
Suppose 2*i + 26 = 2*d, i + 4*d = 3*d - 3. Let u be 6/i*12/(-18). Factor 0 - 1/2*b + u*b**2 + 1/2*b**3 - 1/2*b**4.
-b*(b - 1)**2*(b + 1)/2
Let z(k) be the second derivative of -k**6/105 - k**5/70 + k**4/42 + k**3/21 + 6*k. Factor z(x).
-2*x*(x - 1)*(x + 1)**2/7
Suppose -2*w + 20 + 6 = -4*s, -2*w + 30 = -5*s. Let t(k) be the third derivative of 1/60*k**w + 1/40*k**6 + 0*k - k**2 + 0*k**4 + 0*k**3 + 0. Factor t(g).
g**2*(3*g + 1)
Let j be 4/(-2) + 2 - -4. Let b = j - 2. Factor 2/7*l**3 + 2/7*l**4 + 0 + 0*l + 0*l**b.
2*l**3*(l + 1)/7
Suppose -12*x = -7*x - 10. Solve -17*b**4 - 4 + 3*b**3 - 15*b**4 - b**3 - x*b + 46*b**2 - 10*b**4 = 0.
-1, -2/7, 1/3, 1
Let j(k) be the second derivative of k**4/48 - k**3/6 - 5*k**2/8 + 2*k. What is y in j(y) = 0?
-1, 5
Let y(z) = 24*z**2 + 4. Let b(u) = -47*u**2 + u - 7. Let k(v) = -4*b(v) - 7*y(v). Factor k(p).
4*p*(5*p - 1)
Let t = -4 + 4. Let m(a) = -a**3 - 5*a**2 - 6*a - 5. Let h be m(-4). Determine j, given that t + 8/3*j**h + 7/3*j**2 + 2/3*j + j**4 = 0.
-1, -2/3, 0
Let j(p) be the first derivative of -2*p**3/9 + 2*p**2/3 - 7. Factor j(u).
-2*u*(u - 2)/3
Let h(t) be the second derivative of 1/30*t**3 - 1/5*t**2 + 1/60*t**4 + 0 - t. Let h(n) = 0. Calculate n.
-2, 1
Let n(t) = t**3 - 2*t - 1. Let w be n(2). Let x = 9 + -6. Factor g**3 - g - x*g + w*g - g**2 + 1.
(g - 1)**2*(g + 1)
Let a(d) be the third derivative of 0*d**4 + 0 - 3*d**2 + 0*d - 1/21*d**3 + 1/210*d**5. Factor a(b).
2*(b - 1)*(b + 1)/7
Let u(l) be the first derivative of l**7/1260 - l**6/720 - l**5/360 + l**4/144 + l**2 - 1. Let o(m) be the second derivative of u(m). Factor o(z).
z*(z - 1)**2*(z + 1)/6
Let l(s) be the first derivative of -s**6/105 + s**5/70 + s**4/42 - s**3/21 + 9*s - 1. Let g(n) be the first derivative of l(n). Find u, given that g(u) = 0.
-1, 0, 1
Let u be 1 + -6 + (-621)/(-115). Let k be ((-24)/(-20))/((-6)/(-20)). Factor 0*q**2 + 0*q + 0*q**k - u*q**3 + 0 + 2/5*q**5.
2*q**3*(q - 1)*(q + 1)/5
Let h(g) be the first derivative of -2*g**3/33 + 6*g**2/11 - 18*g/11 - 30. Factor h(v).
-2*(v - 3)**2/11
Let w = -1 + -3. Let t(k) = 7*k**2. Let n(j) = 36*j**2. Let l(h) = w*n(h) + 21*t(h). Factor l(y).
3*y**2
Let o(y) be the third derivative of y**9/20160 - y**8/1680 + y**7/336 - y**6/120 - 7*y**5/60 - 6*y**2. Let h(q) be the third derivative of o(q). Factor h(j).
3*(j - 2)*(j - 1)**2
Let j be 15/60 - (-2)/(-8). Let f(u) be the second derivative of 1/168*u**7 + j*u**2 - 1/120*u**6 + 0 - 1/80*u**5 + 1/48*u**4 - u + 0*u**3. Solve f(b) = 0.
-1, 0, 1
Let y(z) be the third derivative of -z**8/2016 - z**7/252 - z**6/72 - z**5/36 - 5*z**4/144 - z**3/36 + 3*z**2. Find r such that y(r) = 0.
-1
Let s(w) be the third derivative of 2*w**2 + 0*w + 0 + 0*w**5 + 1/8*w**4 + 0*w**3 - 1/40*w**6. Factor s(g).
-3*g*(g - 1)*(g + 1)
Let d(l) be the second derivative of l**5/5 + 4*l**4/3 + 2*l**3 + 7*l. Factor d(a).
4*a*(a + 1)*(a + 3)
Suppose -9*d = -5*d. Let m(t) be the third derivative of d - 2*t**2 + 2/3*t**3 + 0*t - 1/6*t**4 + 1/60*t**5. Let m(j) = 0. Calculate j.
2
Let g(d) be the third derivative of -d**6/420 + 2*d**5/105 - 5*d**4/84 + 2*d**3/21 + 37*d**2. Factor g(k).
-2*(k - 2)*(k - 1)**2/7
Let j = 1235/4 + -307. Suppose -82*b + 48 = -66*b. Solve j*u**b + 1/4*u + 0 + 3/4*u**4 + 5/4*u**2 = 0.
-1, -1/3, 0
Factor 343/5*f**5 - 664/5*f**2 - 176/5*f - 16/5 - 49/5*f**4 - 896/5*f**3.
(f - 2)*(f + 1)*(7*f + 2)**3/5
Let v(g) = -145*g**5 + 84*g**4 + 135*g**3 - 84*g**2 + 12*g. Let k(s) = -s**5. Let w(r) = 2*k(r) + v(r). Let w(i) = 0. What is i?
-1, 0, 2/7, 1
Let q(l) be the third derivative of 0 - 1/450*l**5 - 3*l**2 - 1/1575*l**7 + 0*l - 1/450*l**6 + 0*l**4 + 0*l**3. Find x, given that q(x) = 0.
-1, 0
Let g = -407 - -3679/9. Solve g + 4/3*z**2 - 8/3*z - 2/9*z**3 = 0.
2
Suppose 3*w = 5*u + 32, -11 = 4*w - 2*u - 35. Let -4/3*j**3 - 1/6*j + 0 - 5/6*j**2 - 2/3*j**w = 0. Calculate j.
-1, -1/2, 0
Let r = 4/397 - -694/9925. Let f(l) be the first derivative of -2 + 0*l**2 + 1/10*l**4 - r*l**5 + 0*l + 0*l**3. Find o, given that f(o) = 0.
0, 1
Find p such that 5*p - 2*p**2 + 5*p**2 + 2*p**2 = 0.
-1, 0
Let y(h) be the third derivative of 0*h + 1/420*h**6 + 0*h**4 + 0 + 2*h**2 - 1/105*h**5 + 0*h**3. Solve y(c) = 0 for c.
0, 2
Let s(q) = q**2 + q + 2. Let b(z) = -1. Let n(c) = -2*b(c) - s(c). Let f(t) = -4*t**2 - 4*t - 2. Let g(i) = f(i) - 5*n(i). Factor g(v).
(v - 1)*(v + 2)
Let x(r) be the first derivative of -r**6/36 - r**5/15 - r**4/15 - r**3/3 - 2. Let u(d) be the third derivative of x(d). Find k such that u(k) = 0.
-2/5
Let w(c) be the first derivative of -17*c + 17*c - 7 - c**3. Factor w(u).
-3*u**2
Let f = 440/9 + -871/18. Suppose -1/2*b**2 + f*b**3 + 0 + 0*b = 0. What is b?
0, 1
Let x(r) be the first derivative of -3 - r - 1/3*r**3 - r**2. Factor x(t).
-(t + 1)**2
What is l in 3*l - l**3 - 3*l**2 - 2*l**3 - 2*l**4 + 7*l**4 - 2*l**4 = 0?
-1, 0, 1
Let t(q) be the first derivative of -3 + 1/14*q**4 + 0*q**2 + 0*q**3 + 0*q. Let t(d) = 0. What is d?
0
Let q be (-2)/7 + (-540)/70. Let v(g) = -g - 8. Let f be v(q). Let f - 4*x**3 - 2*x**4 - 1/3*x**5 - 8/3*x**2 + 0*x = 0. What is x?
-2, 0
Let j(f) be the first derivative of 49*f**6/27 - 56*f**5/45 - 5*f**4/2 + 56*f**3/27 - 4*f**2/9 + 14. Let j(s) = 0. Calculate s.
-1, 0, 2/7, 1
Let f(v) be the second derivative of -v**6/10 - 9*v**5/10 - 2*v**4 + 3*v**3 + 27*v**2/2 + 62*v. Factor f(p).
-3*(p - 1)*(p + 1)*(p + 3)**2
Let w(l) be the first derivative of -l**6/24 + l**5/20 + l**4/16 - l**3/12 + 10. Suppose w(d) = 0. What is d?
-1, 0, 1
Let t(b) be the first derivative of 0*b**5 + 1/16*b**4 + 0*b - 1/24*b**6 - 2 + 0*b**2 + 0*b**3. Factor t(r).
-r**3*(r - 1)*(r + 1)/4
Let n(t) be the second derivative of 2*t**6/15 - 4*t. Determine z so that n(z) = 0.
0
Let k(z) be the first derivative of -2*z**6 + 38*z**5/5 - 7*z**4 - 2*z**3/3 + 2*z**2 + 33. Solve k(w) = 0 for w.
-1/3, 0, 1/2, 1, 2
Let z(h) be the first derivative of -3/2*h**4 + 3*h + 3/2*h**2 + 2 + 1/2*h**6 + 3/5*h**5 - 2*h**3. Determine u, given that z(u) = 0.
-1, 1
Suppose 0 = o - 0*o - 2. Factor 0*w - 1/3*w**o + 0.
-w**2/3
Let 2/9*o - 1/9 - 1/9*o**2 = 0. What is o?
1
Factor -4 - 187*n**4 - 8*n**2 - 28*n + 24*n**3 + 4*n**5 + 207*n**4 - 8.
4*(n - 1)*(n + 1)**3*(n + 3)
Determine h, given that -8*h**2 + 9*h - 6*h + 4*h**3 - 7*h + 2*h**4 + 6 = 0.
-3, -1, 1
Let h(c) be the second derivative of 9*c**5/20 + c**4 - 2*c**3 + 47*c. Suppose h(t) = 0. What is t?
-2, 0, 2/3
Let d = 5 + -2. Let n(p) be the second derivative of -29/60*p**5 + 1/3*p**2 - 2*p + 11/12*p**4 + 0 + 1/10*p**6 - 5/6*p**d. Factor n(c).
(c - 1)**3*(9*c - 2)/3
Let f(v) be the third derivative of v**5/210 - v**4/42 - v**3/7 - 3*v**2. Suppose f(n) = 0. Calculate n.
-1, 3
Let d = 169/57 - -45/19. Determine w, given that -10/3*w + 2/3 - 8/3*w**3 + d*w**2 = 0.
1/2, 1
Let b(z) be the first derivative of -z**8/84 + z**7/15 - 23*z**6/150 + 14*z**5/75 - 2*z**4/15 + z**3 - 3. Let k(d) be the third derivative of b(d). Factor k(n).
-4*(n - 1)**2*(5*n - 2)**2/5
Let s(g) be the first derivative of -g**6/51 - 6*g**5/85 - 3*g**4/34 - 2*g**3/51 + 3. Factor s(i).
-2*i**2*(i + 1)**3/17
Solve 4 + k + 5 - k**3 - k**2 - 8 = 0 for k.
-1, 1
Suppose k + 13 = -4*i, 5*k + 0*i - 23 = 2*i. Determine w so that 4*w**2 + 2*w**2 + k + 2*w - 3 = 0.
-1/3, 0
Let u(t) = t**2 - 8*t + 9. Let p be u(7). Suppose 0 = 5*o + p*k - 14, -4 - 12 = -3*o - 5*k. Let 0 - 2/7*m + 0*m**o + 2/7*m**3 = 0. Calculate m.
-1, 0, 1
Let u = -41 - -42. Let v(d) be the first derivative of -u + 0*d**2 + 0*d - 1/20*d**4 + 1/15*d**3. Let v(c) = 0. What is c?
0, 1
Suppose 0 = -8*r + 5*r + 2*d + 8, 0 = -3*r - 4*d + 20. Suppose -4*p + 26 = 14. Find c such that -c**r + 4*c**3 + c**2 - 5*c**p + 0*c + c = 0.
-1, 0, 1
Let o(n) = -29*n**4 + 61*n**3 - 50*n**2 + 12*n. Let z = -20 + 18. Let g(u) = 146*u**4 - 304*u**3 + 251*u**2 - 60*u. Let w(r) = z*g(r) - 11*o(r). Factor w(c).
3*c*(c - 1)*(3*c - 2)**2
Let c(l) = -l**2 + l + 2. Let r be c(0). Suppose 0 = r*v + v. Factor 1/2*m**2 + v*m + 0.
m**2/2
Let l(a) = -a**3 + a. Let u(h) = h**3 - h**2 - 3*h. Let w = -6 - -3. Let y(n) = w*l(n) - u(n). Factor y(r).
r**2*(2*r + 1)
Let h = -38237/40 - -956. Let a(s) be the third derivative of -h*s**5 + 0*s + 0 + 0*s**3 + 1/24*s**4 + 3*s**2 + 7/240*s**6. Factor a(k).
k*(k - 1)*(7*k - 2)/2
Let b(s) be the fir