 1)**2/3
Let t(i) be the third derivative of -i**5/21 + i**4/42 - 16*i**2. Suppose t(s) = 0. Calculate s.
0, 1/5
Let d(m) be the third derivative of -1/18*m**3 - m**2 - 1/60*m**5 + 1/24*m**4 + 1/360*m**6 + 0*m + 0. Factor d(a).
(a - 1)**3/3
Let l(h) = 2*h**3 - h + 2 + 7*h**2 - h**3 - 8. Let g be l(-7). Suppose -2*d**3 + 3*d**2 + g + 3*d**3 - 2*d**3 - 3*d = 0. Calculate d.
1
Let f be -29*1*(-3 - -10). Let h = f + 334. Factor -29*u + 16*u - h*u**2 + 33*u**2 - 8 - 43*u.
-2*(7*u + 2)**2
Factor 3*a**4 + a**5 + 31*a**3 - 31*a**3.
a**4*(a + 3)
Let t(v) = v**3 + 2*v**2 - v - 2. Let n = -34 - -32. Let s be t(n). Factor 0 - d**3 - 3/2*d**4 + 1/2*d**2 + s*d.
-d**2*(d + 1)*(3*d - 1)/2
Solve -m**5 - 5/4*m**4 + 1/2*m**2 + 0 + 7/4*m**3 + 0*m = 0.
-2, -1/4, 0, 1
Let a be -3*((-168)/(-9))/4. Let r be a/(-6) + (-24)/(-36). Solve -2/3*m - 4/3 - 10/3*m**r + 16/3*m**2 = 0.
-2/5, 1
Let z(l) be the third derivative of 0*l - 1/900*l**6 - 1/3*l**3 + l**2 - 1/150*l**5 + 0 - 1/60*l**4. Let j(q) be the first derivative of z(q). Factor j(p).
-2*(p + 1)**2/5
Let v(u) = 5*u**2 + u + 6. Suppose -4*t = -4*k + 20, -3*k + 22 = 3*t + t. Let q(c) = 10*c**2 + 2*c + 13. Let w(h) = k*q(h) - 13*v(h). Factor w(s).
-s*(5*s + 1)
Let f(z) be the first derivative of 3 - 7/2*z**2 - 35/8*z**4 - z - 23/4*z**3 - 5/4*z**5. Suppose f(n) = 0. What is n?
-1, -2/5
Factor -5*h**2 + 7*h + 0*h + 2*h**2 - 37*h - 75.
-3*(h + 5)**2
Factor z**3 - 222 - z**4 - z + 222 + z**2.
-z*(z - 1)**2*(z + 1)
Let k(g) be the second derivative of -3*g**8/4480 - g**7/840 - g**6/1440 + g**4/4 - 3*g. Let y(i) be the third derivative of k(i). Factor y(n).
-n*(3*n + 1)**2/2
Suppose 5*r = 5*q + 3 + 37, 0 = 4*q + 12. Suppose -26 = -r*d - 1. Factor -2*w + d*w - 1 - w**2 - w.
-(w - 1)**2
Let 0*q**2 - 2/7*q**3 + 0*q + 0 = 0. What is q?
0
Let -8/21*j - 2/21*j**4 + 8/21*j**2 + 2/21*j**3 + 0 = 0. What is j?
-2, 0, 1, 2
Let f(z) be the second derivative of -z**6/330 + 3*z**5/220 - 2*z**3/33 - 8*z. Let f(s) = 0. What is s?
-1, 0, 2
Let l be (-72)/(-36) - (-22)/(-12). Let x(j) be the first derivative of 0*j + 3 + 0*j**3 + 0*j**2 - 1/5*j**5 + 0*j**4 + l*j**6. Factor x(r).
r**4*(r - 1)
Let q(z) be the first derivative of -z**5/10 - z**4/8 + 2. Suppose q(i) = 0. What is i?
-1, 0
Let g(h) = h**2 - 3*h - 4. Let u(p) be the first derivative of p**3/3 - p**2 - 3*p - 3. Suppose -2*x + 3*x + 4 = 0. Let m(y) = x*g(y) + 5*u(y). Factor m(q).
(q + 1)**2
Let r(f) be the first derivative of -3*f**4/20 + 12*f**3/5 - 72*f**2/5 + 192*f/5 + 1. Factor r(u).
-3*(u - 4)**3/5
Factor -4*x**3 + 0*x**3 - 2*x**4 - 32 - 16*x**3 - 80*x - 66*x**2.
-2*(x + 1)**2*(x + 4)**2
Suppose 4*w**3 - 2*w**2 + 6*w**2 - 14*w**5 + 10*w**5 - 4*w**4 = 0. What is w?
-1, 0, 1
Suppose -3*u = -7*u. Factor u - 1/3*k + 4/3*k**4 + 7/3*k**3 + 2/3*k**2.
k*(k + 1)**2*(4*k - 1)/3
Let r(s) be the third derivative of 1/96*s**6 + 1/2688*s**8 + 0*s + 1/48*s**5 + 1/48*s**3 - 4*s**2 + 5/192*s**4 + 0 + 1/336*s**7. Find u, given that r(u) = 0.
-1
Solve f**5 + 5*f**2 + 7*f**2 - f**3 - 13*f**2 + f**4 = 0.
-1, 0, 1
Let a(r) be the second derivative of r**5/5 + 2*r**4/3 - 2*r**3/3 - 4*r**2 + 4*r. Solve a(d) = 0 for d.
-2, -1, 1
Let n(t) be the first derivative of -t**5/30 - t**4/2 - 3*t**3 - 5*t**2/2 - 4. Let y(x) be the second derivative of n(x). Factor y(i).
-2*(i + 3)**2
Suppose -60 = 3*y - 2*y. Let z = -172/3 - y. Let -z - 8/3*c - 2/3*c**2 = 0. Calculate c.
-2
Factor 1131*h**2 - 1029*h**5 + 939*h**2 - 840*h**3 + 474*h**2 - 3234*h**4 + 96 - 912*h.
-3*(h + 2)**2*(7*h - 2)**3
Suppose 2*s - 24 = 6*s. Let t be (48/(-54))/(2/s). Suppose 8/3*o - t + 2*o**2 = 0. What is o?
-2, 2/3
Let o(c) be the second derivative of c**6/600 + c**5/150 + c**4/120 + c**2/2 + 2*c. Let t(k) be the first derivative of o(k). Factor t(h).
h*(h + 1)**2/5
Let f be 0*-2*1/4. Let l(z) = -z + 7. Let p be l(5). Factor 0*u**2 + f + u**p - 1.
(u - 1)*(u + 1)
Let k = 3 + -6. Let i = 6 + k. Suppose -3*f + 0*f**i + 3*f**4 - 3*f**2 + 2*f**3 + f**5 - 1 + f**2 = 0. What is f?
-1, 1
Let d(b) = 2*b**3 - 14*b**2. Let q(h) = -h**3 + 1. Let a(z) = d(z) + 8*q(z). Let a(j) = 0. What is j?
-2, -1, 2/3
Let z(y) be the second derivative of 0*y**4 + 0*y**3 + 1/150*y**6 - 2*y + 0 - 1/100*y**5 + 0*y**2. Find l, given that z(l) = 0.
0, 1
Let k = 11 + -10. What is d in 2*d - k - 6*d**2 + d**2 + 4*d**2 - 4*d = 0?
-1
Let n(i) be the second derivative of 7/5*i**5 + i + i**2 - 7/3*i**3 + 11/8*i**4 + 4/15*i**6 + 0. Suppose n(y) = 0. Calculate y.
-2, 1/4
Let j(f) be the second derivative of -1/9*f**3 - 1/54*f**4 - 2/9*f**2 - 6*f + 0. Determine v so that j(v) = 0.
-2, -1
Let s(b) = b + 1. Let y(z) = 5*z + 8. Let f(c) = -3*s(c) + y(c). Let r be f(0). Factor 2/5*t**3 + 0*t + 0 + 2/5*t**r + 0*t**2 + 4/5*t**4.
2*t**3*(t + 1)**2/5
Let x(d) = -d - 1. Let z(g) = 7*g**2 + 9*g + 2. Let l(t) = 3*x(t) + z(t). Factor l(v).
(v + 1)*(7*v - 1)
Let r(t) = -2*t**3 + 14*t**2 - 2*t + 6. Let b = -8 - -13. Let j(a) = -2*a**3 + 13*a**2 - 3*a + 5. Let w(x) = b*r(x) - 6*j(x). Factor w(y).
2*y*(y - 2)**2
Let n(v) = -5*v + 0*v + 8 + 2*v + 2*v. Let g be n(4). Factor -2*z**2 - 2 + 3*z + 3*z**2 - g*z.
(z - 2)*(z + 1)
Let c(d) be the first derivative of 5*d**3/12 + 3*d**2/2 + d + 7. Factor c(p).
(p + 2)*(5*p + 2)/4
Let p = 19 + -19. Let t(o) be the second derivative of -1/40*o**5 + 1/84*o**7 + 1/24*o**4 + p*o**3 - 1/60*o**6 + 0*o**2 + 0 - o. Factor t(x).
x**2*(x - 1)**2*(x + 1)/2
Let o = 61/9 + -19/3. Suppose 2/9*r**2 + 2/9 + o*r = 0. Calculate r.
-1
Let w = 164 + -819/5. Let m(o) be the first derivative of 1 + 1/3*o**3 - 1/4*o**4 - w*o**5 + 0*o + 0*o**2 + 1/6*o**6. Determine s, given that m(s) = 0.
-1, 0, 1
Let v(j) be the second derivative of j**6/30 - j**4/4 - j**3/3 + 7*j. Let v(d) = 0. What is d?
-1, 0, 2
Suppose 31*k**2 - 46*k**2 + 1 - 10 + 24*k + 3*k**3 - 3 = 0. Calculate k.
1, 2
Suppose -a - 8 = -4*k + a, -2*k = 4*a + 16. Suppose 1/3*g**4 - 1/3*g**2 + 0*g + 0*g**3 + k = 0. What is g?
-1, 0, 1
Let j(y) be the second derivative of -2*y - 1/100*y**5 + 1/10*y**2 + 1/20*y**4 + 0 - 1/10*y**3. Find l such that j(l) = 0.
1
Let u be (1 - 0) + (-1670)/1660. Let j = u - -1001/830. Find w such that 2/5*w**3 + 0*w**2 + 4/5 - j*w = 0.
-2, 1
Let a(x) = 18*x**4 + 9*x**3 - 9*x**2 - 3*x - 3. Let q(w) = 17*w**4 + 9*w**3 - 10*w**2 - 4*w - 2. Let y = 10 + -4. Let m(b) = y*q(b) - 5*a(b). Factor m(s).
3*(s - 1)*(s + 1)**2*(4*s - 1)
Let w(u) = 2*u**3 - 10*u**2 + 9*u - 7. Let a(g) = g**3 - g**2 + g - 1. Let j(t) = 14*a(t) - 2*w(t). Factor j(k).
2*k*(k + 1)*(5*k - 2)
Let m = 412/5 + -82. Factor -6/5*h**3 - 4/5 + 6/5*h + m*h**2 + 2/5*h**4.
2*(h - 2)*(h - 1)**2*(h + 1)/5
Suppose u - 2*u = 0. Factor 0*d**2 - 3*d + u*d + d**2 + 2.
(d - 2)*(d - 1)
Let f = -4/109 - -448/327. Suppose -4*n - 4 = -6*n. Factor 0 + 2*d**5 - 2/3*d**3 - f*d**n + 0*d + 8/3*d**4.
2*d**2*(d + 1)**2*(3*d - 2)/3
Let t(w) be the first derivative of -1/12*w**4 + 4/3*w - 1/3*w**3 + 1 + 0*w**2. Let t(o) = 0. Calculate o.
-2, 1
Find t, given that 0*t**2 + 0*t - 2/5*t**5 + 4/5*t**4 + 0 - 2/5*t**3 = 0.
0, 1
Factor 1/2*l**4 + 3/2*l**2 + 0 - 1/2*l - 3/2*l**3.
l*(l - 1)**3/2
Solve -16/11*i - 20/11*i**2 + 14/11*i**4 + 0 + 2*i**3 = 0 for i.
-2, -4/7, 0, 1
Let v(p) be the third derivative of -p**7/630 - p**6/120 - p**5/90 - 2*p**2 - 27*p. Suppose v(b) = 0. What is b?
-2, -1, 0
Factor -8*t**4 - 5*t**5 + 10*t**2 - 10*t**4 - 10*t**3 + 15*t + 5 + 3*t**4.
-5*(t - 1)*(t + 1)**4
Let g(t) be the first derivative of -t**5/3 - 5*t**4/6 + 35*t**3/9 - 10*t**2/3 + 29. Factor g(h).
-5*h*(h - 1)**2*(h + 4)/3
Factor -3*u**3 + 0*u + 0*u**2 + 3/2*u**4 + 3/2*u**5 + 0.
3*u**3*(u - 1)*(u + 2)/2
Let y(r) = r - 7. Let c(t) = t. Let k(b) = c(b) + y(b). Let g be k(6). Let 2 + 2*h - 2 - g*h**2 = 0. Calculate h.
0, 2/5
Let s be (-1 - 3)*(-6)/12. Let c be (-1 - -2)*(s - 0). Let 0 + 1/2*p**3 - 7/4*p**4 + 0*p + 0*p**c = 0. Calculate p.
0, 2/7
Let h(n) be the third derivative of n**6/40 - n**5/5 + n**4/2 - 2*n**2. Factor h(o).
3*o*(o - 2)**2
Suppose 21 - 6 = 3*i. Let 14*k**2 + i - 3 - 16*k**2 = 0. Calculate k.
-1, 1
Let y(t) be the first derivative of 1/4*t**2 - 2/5*t**5 - 1/3*t**6 - 2 + 0*t + 2/3*t**3 + 3/8*t**4. Solve y(j) = 0 for j.
-1, -1/2, 0, 1
Let q(k) = 2*k**2 - 2*k - 1. Let w be q(-2). Let f = 16 - w. What is g in -3*g**2 - 3*g**4 + g**3 - 2*g + 4*g**5 + 6*g**2 - 3*g**f = 0