Let w(f) be the first derivative of -4*f**3/3 + 2*f**2 + 32. Solve w(h) = 0 for h.
0, 1
Let t = 4 + 0. Factor 4*g**3 - 7*g**3 + g**3 - 2*g**t.
-2*g**3*(g + 1)
Let v(g) be the first derivative of g**7/1260 - g**5/180 + 3*g**3 - 1. Let u(f) be the third derivative of v(f). Solve u(s) = 0.
-1, 0, 1
Suppose 0*n = -3*n + 12. Let z(q) be the first derivative of -3*q**2 + 1 + 2*q**2 + q**n - 2*q**4 + 2*q**3. Determine t, given that z(t) = 0.
0, 1/2, 1
Suppose t - 10 = i, 0*t = 5*t - i - 54. Let x = 14 - t. What is b in 1/2*b**2 - 1/2*b + 1/2*b**x - 1/2 = 0?
-1, 1
Let x(v) be the second derivative of v**5/80 - v**4/24 - v**3/24 + v**2/4 - 8*v. Determine w, given that x(w) = 0.
-1, 1, 2
Solve 4*h**2 - h**2 - 2*h**2 + h**2 = 0 for h.
0
Find n, given that 2*n - 25*n**3 + 21*n**3 + 2*n = 0.
-1, 0, 1
Suppose -4*y + 5 + 26 = -3*x, -5*y = 5*x + 75. Let z = x - -38. Determine m, given that -8*m**3 + m**5 - 6*m**2 - z*m**3 - 48*m**4 - 22*m**5 = 0.
-1, -2/7, 0
Let l(v) be the third derivative of v**6/540 - v**5/270 + 7*v**2. Determine d, given that l(d) = 0.
0, 1
Suppose 2*w - 4*w - 15 = -5*q, q - 3 = -4*w. What is c in -3 - c**2 + 7*c - 3*c - 4 + q = 0?
2
Suppose 3*p + 12 = 3*i, -4*i - 12*p = -13*p - 4. Factor 1/2*a**2 + i + 1/2*a - 1/2*a**3 - 1/2*a**4.
-a*(a - 1)*(a + 1)**2/2
Let n(m) be the second derivative of m**9/4536 - m**7/630 + m**5/180 - m**3/2 + 2*m. Let y(k) be the second derivative of n(k). Let y(r) = 0. What is r?
-1, 0, 1
Let c be 2/32*28 - 9/(-36). Factor -2/3*l**c - 8/3*l - 8/3.
-2*(l + 2)**2/3
Let i(y) = 72*y**2 - 33*y. Let g(d) = 71*d**2 - 34*d - 1. Let a(o) = -3*g(o) + 4*i(o). Factor a(z).
3*(5*z - 1)**2
Let w(t) be the second derivative of -3/55*t**6 - 1/3*t**4 + 8/33*t**3 + 2*t + 0 + 12/55*t**5 - 1/11*t**2. Factor w(n).
-2*(n - 1)**2*(3*n - 1)**2/11
Let m(a) be the third derivative of -a**6/360 + a**5/60 - 2*a**3/9 - 15*a**2. Factor m(z).
-(z - 2)**2*(z + 1)/3
Let i(u) = 2*u**3 - 18*u**2 - 34*u - 14. Let o(w) = w**3 - 17*w**2 - 33*w - 15. Let z(c) = 3*i(c) - 4*o(c). Factor z(f).
2*(f + 1)*(f + 3)**2
Factor -7/2*k + 5/2*k**2 - 1/2*k**3 + 3/2.
-(k - 3)*(k - 1)**2/2
Solve -m - 1/2*m**2 + 1/2*m**3 + 0 = 0.
-1, 0, 2
Let y(m) = -m**2 - m - 1. Let n(r) be the third derivative of -r**5/30 - r**4/12 - 2*r**3/3 - r**2. Let z(b) = -3*n(b) + 8*y(b). Factor z(l).
-2*(l - 1)*(l + 2)
Let i be 2/7 + -938 + -1. Let q = -937 - i. Factor 18/7*c**4 + 4/7*c**5 + 32/7*c**3 + q*c + 2/7 + 4*c**2.
2*(c + 1)**4*(2*c + 1)/7
Let i(j) be the first derivative of -j**7/630 - j**6/360 + j**2/2 - 5. Let s(v) be the second derivative of i(v). Factor s(l).
-l**3*(l + 1)/3
Factor -1/4*d**4 - 1/4*d**3 + 3/4*d**2 + 1/2 + 5/4*d.
-(d - 2)*(d + 1)**3/4
Suppose p - s - 3 = 0, 5*p + s - 1 + 16 = 0. Let h be 39/54 - p/(-9). Find j, given that 0*j**4 + 1/4*j + 1/4*j**5 + 0*j**2 + 0 - h*j**3 = 0.
-1, 0, 1
Let n be (4/2)/((-8)/(-12)). Let q be 0/(-3 + 6/n). Factor k**2 + k**4 + q*k**2 - 2*k**4.
-k**2*(k - 1)*(k + 1)
Let t(v) be the third derivative of -2*v**2 + 0*v**5 + 0 + 0*v**3 + 1/60*v**6 - 1/12*v**4 + 0*v. Let t(g) = 0. Calculate g.
-1, 0, 1
Let z = 0 + 2. Factor 2*y + 2*y**5 - 3*y + z*y**4 + y.
2*y**4*(y + 1)
Suppose -4 = 3*t - 8*k + 3*k, 0 = 4*t + 3*k - 14. Factor -3 + t*a**2 + 4 - 1.
2*a**2
Let d = -38 + 685/18. Let c(p) be the first derivative of -2/9*p**3 + 1/5*p**5 - d*p**6 - 1/3*p - 1 - 1/6*p**4 + 1/2*p**2. Factor c(o).
-(o - 1)**4*(o + 1)/3
Let a be (28/(-378))/(1/(-6)). Let l(f) be the first derivative of -1 + 2/3*f + 7/6*f**2 - a*f**3. Determine x so that l(x) = 0.
-1/4, 2
Suppose -4*y = -2*w - 4, y + 2 = 2*w - y. Let g(k) be the first derivative of -2/21*k**3 + 0*k + 0*k**2 - 2 - 1/14*k**w. Factor g(t).
-2*t**2*(t + 1)/7
Factor 0 + 1/5*b**2 + 1/5*b**3 - 1/5*b**4 - 1/5*b.
-b*(b - 1)**2*(b + 1)/5
Let a(z) be the first derivative of z**3/30 + z**2/5 + 2*z/5 + 26. Let a(m) = 0. What is m?
-2
Suppose -3*b + 3*l + 33 = 0, -b + 4*l + 53 = 4*b. Factor -9*n**2 + b*n - 4*n**3 - 11*n - 3*n**3.
-n*(n + 1)*(7*n + 2)
Let z(h) be the first derivative of 8*h**6 + 24*h**5 - 69*h**4/4 - 61*h**3 + 48*h**2 - 12*h + 1. Solve z(p) = 0 for p.
-2, 1/4, 1
Let u(a) be the second derivative of a**8/560 + a**7/420 - a**6/120 - a**5/60 - a**3/6 + 2*a. Let d(h) be the second derivative of u(h). Factor d(g).
g*(g - 1)*(g + 1)*(3*g + 2)
Let x(p) be the second derivative of 1/12*p**4 - 3*p + 0 + 3/20*p**5 - 1/28*p**7 - 1/4*p**2 - 1/60*p**6 - 1/4*p**3. Find n such that x(n) = 0.
-1, -1/3, 1
Let l(s) be the first derivative of 7*s**4/6 - 16*s**3/3 + 4*s**2 - 2*s - 2. Let f(q) be the first derivative of l(q). Determine z, given that f(z) = 0.
2/7, 2
Let y be (-10)/(-4)*40/50. Factor 12*k**y - k + 4*k**3 + 4 - 3*k + 4*k + 12*k.
4*(k + 1)**3
Let d(q) be the second derivative of -1/72*q**4 + 1/12*q**2 + 1/120*q**5 - 1/36*q**3 + 0 - 7*q. Factor d(o).
(o - 1)**2*(o + 1)/6
Let n = 53/5 - 9. Factor 2/5*y**4 + 2*y**3 - n - 16/5*y - 2/5*y**5 - 2/5*y**2.
-2*(y - 2)**2*(y + 1)**3/5
Suppose 5*v - 18 = 2*d - 0*d, 20 = 2*v - 4*d. Solve n**3 - v + 0 + 3*n**3 + 4*n**2 + 0*n**4 - 2*n**4 - 2*n**5 - 2*n = 0.
-1, 1
Factor 4/5*f**2 - 2/5*f**3 + 14/5*f + 8/5.
-2*(f - 4)*(f + 1)**2/5
Let b(g) = 12*g**3 - 21*g**2 + 9*g. Let a = -5 + 14. Let x(j) = -3*j**3 + 5*j**2 - 2*j. Let p(r) = a*x(r) + 2*b(r). Find h such that p(h) = 0.
0, 1
Let n be 32/160 + (-1)/((-15)/2). Let g(k) be the first derivative of -3 + k - n*k**3 + 0*k**2. Factor g(o).
-(o - 1)*(o + 1)
Let q(f) = -2*f - 1 - f + 5*f - 3*f. Let k(b) = b**2 + 15*b + 23. Let v(x) = -3*k(x) - 21*q(x). Factor v(w).
-3*(w + 4)**2
Let v be (-72)/(-315)*(12 + -4 + 2). Suppose -1/7*t**5 - 9/7*t + 2/7 + v*t**2 - 2*t**3 + 6/7*t**4 = 0. What is t?
1, 2
Let h(l) be the first derivative of -2/3*l**3 + 7*l**2 - 4*l + 6/5*l**5 - 7/2*l**4 - 4. Find u, given that h(u) = 0.
-1, 1/3, 1, 2
Factor 6/13*r**3 + 8/13 + 0*r - 14/13*r**2.
2*(r - 2)*(r - 1)*(3*r + 2)/13
Suppose -4*t + z + 15 = 0, -t - 4*z = -2*t. Solve -1 + 1/2*b**3 - 5/2*b - 3/2*b**2 + 1/2*b**t = 0.
-1, 2
Let c(u) be the second derivative of 0 - 1/90*u**6 - 6*u + 0*u**4 - 1/126*u**7 + 0*u**2 + 0*u**3 + 0*u**5. Suppose c(t) = 0. What is t?
-1, 0
Let n be 1/(-2) + 5/2. Suppose -p = u, -2*u + 0*u = -p + 6. Let p*i**n - i**2 + i**2 = 0. Calculate i.
0
Let h(b) be the first derivative of -b**9/1008 + b**7/280 - b**3/3 + 1. Let f(i) be the third derivative of h(i). Factor f(n).
-3*n**3*(n - 1)*(n + 1)
Let a be 3/(4*1/4). Factor a*p**2 + 2 - 12*p + 5 + 2.
3*(p - 3)*(p - 1)
Let a(w) be the first derivative of 8*w**4/7 + 16*w**3/21 + w**2/7 - 19. Find v such that a(v) = 0.
-1/4, 0
Let z(q) be the first derivative of -q**5/45 - q**4/9 - 5*q**3/27 - q**2/9 - 8. Determine d so that z(d) = 0.
-2, -1, 0
Let h(w) = -w**2 + 9*w + 4. Let q be h(9). Suppose 0 = -3*d - 5*s - 11, 5*d + 4*s = -4 + 3. Let 8*l**3 + 7*l + 14*l**2 - 8*l**q - 6*l + d*l = 0. Calculate l.
-1/2, 0, 2
Determine b, given that 0 + 2/5*b**2 + 0*b - 2/5*b**3 = 0.
0, 1
Let o(t) = t**4 - t**3 + t**2 + 1. Let l(r) = 7*r**4 - 5*r**3 + 4*r**2 + 6. Let y(b) = -l(b) + 6*o(b). Factor y(k).
-k**2*(k - 1)*(k + 2)
Factor -8*b**2 + 0*b**4 + 2/5*b**5 - 4*b**3 - 6*b - 8/5.
2*(b - 4)*(b + 1)**4/5
Let r = -43 - -87/2. Solve r*l + 1/2 - 1/2*l**3 - 1/2*l**2 = 0.
-1, 1
Suppose 41*g - 37 = 45. Factor -7/2*b + 8*b**3 - 1/2 - 4*b**g.
(b - 1)*(4*b + 1)**2/2
Suppose 0 = z - 3*s - 7, 2*z - 2*s - 4 = 6. Let x be z/16 + (-4)/(-16). Find p such that 1/2*p + 0 + x*p**2 = 0.
-1, 0
Let b(d) = -6*d**2 + 2. Let w(h) = -h**3 - h**2 - h + 1. Let j(t) = -2*b(t) + 4*w(t). Factor j(x).
-4*x*(x - 1)**2
Let g(z) be the first derivative of z**7/63 + z**6/45 - z**5/30 - z**4/18 + 4*z - 5. Let i(m) be the first derivative of g(m). Factor i(v).
2*v**2*(v - 1)*(v + 1)**2/3
Let t be ((-6)/8)/(8/(-32)). Let u be ((-3)/(-42))/(t/24). What is b in -u*b + 4/7*b**2 - 2/7 - 4/7*b**5 - 2/7*b**4 + 8/7*b**3 = 0?
-1, -1/2, 1
Factor 14*n**3 + 18*n**2 - 5*n**4 + 2*n**2 - 14*n**3.
-5*n**2*(n - 2)*(n + 2)
Let d(x) = -x**3 - 2*x. Let p(l) = -2*l. Let m(b) = -4*d(b) + 6*p(b). Factor m(y).
4*y*(y - 1)*(y + 1)
Let y(q) be the first derivative of -3*q - 3/2*q**4 + 9/2*q**2 - 2*q**3 - 1/2*q**6 + 9/5*q**5 - 7. Factor y(b).
-3*(b - 1)**4*(b + 1)
Let i(r) = -r**3 + 4*r**2 + 3. Let f(y) = y**3 - 4*y**2 - y - 3. Let q(z) = -4*f(z) - 5*i(z). Let n be q(3