3*q**2/2 + 3. Let z(u) be the second derivative of m(u). Factor z(x).
-2*x*(x + 2)
Let p(h) be the third derivative of -h**5/60 - h**4/3 - 8*h**3/3 - 5*h**2. Determine s, given that p(s) = 0.
-4
Let k be ((-5)/2 + -1)*4/(-7). Let m(v) be the first derivative of 1/6*v**4 - 1/3*v**k + 0*v + 1 + 0*v**3. Determine c, given that m(c) = 0.
-1, 0, 1
Let u(h) = 7*h**3 + h. Let a be u(1). Factor -n**2 - 6*n**3 + a*n + n**2 - 2*n**4.
-2*n*(n - 1)*(n + 2)**2
Suppose -c + 4 = c. Solve -21*b + b**4 - 2*b**5 - 2 - 16*b**4 - 4 + 33*b**3 + 21*b**c - 10*b**5 = 0 for b.
-2, -1, -1/4, 1
Suppose -5*z + 0*s - 158 = -2*s, 0 = -z - 5*s - 37. Let f = z - -34. Let -2/5*r**f - 8/5 - 8/5*r = 0. What is r?
-2
Let a(t) be the second derivative of 3*t**5/20 + t**4/2 - t**3/2 - 3*t**2 + 8*t. Find j, given that a(j) = 0.
-2, -1, 1
Factor 2/5*m**2 + 0*m + 0.
2*m**2/5
Let p = 113 + -549/5. Let i(t) be the first derivative of p*t**4 + 49/15*t**6 + 154/25*t**5 + 8/15*t**3 + 0*t + 0*t**2 - 2. Factor i(c).
2*c**2*(c + 1)*(7*c + 2)**2/5
Let l be 3 + 0 - -1 - -2. Suppose 5*v - 5*s + 5 = 0, -3*v + 5*s = -0*v + 9. Factor -v + 2*h**3 + 3*h**4 + 4*h + 3*h**4 - l*h**3 - 4*h**4.
2*(h - 1)**3*(h + 1)
Let p(o) be the second derivative of -2/105*o**6 - 2*o + 0*o**4 + 0*o**2 + 0*o**3 + 1/70*o**5 + 1/147*o**7 + 0. Factor p(r).
2*r**3*(r - 1)**2/7
Let q = -30 - -30. Let y(o) be the second derivative of 11/3*o**3 + 2*o**2 + 3*o + 5/8*o**5 + q + 35/12*o**4. Find k such that y(k) = 0.
-2, -2/5
Factor 2 - 122*p**3 + 18 - 4*p - 116*p - 3*p**3 + 225*p**2.
-5*(p - 1)*(5*p - 2)**2
Let x = -772 - -774. Determine f so that 32/11 + 2/11*f**x - 16/11*f = 0.
4
Factor 12*z**4 + 16*z**2 - 804 + 804 - 52*z**3.
4*z**2*(z - 4)*(3*z - 1)
Let j(p) be the first derivative of 6*p**3 + 7*p**2 - 4*p + 6. Suppose j(w) = 0. What is w?
-1, 2/9
Let a(o) be the second derivative of -o**7/14 + 9*o**5/20 - o**4/2 - 2*o. Let a(m) = 0. What is m?
-2, 0, 1
Suppose 0 = j + 2*t + 4 - 10, -3*t - 26 = -j. Let k = j - 11. Factor 10/3*o**k + 8*o**2 + 4/3 + 6*o.
2*(o + 1)**2*(5*o + 2)/3
Factor 25/6*b**2 + 20/3*b + 8/3.
(5*b + 4)**2/6
Let r(j) = -j + 3. Let d be r(3). Suppose d = -5*b - 10, -y - 2*b + 0*b - 2 = 0. Factor 0 - 8/5*q**y - 2/5*q**5 - 12/5*q**3 - 8/5*q**4 - 2/5*q.
-2*q*(q + 1)**4/5
Suppose 2 + 1/2*o**2 + 2*o = 0. What is o?
-2
Let g be 4/((-896)/(-452)) + -2. Let x = 115/168 - g. Determine u so that -1/3 - 1/3*u**2 + x*u = 0.
1
Find t such that 8*t + 50*t**3 - 2*t**3 + 36*t**2 - t + 20*t**4 + t = 0.
-1, -2/5, 0
Let -14/3*t**3 + 14/3*t - 2*t**2 + 10/3*t**4 - 4/3 = 0. What is t?
-1, 2/5, 1
Let z(d) be the first derivative of -d**6/1440 + d**5/480 + d**3/3 + 2. Let k(b) be the third derivative of z(b). Determine t, given that k(t) = 0.
0, 1
Let q(d) be the third derivative of -d**6/8 + 23*d**5/12 - 25*d**4/3 - 40*d**3/3 - 4*d**2. Solve q(k) = 0.
-1/3, 4
Solve -19*s**3 - 8*s**3 + s**4 + 2*s**4 + 24*s**2 = 0 for s.
0, 1, 8
Factor -2/5*l**4 - 2/5*l**3 + 0*l + 0 + 0*l**2.
-2*l**3*(l + 1)/5
Let x be (-50)/(-8) + 5/(-20). Let p be 0/(-4*x/(-8)). Factor p*m**3 - 2/7*m**5 + 2/7*m + 4/7*m**2 + 0 - 4/7*m**4.
-2*m*(m - 1)*(m + 1)**3/7
Let a(k) be the second derivative of -k**3/6 - 2*k**2 + 3*k. Let r be a(-7). Factor -3/2*b + 1 - b**2 + 3/2*b**r.
(b - 1)*(b + 1)*(3*b - 2)/2
Let u(f) be the third derivative of f**7/280 + f**6/90 + f**5/90 + f**3/6 - 3*f**2. Let h(c) be the first derivative of u(c). Determine n, given that h(n) = 0.
-2/3, 0
Let a = 13 - 9. Factor -4*g**2 + 2*g**2 - 11 + a - 4*g + 5.
-2*(g + 1)**2
Let b = 42 + -21. Let y be (b/28)/(15/8). Factor -1/5*o**2 + y + 1/5*o.
-(o - 2)*(o + 1)/5
Let y(b) = b**3 + b - 1. Let v(g) = -7*g**3 + 3*g**2 + 3*g - 21. Let n(a) = v(a) + 6*y(a). Find p, given that n(p) = 0.
-3, 3
Determine u, given that 2/3 + 2*u + 2*u**2 + 2/3*u**3 = 0.
-1
Let m(f) be the third derivative of f**6/40 - f**5/30 - f**4/24 + 8*f**2. Find n, given that m(n) = 0.
-1/3, 0, 1
Let h(d) be the first derivative of 2*d**6/15 - 4*d**5/5 - 11. Suppose h(s) = 0. What is s?
0, 5
Let b be (-9)/(-6) + (-43)/34. Let t = -2/153 + b. Factor -2/9*o**2 + 2/9 + t*o**3 - 2/9*o.
2*(o - 1)**2*(o + 1)/9
Factor 3*j**3 + 51/7*j**2 + 3/7*j**4 + 51/7*j + 18/7.
3*(j + 1)**2*(j + 2)*(j + 3)/7
Let d(i) be the third derivative of -i**6/120 - i**5/180 + i**4/18 + 4*i**2 - i. Solve d(h) = 0 for h.
-4/3, 0, 1
Let i be (6/8)/((-630)/(-240)). Factor i*l**2 + 0 + 6/7*l.
2*l*(l + 3)/7
Suppose 0 = s - 8*s. Let v(a) be the first derivative of 0*a**5 + 0*a**2 + 1/4*a**4 + 1 + 0*a**3 + s*a - 1/6*a**6. Factor v(i).
-i**3*(i - 1)*(i + 1)
Let g(m) = -3*m**5 + 9*m**4 - 8*m**3 - 6*m**2 + 11*m - 3. Let n(i) = i**3 - i. Let f(t) = -g(t) - 2*n(t). Factor f(l).
3*(l - 1)**4*(l + 1)
Suppose -3*s + 6*s + 33 = 0. Let k = 11 + s. Find z such that 0*z**2 + 2/9*z**3 + k - 2/9*z = 0.
-1, 0, 1
Let v = -719 + 724. Let 2/7*u + 2/7*u**v + 12/7*u**3 - 8/7*u**2 + 0 - 8/7*u**4 = 0. What is u?
0, 1
Let i(z) be the second derivative of z**6/15 - 9*z**5/10 + 9*z**4/2 - 9*z**3 + 5*z. Factor i(w).
2*w*(w - 3)**3
Solve 9*a**3 - 4*a**2 - a**3 - 6*a**3 = 0 for a.
0, 2
Let c(n) be the second derivative of n**6/480 - 3*n**5/80 + 9*n**4/32 - n**3/6 + 4*n. Let k(y) be the second derivative of c(y). What is d in k(d) = 0?
3
Let h(u) be the third derivative of 0 + 3*u**2 - 9/50*u**5 - 11/525*u**7 - 1/12*u**4 - 31/300*u**6 + 0*u + 2/15*u**3. Let h(c) = 0. Calculate c.
-1, 2/11
Let a(n) be the second derivative of -3*n**2 + 0 + 3/2*n**4 - 7/2*n**3 - 4*n - 2/5*n**6 + 21/20*n**5. Suppose a(f) = 0. Calculate f.
-1, -1/4, 1, 2
Let p = -764 - -3687/5. Let o = p + 27. Find b, given that -o*b - 1/5*b**4 - 4/5*b**3 - b**2 + 0 = 0.
-2, -1, 0
Let m(f) = -f**3 - 3*f**2 - 4*f - 2. Let z be m(-2). Suppose 0 = -4*k + z + 10. Factor -5/2*u**2 + 1/4 - 2*u**k - 1/4*u.
-(u + 1)*(2*u + 1)*(4*u - 1)/4
Let n(q) be the first derivative of q**4/12 + q**3/9 + 21. Factor n(f).
f**2*(f + 1)/3
Determine u, given that 26/11*u + 76/11*u**3 + 10/11*u**5 - 4/11 - 64/11*u**2 - 4*u**4 = 0.
2/5, 1
Let l(u) = 6*u**5 + 4*u**4 + 2*u**3 - 4*u**2 - 2*u. Let k(h) = -h**5 + h**4 - h**3 - h**2. Let o(y) = -6*k(y) - 2*l(y). Find n, given that o(n) = 0.
-2, -1, -1/3, 0, 1
Let h(l) be the second derivative of -5/3*l**4 - 5*l - l**5 - 5/3*l**3 - 1/21*l**7 + 0 - l**2 - 1/3*l**6. Suppose h(o) = 0. What is o?
-1
Let a = -548 - -38361/70. Let f(v) be the third derivative of -2*v**2 - 1/28*v**4 + 0*v + 1/245*v**7 + a*v**5 - 2/21*v**3 + 0 + 1/60*v**6. Factor f(t).
2*(t + 1)**3*(3*t - 2)/7
Let l be 3160/(-35) + (-4)/(-14). Let w be (-6)/l + 2/6. Factor -2/5 - w*n**2 - 4/5*n.
-2*(n + 1)**2/5
Let r(b) be the second derivative of 1/50*b**5 + 0 + 0*b**2 + 0*b**3 - 1/30*b**4 - b. Factor r(a).
2*a**2*(a - 1)/5
Suppose 0 = d - 10 - 18. Factor -18*x**2 + d*x + 7*x**3 - 3*x**3 - x - x**3.
3*x*(x - 3)**2
Let v(a) be the first derivative of a**5/30 - a**4/18 - a**3/9 + a**2/3 - 5*a - 3. Let s(n) be the first derivative of v(n). Let s(x) = 0. What is x?
-1, 1
Suppose 3*p - p + 20 = 4*x, 0 = -2*x + 10. Let h(d) be the second derivative of -1/20*d**5 + 3*d + p + 1/2*d**2 - 1/12*d**4 + 1/6*d**3. Factor h(k).
-(k - 1)*(k + 1)**2
Let o(m) = -m**3 + 3*m**2 - 16*m + 8. Let q(z) = -2*z**3 + 7*z**2 - 32*z + 17. Let f(l) = -7*o(l) + 4*q(l). Determine n so that f(n) = 0.
2, 3
Find y, given that -y + 5*y**2 - 3*y**4 - 3*y**3 - 2*y**2 + 4*y**4 = 0.
0, 1
Let g(a) be the first derivative of -a**3/3 - 4*a**2 - 16*a - 5. Let g(n) = 0. What is n?
-4
Let p(m) = 2*m**2 + 6*m + 6. Let x be p(-1). Factor -3*j + 1/2*j**x + 9/2.
(j - 3)**2/2
Let a = 2137/7 - 305. Factor 6/7*q**2 + a*q**3 + 6/7*q + 2/7.
2*(q + 1)**3/7
Suppose n - 8 = -4. Suppose 0 + 20 = n*m. Factor 0*r**4 + 2*r - 4*r**2 + 4*r**4 - r**m - r**5.
-2*r*(r - 1)**3*(r + 1)
Let w(o) be the third derivative of 1/90*o**5 + 0*o**3 + 0 + 1/360*o**6 + 0*o**4 - 5*o**2 + 0*o. Solve w(h) = 0 for h.
-2, 0
Let i(l) be the third derivative of 0*l + 0 + 1/240*l**6 + 1/120*l**5 + 2*l**2 - 1/24*l**4 + 0*l**3. Find h, given that i(h) = 0.
-2, 0, 1
Let p be ((12/(-2))/2)/((-33)/22). Let w(m) be the first derivative of 0*m - 1/3*m**3 + 3 + 1/2*m**p. Solve w(y) = 0.
0, 1
Suppose -y**5 + 11*y**4 - 3*y**2 + 2*y - 4*y**4 + y**3 - 2*y**3 - 4*y**4 = 0. Calculate y.
-1, 0, 1, 2
Let y(b) be the first derivative of b**7/630 - b**6/360 - b**5