40/7*u**2 + 72/7 + 4/7*u**3 + 108/7*u = 0.
-6, -3, -1
Let j(f) be the second derivative of 2*f**6/75 - 44*f**5/25 - 179*f**4/60 - 3*f**3/2 - 12*f - 9. Factor j(w).
w*(w - 45)*(2*w + 1)**2/5
Let s be -4 + (8 - 8 - -6). Let f(n) be the first derivative of -2*n - 2/5*n**5 - 1/3*n**6 + 4/3*n**3 - 6 - n**s + n**4. Factor f(q).
-2*(q - 1)**2*(q + 1)**3
Let p = 11 + 9. Let c(n) = -n**4 - n**3 + n. Let d(z) = 10*z**4 + 3*z**3 - 5*z**2 - 3*z. Let a(o) = p*c(o) + 4*d(o). Factor a(v).
4*v*(v - 1)*(v + 1)*(5*v - 2)
Suppose 4*l = 2*t + 22, -l - 3*t = -1 + 6. Factor -3*u**3 + l*u**3 + 4*u**2 + 0*u + 0*u - u - 4.
(u - 1)*(u + 1)*(u + 4)
Let z(b) be the second derivative of -b**5/10 + b**4/6 + b**3/3 - b**2 + 80*b. Factor z(h).
-2*(h - 1)**2*(h + 1)
Let h be ((-10)/36)/(-8 + (-176)/(-24)). Factor h*p - 1/6 + 1/3*p**2 - 1/4*p**3.
-(p - 2)*(p + 1)*(3*p - 1)/12
Let g(i) be the first derivative of 15*i**4/2 - 35*i**3/3 + 5*i**2/2 + 63. Factor g(s).
5*s*(s - 1)*(6*s - 1)
Let z be ((77/21)/11)/((-1)/(-6)). Let q be -4 + z + (-12)/(-5). Factor -4/5*l**2 + 0*l**3 + 2/5 + q*l**4 + 0*l.
2*(l - 1)**2*(l + 1)**2/5
Let y(b) = -b**2 - b. Suppose 5*w - 12 = -w. Let t(m) = -8 - m - m + 3*m**2 + 3*m**2. Let x(i) = w*y(i) + t(i). Factor x(c).
4*(c - 2)*(c + 1)
Let r = 323/6183 - -5/229. Let w(q) be the first derivative of 1/9*q**2 - r*q**3 + 2/9*q + 2 - 1/18*q**4. Solve w(l) = 0.
-1, 1
Solve 14 + 155*x**3 + 50*x**4 - 160*x + 110*x**2 + 131 - 305 + 5*x**5 = 0 for x.
-4, -2, -1, 1
Suppose 8*r + 7*r = 375. Determine g so that g**4 - 11*g**4 - 38*g**2 + 2*g**4 - r*g**3 - 9 + 1 - g**5 - 28*g = 0.
-2, -1
Let v(y) be the first derivative of 18*y**3 + 56 + 12*y - 2*y**2 + 10*y**3 - 25*y**2 - 5*y**4 - 11*y**2. Suppose v(r) = 0. What is r?
1/5, 1, 3
Let f(d) be the first derivative of -2*d**3/3 - 7*d**2 - 24*d + 82. Factor f(t).
-2*(t + 3)*(t + 4)
Let l(x) = -x**2 - x. Let r(i) = 4*i**3 + 13*i**2 + 17*i + 8. Let z(a) = 3*l(a) - r(a). Factor z(y).
-4*(y + 1)**2*(y + 2)
Factor 13/8*g + 21/8*g**3 + 19/4*g**2 - 1/2.
(g + 1)**2*(21*g - 4)/8
Let u be 1*(-1)/(-2 - -3) + 3. Let t(z) be the third derivative of 0 + 0*z + 0*z**3 - 1/300*z**6 + 1/150*z**5 + 1/60*z**4 + z**u - 1/525*z**7. Factor t(b).
-2*b*(b - 1)*(b + 1)**2/5
Factor 4/5 + 0*i - 3/5*i**2 + 1/5*i**3.
(i - 2)**2*(i + 1)/5
Let q(u) be the first derivative of 3*u**7/70 + 7*u**6/40 + u**5/4 + u**4/8 + 4*u**2 - 10. Let b(d) be the second derivative of q(d). What is c in b(c) = 0?
-1, -1/3, 0
Suppose 0 = 2*s - 3*f + 5, -3*s - 5*f + 13 = -8. Determine u, given that -u + 47*u**4 + 9*u + 45*u**4 - 18*u**3 + 3*u**5 - 32*u**s + 67*u**5 = 0.
-1, 0, 2/7, 2/5
Suppose -2*h + 6 = -g, 7*h - 2*h + g = 8. Let u(r) = -r**3 + 3*r**2 - 2*r + 2. Let k be u(h). Factor 2*z**2 - 10*z + k + 7*z - z.
2*(z - 1)**2
Factor 55*u + 309 - 95 + 5*u**2 + 46 + 30*u.
5*(u + 4)*(u + 13)
Let d(o) = -o**3. Let z(i) = 2*i**3 + 67 - 38 - 25*i**2 - 49 + 40*i. Let r(w) = 3*d(w) - z(w). Factor r(p).
-5*(p - 2)**2*(p - 1)
Let k = 1977 + -1975. Suppose -2*u = -b - 5, 2*b = -3*u + u - 10. Factor 2/3*f**3 + 0 + 0*f + u*f**k.
2*f**3/3
Let a(c) be the first derivative of c**5/25 - c**4/20 - c**3/5 + c**2/10 + 2*c/5 + 56. Factor a(h).
(h - 2)*(h - 1)*(h + 1)**2/5
Factor -53*o**2 - 630*o**4 - 245*o**5 - 82*o**2 - 8*o - 12*o - 72*o**2 - 545*o**3 + 27*o**2.
-5*o*(o + 1)**2*(7*o + 2)**2
Suppose -7*n**2 - 12*n - 10*n**2 + 32 + 0*n**3 + 10*n**2 - 11*n**2 - 2*n**3 = 0. What is n?
-8, -2, 1
Let f(y) be the third derivative of y**8/252 - 16*y**7/315 - 19*y**6/90 - 2*y**5/9 + 135*y**2. Factor f(t).
4*t**2*(t - 10)*(t + 1)**2/3
Factor -27225*y - 495/2*y**2 - 998250 - 3/4*y**3.
-3*(y + 110)**3/4
Let g = 90/617 - -5900/1851. Factor -g*k**2 - 4 + 22/3*k.
-2*(k - 1)*(5*k - 6)/3
Suppose 4*o = 3*o. Let y = o - -13. Suppose m - 6*m**4 + 5*m**5 - y*m**5 + 10*m**3 + 6*m**2 - 3*m = 0. Calculate m.
-1, 0, 1/4, 1
Let i(n) = -2*n**3 + n + 2. Let p(h) = 54*h**3 - 120*h**2 + 48*h - 12. Let m(q) = 3*i(q) + p(q). Find w such that m(w) = 0.
1/4, 2
Suppose -17 - 61 = -39*c. Let u(s) be the second derivative of 1/48*s**4 + 0*s**3 + 1/168*s**7 + 0*s**c + 12*s - 1/80*s**5 - 1/120*s**6 + 0. Factor u(l).
l**2*(l - 1)**2*(l + 1)/4
Determine b so that -5*b**4 - 63*b**2 + 3*b**5 + b**5 + 45*b**3 + 8*b**2 - 11*b**5 + 20*b + 2*b**5 = 0.
-4, 0, 1
Let m(a) be the first derivative of 0*a + 9/16*a**4 + 3/2*a**2 - 1/8*a**6 + 27 + 3/10*a**5 - 2*a**3. Let m(i) = 0. Calculate i.
-2, 0, 1, 2
Let p = 12 - 17. Let g(u) = -32*u**4 + 40*u**3 - 32*u**2 - 12. Let s(b) = -13*b**4 + 16*b**3 - 13*b**2 - 5. Let w(x) = p*g(x) + 12*s(x). Solve w(i) =