*d**y = 0.
0, 1
Let g(f) be the third derivative of 2*f**7/21 + f**6/15 - 6*f**2. Solve g(p) = 0.
-2/5, 0
Factor 0*z + 0 - 1/6*z**4 - 1/3*z**2 - 1/2*z**3.
-z**2*(z + 1)*(z + 2)/6
Let y(b) = -2*b**4 + 4*b**3 + 6*b**2 - 22*b + 18. Let l(r) = r**3 - r**2 - r - 1. Let g(t) = -2*l(t) - y(t). Factor g(w).
2*(w - 2)**2*(w - 1)*(w + 2)
Let z(h) be the third derivative of -5/12*h**4 + 1/168*h**8 - 1/15*h**5 + 4/105*h**7 - 2/3*h**3 + 0 + 0*h + 3*h**2 + 1/15*h**6. Factor z(a).
2*(a - 1)*(a + 1)**3*(a + 2)
Suppose 6*z = 2*z + 8. Let b be 3 - (0 - z)/(-2). Factor 0 + 4/5*n + 2/5*n**b.
2*n*(n + 2)/5
Let i(x) be the second derivative of x**4/18 - 4*x**3/9 + 4*x**2/3 + 55*x. Factor i(w).
2*(w - 2)**2/3
Let d(g) be the second derivative of g**7/105 - g**6/75 - g**5/50 + g**4/30 + 9*g. Find l, given that d(l) = 0.
-1, 0, 1
Let l = -1891/9 + 213. Let u = 1401 - 12607/9. Find w such that u + l*w**4 - 44/9*w**3 + 4*w**2 - 2/3*w**5 - 14/9*w = 0.
1/3, 1
Let l = 1183313 + -422443220/357. Let g = -1/119 - l. Factor 2/3*w**2 - g*w + 2/3.
2*(w - 1)**2/3
Factor 3/7*x**2 - 27/7*x + 24/7.
3*(x - 8)*(x - 1)/7
Factor 2*a + 0*a - 3*a**4 + 3*a**3 + 3*a**2 - 5*a.
-3*a*(a - 1)**2*(a + 1)
Let 0*j + 0 + 6/5*j**3 - 2*j**4 + 4/5*j**2 = 0. Calculate j.
-2/5, 0, 1
Let g(p) be the third derivative of -p**8/10080 + p**5/20 + p**2. Let r(d) be the third derivative of g(d). Factor r(a).
-2*a**2
Let a(m) = -31*m**3 + 60*m**2 - 49*m + 20. Let t(o) = 6*o**3 - 12*o**2 + 10*o - 4. Let p(s) = 2*a(s) + 11*t(s). Factor p(d).
4*(d - 1)**3
Let r(i) = -i**3 - i**2 - i - 1. Let f(x) = -2*x**4 + 5*x**3 + 5*x**2 + x + 3. Suppose 0 = -3*u - 2*m + 19, 4*m - 5 = 15. Let c(s) = u*r(s) + f(s). Factor c(q).
-2*q*(q - 1)**2*(q + 1)
Solve -57/8*y**3 - 105/4*y**4 + 3 + 93/4*y**2 - 75/8*y**5 + 33/2*y = 0 for y.
-2, -1, -2/5, 1
Let c(y) = -2*y**2 - 10*y - 8. Let x be c(-4). Factor 0*o - 1/2*o**4 - 1/2 + o**2 + x*o**3.
-(o - 1)**2*(o + 1)**2/2
Factor 0*y**3 - 2/7*y + 2/7*y**5 + 0 - 4/7*y**4 + 4/7*y**2.
2*y*(y - 1)**3*(y + 1)/7
Let y = -12 - -14. Factor -2*p - 2*p**y + 7 + 3 - 6.
-2*(p - 1)*(p + 2)
Let u(m) be the second derivative of -m**5/5 - 4*m**4/3 - 2*m**3 - 7*m. What is z in u(z) = 0?
-3, -1, 0
Suppose -k = 4*y - 22, 2*k - 2*y - 5 = 3*y. Suppose 0*l + k = 5*l. Factor -1/2 + 1/2*q**l + 0*q.
(q - 1)*(q + 1)/2
Let g(n) be the first derivative of -n**3/24 + n**2/2 - 7*n/8 + 34. Find r such that g(r) = 0.
1, 7
Let b(x) = -x**2. Let k(q) = -6*q**2 + q. Let n(r) = -35*b(r) + 5*k(r). Factor n(f).
5*f*(f + 1)
Let x(h) = -h - 1. Let g be x(9). Let t = 14 + g. Solve 0*z**4 + 5*z**2 + 3*z - 5*z**t - 17*z**2 - 14*z**3 + 1 - 5*z = 0.
-1, 1/5
Let t(x) = 2*x**4 - 12*x**3 + 14*x**2 - 2*x + 2. Let z(f) = -9*f**4 + 60*f**3 - 71*f**2 + 9*f - 11. Let l(a) = 11*t(a) + 2*z(a). Factor l(y).
4*y*(y - 1)**3
Determine i, given that -10/9*i - 2/9*i**2 - 8/9 = 0.
-4, -1
Let p = -103/240 - -9/16. Let q(f) be the first derivative of p*f**3 - 2/5*f + 4 + 0*f**2. Factor q(r).
2*(r - 1)*(r + 1)/5
Let m(w) = w**3 + 5*w**2 + 3. Let k be m(-5). Let p = k - 1. Factor 2*y + 4 - y**2 - 4 + p*y**2.
y*(y + 2)
Let z = 3 - 11. Let k = z - -19. Factor 2 - 5*i**2 - k*i**3 + 2*i - 4*i**4 - 2.
-i*(i + 1)*(i + 2)*(4*i - 1)
Find g, given that 123*g - 118*g - 10 - 4*g**4 - 5*g**3 - g**4 + 15*g**2 = 0.
-2, -1, 1
Let o(s) = -9*s**3 - 27*s**2. Let z(y) = -8*y**3 - 28*y**2 + y. Let f(n) = -7*o(n) + 6*z(n). Factor f(m).
3*m*(m + 1)*(5*m + 2)
Let o(n) be the third derivative of n**6/54 - 7*n**5/135 + n**4/27 + 13*n**2. Find m such that o(m) = 0.
0, 2/5, 1
Let r(k) be the second derivative of -k - 2/3*k**3 - 3/2*k**2 + 1/30*k**5 + 0 - 1/12*k**4. Let a(d) be the first derivative of r(d). Factor a(j).
2*(j - 2)*(j + 1)
Let r(h) be the second derivative of -10*h**7/21 + 14*h**6/15 + 13*h**5/5 - 11*h**4/3 - 16*h**3/3 + 8*h**2 - 7*h. Find j, given that r(j) = 0.
-1, 2/5, 1, 2
Let h(q) be the third derivative of 1/360*q**5 - 2*q**2 - 1/3*q**3 + 0 + 0*q**4 + 1/1080*q**6 + 0*q. Let y(i) be the first derivative of h(i). Factor y(z).
z*(z + 1)/3
Let a(w) be the third derivative of -w**5/240 + w**4/96 + w**3/4 + 21*w**2. Suppose a(f) = 0. Calculate f.
-2, 3
Let g(m) be the second derivative of -m**9/30240 + m**7/5040 + m**4/6 - 4*m. Let b(w) be the third derivative of g(w). Let b(n) = 0. What is n?
-1, 0, 1
Let n be (-30)/(-4) - 3/(-6). Let f(k) = -14*k**4 + 6*k**3 - 2*k**2 + 2*k. Let x(o) = -9*o**4 + 4*o**3 - o**2 + o. Let q(g) = n*x(g) - 5*f(g). Factor q(i).
-2*i*(i - 1)**2*(i + 1)
Let r(w) be the first derivative of -2*w**6/3 + 4*w**5/5 + 2*w**4 - 8*w**3/3 - 2*w**2 + 4*w - 10. Factor r(x).
-4*(x - 1)**3*(x + 1)**2
Suppose 3*w + 192 = w. Let u be w/(-90) + (-4)/6. Factor 4/5*m + 0 + u*m**2.
2*m*(m + 2)/5
Determine z so that 14 + 262*z + 55*z**2 + 6 - 15*z**3 - 322*z = 0.
2/3, 1, 2
Let o(j) be the third derivative of j**7/455 - j**6/390 - j**5/390 + 4*j**2. Factor o(u).
2*u**2*(u - 1)*(3*u + 1)/13
Solve 0*a + 1/2 + 2*a**3 + 6*a**4 - 9/2*a**2 = 0.
-1, -1/3, 1/2
Let x(i) = i**2 - 4*i + 7. Let f(t) = 3*t**2 - 11*t + 20. Let g = -6 + -11. Suppose d = -j + 3*d + 16, 5*j - 10 = -4*d. Let h(y) = g*x(y) + j*f(y). Factor h(a).
(a + 1)**2
Let p be (-34)/(-40) + 117/(-195). Determine h so that -1/2*h + 1/4 + p*h**2 = 0.
1
Let g(w) be the third derivative of w**8/336 + 2*w**7/105 + w**6/24 + w**5/30 - 2*w**2. Factor g(s).
s**2*(s + 1)**2*(s + 2)
Let p be -3 - 14*(-1)/2. Factor -3/2*r**3 + 1/2*r**2 + 0 + r**p + 0*r.
r**2*(r - 1)*(2*r - 1)/2
Let r(m) = m**3 - 5*m**2 - 7*m + 8. Let t be r(6). Factor -j**2 + 2*j**2 - 2 - j**4 + t.
-j**2*(j - 1)*(j + 1)
Let f(p) be the first derivative of p**4/12 - 5*p**3/9 - 47. Solve f(k) = 0 for k.
0, 5
Factor -65*f**5 + 37*f**5 - f**3 + 32*f**5 + 8*f**4 + 5*f**3.
4*f**3*(f + 1)**2
Let c(d) be the second derivative of -d**4/6 - d**3/3 - 6*d. Solve c(n) = 0.
-1, 0
Let y = -20 - -20. Let h(t) be the third derivative of t**2 + 0 + 1/180*t**5 - 1/360*t**6 + y*t**3 + 1/36*t**4 + 0*t. Factor h(g).
-g*(g - 2)*(g + 1)/3
Let c(m) be the first derivative of -m**8/840 - m**7/420 + m**6/180 + m**5/60 - m**3 - 1. Let n(d) be the third derivative of c(d). Factor n(u).
-2*u*(u - 1)*(u + 1)**2
Factor 4/5 - 6/5*u**3 - 12/5*u + 13/5*u**2 + 1/5*u**4.
(u - 2)**2*(u - 1)**2/5
Let y be (-8)/(-14)*(11 + -4). Solve 4*u**2 + 0*u**4 - 4*u**y + 0*u**2 = 0 for u.
-1, 0, 1
Solve 0 + 5*c + 5/2*c**4 - 25/2*c**2 + 15/2*c**3 - 5/2*c**5 = 0 for c.
-2, 0, 1
Find i such that -1 + 1/5*i**2 + 4/5*i = 0.
-5, 1
Let n(g) = -2*g**5 - 2*g**4 + 8*g**3 - 4*g**2 + 4*g. Let o(m) = m**5 + 3*m**4 - 7*m**3 + 3*m**2 - 3*m. Let t(p) = -3*n(p) - 4*o(p). Factor t(l).
2*l**3*(l - 2)*(l - 1)
Let k(n) = -21*n**3 + 47*n**2 - 80*n + 23. Let m(g) = 5*g**3 - 12*g**2 + 20*g - 6. Let y(p) = 2*k(p) + 9*m(p). Factor y(z).
(z - 2)**2*(3*z - 2)
Suppose 22 = 2*c + k, -2*c + 5 = -c - k. Factor 8*l**2 + 3*l**4 + 2*l**2 - 6 - 7*l**2 - 9*l**3 + c*l.
3*(l - 2)*(l - 1)**2*(l + 1)
Let f(p) be the second derivative of 0*p**2 - 27/20*p**5 - 1/6*p**7 + 0 + 2*p - 1/3*p**3 + 13/12*p**4 + 23/30*p**6. Factor f(b).
-b*(b - 1)**3*(7*b - 2)
Let j(r) be the third derivative of -1/24*r**4 + 0*r**3 + 1/210*r**7 + 0*r + 1/120*r**6 - r**2 + 0 - 1/60*r**5. Factor j(v).
v*(v - 1)*(v + 1)**2
Let b(a) be the first derivative of 2*a**6/15 - 4*a**5/25 - a**4/5 + 4*a**3/15 + 25. Factor b(k).
4*k**2*(k - 1)**2*(k + 1)/5
Let r(c) = -c**3 + c**2 - 1. Let n(y) = 4*y**3 - 9*y**2 - 5*y + 3. Let p(i) = n(i) + 5*r(i). Factor p(w).
-(w + 1)**2*(w + 2)
Let n be 1/(-1*3/6). Let s = n - -5. Factor -2*l**3 - 2*l**3 + 6*l**s + l + 4*l**2 + l.
2*l*(l + 1)**2
Find d, given that 3/8*d**4 - 3/8*d**5 + 0 + 0*d + 3/8*d**3 - 3/8*d**2 = 0.
-1, 0, 1
Let l(m) be the third derivative of 0*m + 0 - 1/360*m**5 + m**2 - 1/72*m**4 + 0*m**3. Factor l(x).
-x*(x + 2)/6
Let j(d) be the first derivative of 2/5*d**5 + 3 + 0*d**2 + 0*d**4 - 4/3*d**3 + 2*d. What is g in j(g) = 0?
-1, 1
Let y(c) be the second derivative of -c**7/56 - c**6/16 + 5*c**4/32 + c**3/8 - 11*c. Solve y(r) = 0 for r.
-2, -1, -1/2, 0, 1
Let n(t) be the third derivative of -2*t**2 + 0 + 0*t**4 + 0*t**6 + 0*t - 1/75*t**5 + 1/525*t**7 + 1/15*t**3. Solve n(l) = 0 for l.
-1, 1
Let v be (-92)/(-28) - -1*2/(-7). Let n(b) be the first derivative of -1/4*b**v + 1/20*b**5 + 0*b**4 - 3 - 1/4*b**2 + 0*b. Factor n(q).
q*(q