*v + 1)*(3*v - 1)/4
Let n(u) be the first derivative of 0*u**2 + 1/6*u**4 + 3 + 3*u + 1/3*u**3. Let c(f) be the first derivative of n(f). Factor c(i).
2*i*(i + 1)
Determine u so that -33*u**2 - 105*u + 3*u**2 - 30*u**2 - 5*u**3 - 27 - 23 = 0.
-10, -1
Let v(p) = p**2 + 3*p. Let m be v(-3). Suppose g - 12 = 4*g, -3*w + 7 = 2*g. Factor m*o**4 - o**4 + o**3 + 4*o**2 - 3*o**2 - o**w.
-o**2*(o - 1)*(o + 1)**2
Let f(n) be the second derivative of -n**8/10080 + n**7/3780 + n**6/1080 - n**5/180 - n**4/12 + 2*n. Let j(o) be the third derivative of f(o). Factor j(m).
-2*(m - 1)**2*(m + 1)/3
Let j(n) be the third derivative of -n**11/1330560 - n**10/302400 + n**5/15 - n**2. Let t(p) be the third derivative of j(p). Suppose t(y) = 0. Calculate y.
-2, 0
Let b(v) be the second derivative of -2*v + 3/4*v**4 + 3/20*v**5 + 0 + v**3 + 0*v**2. Determine o, given that b(o) = 0.
-2, -1, 0
Suppose -2/5*w - 1/10*w**3 - 2/5*w**2 + 0 = 0. Calculate w.
-2, 0
Let w = -292 + 295. Factor -2/9*o**4 + 2/9*o**w - 2/9*o**5 + 0*o + 2/9*o**2 + 0.
-2*o**2*(o - 1)*(o + 1)**2/9
Let c(p) be the second derivative of p**4/6 - 2*p**3 + 9*p**2 - 27*p. Let c(q) = 0. What is q?
3
Let x be -3*((-10)/75 - 0). Suppose 5*a - 6 = 3*a, 0 = 3*c - 4*a + 12. Factor 2/5*b**2 + c*b - x.
2*(b - 1)*(b + 1)/5
Let p(l) = -l**2 - 11*l. Let w(n) = n**2 + n. Let h(z) = -p(z) - 3*w(z). Factor h(i).
-2*i*(i - 4)
Let p(w) be the first derivative of -w**4/8 + w**3/3 - w**2/4 + 7. Suppose p(n) = 0. Calculate n.
0, 1
Let g(d) be the third derivative of d**6/420 + d**5/14 + 25*d**4/28 + 125*d**3/21 + d**2 - 4. Factor g(c).
2*(c + 5)**3/7
Let f(u) be the third derivative of -1/273*u**7 - 1/60*u**6 - 4*u**2 + 1/156*u**4 + 2/39*u**3 - 3/130*u**5 + 0 + 0*u. Find t, given that f(t) = 0.
-1, 2/5
Suppose -3*t = -t - 18. Suppose 0 = 3*q + 3 - t. What is b in 8/9*b - 2/9*b**q - 8/9 = 0?
2
What is x in -45/4*x + 21/4*x**2 + 27/4 - 3/4*x**3 = 0?
1, 3
Suppose -n = 2*v + 2*n - 4, -4*n = 4*v - 8. Factor 2/3*u**v + 4/3*u + 2/3.
2*(u + 1)**2/3
Let q(x) be the first derivative of x**5 + 5*x**4/2 + 5*x**3/3 + 38. Factor q(j).
5*j**2*(j + 1)**2
Suppose -7*r + 5*r = -4. What is w in 2*w**5 - w + 12*w**3 + 8*w**4 + 3*w + 11*w**r - 3*w**2 = 0?
-1, 0
Let w(q) = 13*q**2 - 10*q - 7. Let y(a) = 25*a**2 - 20*a - 15. Let p(v) = -5*w(v) + 2*y(v). Factor p(c).
-5*(c - 1)*(3*c + 1)
Find r, given that 15 + 95*r**2 + 29*r**3 + 79*r - 14*r + 12*r**4 - 2*r**4 + 26*r**3 = 0.
-3, -1, -1/2
Let z(f) be the third derivative of -f**6/24 - f**5/4 - 5*f**4/12 - 4*f**2. What is i in z(i) = 0?
-2, -1, 0
Let c(a) = -a + 1. Let s(m) = -m**2 + 2*m - 3. Let o(h) = -h**3 + 5*h**2 + 4*h + 6. Let z be o(6). Let d(l) = z*c(l) - 2*s(l). Find y such that d(y) = 0.
-1, 0
Let h be (-105)/(-28) + (-2)/(-8). Let t = h + -2. Solve 0*y + 0 - 1/4*y**t = 0 for y.
0
Let b(j) be the first derivative of j**4/4 + 4*j**3/3 + 2*j**2 - 14. Solve b(t) = 0 for t.
-2, 0
Let s(j) be the second derivative of -j**6/10 - 9*j**5/10 - j**4 + 3*j**3 + 15*j**2/2 - 28*j. Suppose s(l) = 0. Calculate l.
-5, -1, 1
Let k(f) be the second derivative of 0*f**3 - 1/30*f**5 + 0 + f + 1/12*f**4 - 1/2*f**2. Let h(a) be the first derivative of k(a). Factor h(b).
-2*b*(b - 1)
Let j(p) be the first derivative of 1/8*p**4 + 0*p**2 + 0*p - 1/12*p**3 + 2 - 1/20*p**5. Factor j(a).
-a**2*(a - 1)**2/4
Let s(x) = x**3 + 9*x**2 + x + 11. Let j be s(-9). Factor -j*h - h + 6*h**2 - 3*h**2.
3*h*(h - 1)
Let j(t) = 2*t**2 - 19*t + 11. Let g be j(9). Factor 2/3*d**g + 2/3 - 4/3*d.
2*(d - 1)**2/3
Let g = -1/211 + 3803/1055. Determine i, given that 24/5*i**2 - g*i - 2*i**3 + 4/5 = 0.
2/5, 1
Let b(w) = -w**2 + 4*w - 18. Let t(f) = f + 1. Let m(g) = b(g) + 6*t(g). Let o be m(8). Factor -o*q**4 + 2*q**5 + 2*q**4 - 2*q**2 + 4*q**4 - 2*q**3.
2*q**2*(q - 1)*(q + 1)**2
Let l(q) be the second derivative of -7*q**4/102 - 10*q**3/17 - 8*q**2/17 - 22*q. Factor l(z).
-2*(z + 4)*(7*z + 2)/17
Let u(l) be the second derivative of 0*l**2 + 1/6*l**4 - 1/10*l**5 + l + 0 + 0*l**3. Factor u(n).
-2*n**2*(n - 1)
Let w(k) be the third derivative of -k**8/8400 - k**7/1400 - k**6/900 + k**3/2 - 3*k**2. Let p(o) be the first derivative of w(o). Solve p(u) = 0 for u.
-2, -1, 0
Let h(i) = i**2 - 41*i - 5. Let a(s) = 2*s**2 - 42*s - 6. Let o(t) = 5*a(t) - 6*h(t). Determine v, given that o(v) = 0.
-9, 0
Let b(q) be the second derivative of q**6/60 + q**5/15 - q**4/12 - 2*q**3/3 - q**2/2 - 3*q. Let h(o) be the first derivative of b(o). Factor h(k).
2*(k - 1)*(k + 1)*(k + 2)
Let k(b) be the second derivative of -2*b**7/105 + 2*b**5/15 - 2*b**3/3 - 2*b**2 + 6*b. Let y(z) be the first derivative of k(z). Factor y(s).
-4*(s - 1)**2*(s + 1)**2
Factor 10/11*q**4 + 0 + 0*q + 0*q**2 + 4/11*q**3.
2*q**3*(5*q + 2)/11
Let o(l) be the third derivative of l**5/30 - 2*l**2. Factor o(j).
2*j**2
Let -6*f**2 + 24 - 3*f**3 + 0*f + 11*f - 5*f + 6*f = 0. Calculate f.
-2, 2
Let f(d) = d**2 - 18*d - 81. Let j(o) = -4*o**2 + 54*o + 243. Let h(c) = 7*f(c) + 2*j(c). Let h(y) = 0. Calculate y.
-9
Let c be (1 + 1 - 3) + 13. Let i(n) = c*n + 0 - 1 - 11*n. Let m(v) = v**2 - 10*v + 10. Let k(r) = -6*i(r) - m(r). Let k(b) = 0. What is b?
2
Determine a so that 9*a**4 - 19*a**4 + 20*a + 5*a**4 - 15*a**3 + 10*a**4 = 0.
-1, 0, 2
Let n(p) = p**2 - 19*p - 17. Let k be n(20). Let b = 62/3 - 428/21. Suppose 0 - 4/7*z**k + b*z**2 + 2/7*z**4 + 0*z = 0. What is z?
0, 1
Suppose 4/13*o**2 + 0*o + 0 - 14/13*o**3 = 0. What is o?
0, 2/7
Let c(d) = -24*d**2 - 68*d - 20. Let k(h) = -71*h**2 - 204*h - 61. Let u(f) = 11*c(f) - 4*k(f). Factor u(l).
4*(l + 3)*(5*l + 2)
Let -12/5*s**5 - 21/5*s**2 + 0 - 3/5*s - 9*s**3 - 39/5*s**4 = 0. What is s?
-1, -1/4, 0
Let z(k) be the first derivative of -4*k**2 + 0*k + 2 + 11/2*k**4 - 7/3*k**6 - 8*k**3 + 24/5*k**5. Let z(x) = 0. What is x?
-1, -2/7, 0, 1, 2
Let n = -283 + 529/2. Let r = n + 19. Let 1/4*a**2 - r + 1/4*a = 0. Calculate a.
-2, 1
Let y(u) be the third derivative of u**9/45360 + u**8/10080 + u**7/7560 - u**4/8 + 4*u**2. Let x(z) be the second derivative of y(z). Let x(c) = 0. What is c?
-1, 0
Let a(w) be the first derivative of 1/3*w**6 + 0*w**4 - 3 - 4/5*w**5 + 0*w + 4/3*w**3 - w**2. Factor a(n).
2*n*(n - 1)**3*(n + 1)
Let w = -1880/7 - -269. Find j such that w*j**2 + 3/7*j**3 - 3/7*j**5 + 0*j + 0 - 3/7*j**4 = 0.
-1, 0, 1
Let p be ((-6)/20)/((-36)/96). Factor 2/5*v**2 + 2/5 + p*v.
2*(v + 1)**2/5
Let x be 4/24 + (-29)/(-6). Suppose 4*b = -x*a + 3*b + 15, a + 3 = b. Factor 0*t - 1/2*t**a + 1/2.
-(t - 1)*(t + 1)/2
Let z(f) = -9*f**2 - 2*f - 100 + 103 + f**3 - 2*f**3. Let h(t) = 6*t + 15*t**2 + 2*t**3 - 10 + 6*t**2 + 7*t**2. Let y(v) = 3*h(v) + 10*z(v). Factor y(x).
-2*x*(x + 1)*(2*x + 1)
Determine w so that 3*w**3 + 13 - 13 + 9*w**2 = 0.
-3, 0
Let a be -2*8/12*18/(-8). Let d(w) be the third derivative of -1/105*w**7 + 0*w**4 + 0*w - 1/3*w**a - 2*w**2 + 0 + 1/15*w**5 + 0*w**6. Factor d(g).
-2*(g - 1)**2*(g + 1)**2
Let n(k) = 25*k**5 + 5*k**4 + 20*k**2 - 20*k + 20. Let m(w) = -w**5 - w**2 + w - 1. Let c(q) = -20*m(q) - n(q). Factor c(i).
-5*i**4*(i + 1)
Let z(w) be the second derivative of 0 - w + 0*w**3 + 0*w**2 - 3/10*w**5 - 1/15*w**6 - 1/3*w**4. What is u in z(u) = 0?
-2, -1, 0
Suppose -p = p - 92. Let q = p + -137/3. Find n such that -q*n**2 + 2/3*n - 1/3 = 0.
1
Let l(n) be the second derivative of -1/9*n**2 - 7/54*n**4 + 4*n + 0 - 5/27*n**3 - 1/30*n**5. Find x, given that l(x) = 0.
-1, -1/3
Let p(c) be the second derivative of -c**7/126 + c**5/30 - c**3/18 + 2*c. Find w such that p(w) = 0.
-1, 0, 1
Suppose 0 = 6*g - g - 10. Let -g*t**3 + 4*t**4 + 2*t**3 + 0*t**3 - 4*t**2 = 0. Calculate t.
-1, 0, 1
Let n(d) be the second derivative of 1/90*d**6 - 4*d + 0 - 1/12*d**4 - 1/3*d**2 - 5/18*d**3 + 1/60*d**5. Factor n(w).
(w - 2)*(w + 1)**3/3
Let p(o) be the first derivative of o**8/420 - o**7/105 - o**6/90 + o**5/15 + 3*o**3 - 4. Let g(s) be the third derivative of p(s). Factor g(l).
4*l*(l - 2)*(l - 1)*(l + 1)
Let z(q) be the second derivative of -q**6/45 - 2*q**5/35 - q**4/42 + 2*q**3/63 + 12*q. Factor z(m).
-2*m*(m + 1)**2*(7*m - 2)/21
Let v(t) be the third derivative of 0*t + 2*t**2 - 1/30*t**5 + 0 + 1/6*t**3 + 1/24*t**4. Find g such that v(g) = 0.
-1/2, 1
Let g(y) = -9*y. Let t(x) be the first derivative of x**3/3 - 5*x**2 - 2. Let q(p) = -4*g(p) + 3*t