3)*(k + 1)/2
Let u(x) be the first derivative of 4*x**6/27 - 2*x**5/3 + 4*x**4/9 + 38*x**3/27 - 4*x**2/3 - 8*x/9 - 7. What is a in u(a) = 0?
-1, -1/4, 1, 2
Determine q so that 5*q**3 - 2*q - 10 - 10 - 3*q - 6*q**2 + 26*q**2 = 0.
-4, -1, 1
Let q = 100 - 2099/21. Let n(u) be the third derivative of 0 - 3*u**2 + 0*u - 1/84*u**4 + 1/210*u**5 + 1/420*u**6 - q*u**3. Factor n(a).
2*(a - 1)*(a + 1)**2/7
Let g(s) = 3*s**2 - s - 4. Let i(b) be the first derivative of b**3/3 - b - 4. Let l = -1 + 8. Let h(v) = l*i(v) - 2*g(v). Solve h(p) = 0.
-1
Let g = -9 + 4. Let u(o) = -3*o**4 + 7*o**3 + 3*o**2 - 2*o - 5. Let l(x) = 2*x**4 - 6*x**3 - 2*x**2 + 2*x + 4. Let s(n) = g*l(n) - 4*u(n). Solve s(t) = 0 for t.
-1, 0, 1
Suppose 0 = -3*s + i + 310, -4 = -4*s + i + 408. Let k be s/90 - (-1)/5. Factor k - 2/3*n - 2/3*n**2.
-2*(n - 1)*(n + 2)/3
Let x(f) = 2*f + 2. Let h be x(-1). Let i(v) be the third derivative of 1/15*v**5 + 1/210*v**7 + 0 + 1/30*v**6 + 0*v + 0*v**4 + h*v**3 - v**2. Factor i(r).
r**2*(r + 2)**2
Let f(r) be the third derivative of r**8/168 - r**6/15 + r**5/15 + r**4/4 - 2*r**3/3 + 6*r**2. Factor f(q).
2*(q - 1)**3*(q + 1)*(q + 2)
Let -1/9*o**2 - 196/9 - 28/9*o = 0. What is o?
-14
Let q = 54 + -49. Let z(a) be the first derivative of -2 - 1/4*a**4 + 13/18*a**3 + 2/3*a - a**2 + 1/30*a**q. Factor z(g).
(g - 2)**2*(g - 1)**2/6
Let x(c) = -c**2 - 4*c + 1. Let f be x(-3). Factor -2*s**5 + 2*s + 6*s**f + 3*s**2 + s**2 - 10*s**4.
-2*s*(s - 1)*(s + 1)**3
Let d = 56 + -223/4. Factor -1/4*z**2 + d*z + 0.
-z*(z - 1)/4
Suppose 3*u - 3*i - 2*i + 40 = 0, -5*u = 5*i + 80. Let d = -15 - u. Factor -2/5*m**2 + 0*m - 2/5*m**3 + d.
-2*m**2*(m + 1)/5
Factor 0 + 2/7*b**5 - 10/7*b**3 - 2/7*b**4 - 6/7*b**2 + 0*b.
2*b**2*(b - 3)*(b + 1)**2/7
Factor 75*y + 8*y**3 + 4*y**3 - y**3 - 6*y**3 - 35*y**2 - 45.
5*(y - 3)**2*(y - 1)
Let t be (8 + -10)*(-5 - -3). What is p in 4/7 - 2/7*p + 68/7*p**3 + 2*p**5 - 32/7*p**2 - 52/7*p**t = 0?
-2/7, 1
Suppose -1/2*o**3 - 3/2*o + 2*o**2 + 0 = 0. Calculate o.
0, 1, 3
Let k = -2 - -4. Suppose 5*u - 14 = -4. Factor 0*b**4 - 2*b**k + b**u + b**4.
b**2*(b - 1)*(b + 1)
Let d be (1 + -1)/(2/(14/21)). Factor 2/9*f + d - 2/9*f**2.
-2*f*(f - 1)/9
Let v(p) be the first derivative of -p**6/480 + 3*p**5/160 - p**4/16 + 4*p**3/3 - 4. Let z(g) be the third derivative of v(g). Factor z(a).
-3*(a - 2)*(a - 1)/4
Let q(n) be the third derivative of 0*n**3 + 1/1848*n**8 + 0 + 4/1155*n**7 + 0*n + 1/132*n**6 + 1/165*n**5 + 5*n**2 + 0*n**4. Determine w, given that q(w) = 0.
-2, -1, 0
Let g(p) be the second derivative of 0 - 2*p**2 - 1/12*p**4 + p - 2/3*p**3. Factor g(s).
-(s + 2)**2
Let y = -5 + 8. Suppose c + y = -4*m - 2, m - 13 = -5*c. Determine n so that 24*n**2 - 18*n**4 + 6*n**3 - 10*n**c + 4*n - 6*n**2 = 0.
-1, -2/9, 0, 1
Let q(j) = -j - 1. Let s = -3 + -2. Let g be q(s). Factor 2*z**g + 2*z**3 - 6*z**4 - 3*z**3.
-z**3*(4*z + 1)
Let p(x) be the third derivative of x**6/120 + x**5/40 - 2*x**3/3 - 2*x**2. Let g(y) be the first derivative of p(y). Solve g(r) = 0 for r.
-1, 0
Let z(f) be the first derivative of f**4/3 + 4*f**3 + 18*f**2 + 36*f + 33. Determine q so that z(q) = 0.
-3
Find p, given that 0 - 3/4*p**3 - 1/4*p**2 + 1/2*p**5 + 1/4*p**4 + 1/4*p = 0.
-1, 0, 1/2, 1
Let u(t) be the second derivative of -t**4/16 - t**3/2 + 14*t + 1. Suppose u(x) = 0. Calculate x.
-4, 0
Suppose -21/2*j**2 + 36*j**3 + 0 + j - 81/2*j**4 = 0. Calculate j.
0, 2/9, 1/3
Let w(p) be the third derivative of p**5/20 - 9*p**4/4 + 81*p**3/2 - 5*p**2. Suppose w(x) = 0. Calculate x.
9
Suppose 5*f - w - 19 = -0*w, 3*w = 3*f - 9. Let o(m) be the second derivative of m + 0*m**2 + 0 - 1/48*m**f + 1/24*m**3. Factor o(i).
-i*(i - 1)/4
Let w(l) be the first derivative of -l**4/4 + 5*l**3/3 + l**2/2 - 2*l - 1. Let a be w(5). Suppose 8/7*b**4 + 2/7*b + 18/7*b**a + 0 + 12/7*b**2 = 0. What is b?
-1, -1/4, 0
Let x(i) be the first derivative of -9*i**5/35 + 15*i**4/14 - 4*i**3/7 - 15*i**2/7 + 3*i + 28. Find p, given that x(p) = 0.
-1, 1, 7/3
Let c = 1/284 + 2267/1420. Let u(r) be the first derivative of 3/2*r**4 - 2/3*r**3 + 0*r + 0*r**2 + c*r**5 + 1. Find q such that u(q) = 0.
-1, 0, 1/4
Suppose 4*d = -5*s, -2*d - 5*s + 0*s = 0. Let v(f) be the third derivative of 0 + d*f - 1/240*f**5 + 1/24*f**3 + 0*f**4 - 3*f**2. Determine j so that v(j) = 0.
-1, 1
Let m be (0 - 3)/(3/(-4)). Let q(v) = 4*v - 24. Let c be q(7). Find j such that m*j + 0*j**3 - 4*j**3 - j**2 - 2*j**c + 3*j**2 = 0.
-2, -1, 0, 1
Let y(t) be the third derivative of -1/32*t**4 + 0 + 0*t**3 + 1/280*t**7 + 0*t + 1/160*t**6 - 1/80*t**5 - 2*t**2. Determine v, given that y(v) = 0.
-1, 0, 1
Let n(y) be the first derivative of -y**4/6 - 2*y**3/9 + 2*y**2/3 - 8. Factor n(g).
-2*g*(g - 1)*(g + 2)/3
Suppose -5*g + 104 = 34. Let p(h) = -49*h**2 - 21*h - 11. Let y(s) = -s + 1. Let r(f) = g*y(f) + 2*p(f). Factor r(j).
-2*(7*j + 2)**2
Let b(f) be the first derivative of f**6/45 - f**5/10 + f**4/9 - 2*f - 2. Let z(h) be the first derivative of b(h). Factor z(k).
2*k**2*(k - 2)*(k - 1)/3
Let o = 64/189 - -14/27. Factor 8/7 - 2/7*d**2 + o*d.
-2*(d - 4)*(d + 1)/7
Let g(s) = -4*s**3 + 13*s**2 - 16*s - 7. Let j(m) = -m**3 + 4*m**2 - 5*m - 2. Let r(u) = 4*g(u) - 14*j(u). Find b such that r(b) = 0.
-3, 0, 1
Solve 14*f**2 - 4*f + 2/7 = 0.
1/7
Suppose -65 - 5 = -10*o. Let h(b) be the third derivative of 1/540*b**6 + 0 + 1/1512*b**8 + 0*b**5 + 0*b + b**2 + 2/945*b**o + 0*b**3 + 0*b**4. Factor h(q).
2*q**3*(q + 1)**2/9
Let l(u) be the third derivative of u**6/150 + u**5/75 - u**4/30 - 2*u**3/15 + u**2. What is o in l(o) = 0?
-1, 1
Suppose 3*c = 9, 2*p - 3*c + 21 = 6*p. Determine x, given that -5/3*x**p + 5/3*x - 1/3*x**2 - 2/3 + x**4 = 0.
-1, 2/3, 1
Let h(f) be the first derivative of f**4/2 - f**2 - 6. What is d in h(d) = 0?
-1, 0, 1
Let c be (-4 + 3)*(1 - 16). Suppose 8*a - c = 3*a. Factor -3*v**2 + 0*v**2 - v**a + 2*v**2.
-v**2*(v + 1)
Find d, given that 16*d**4 - 12*d**3 + 10*d - 10*d**3 - 18*d**3 + 9*d**4 + 5*d**2 = 0.
-2/5, 0, 1
Factor 3/5*z**2 - 12/5*z - 12/5 + 3/5*z**3.
3*(z - 2)*(z + 1)*(z + 2)/5
Let x be 0/(-3)*((-3)/3 - -2). Let z(j) be the second derivative of 2*j + 1/54*j**4 - 2/27*j**3 + x + 1/9*j**2. Factor z(g).
2*(g - 1)**2/9
Suppose 10/3*q**4 - 20/3*q**3 + 2/3 + 20/3*q**2 - 10/3*q - 2/3*q**5 = 0. Calculate q.
1
Let k = -9509 - -84485/9. Let l = k - -122. Factor -l*s**2 - 2/9 - 4/9*s.
-2*(s + 1)**2/9
Suppose 0 = -3*o - 0*o + 3. Let y(i) = -i**3 - i - 1. Let f(t) = -t**3 + 6*t**2 + 10*t + 6. Let k(b) = o*f(b) - 2*y(b). Let k(s) = 0. What is s?
-2
Factor 1/3*a**2 + 4/3 - 5/3*a.
(a - 4)*(a - 1)/3
Let k be (8 - 2)/(33 - -1). Let d = 49/85 - k. Suppose -4/5*w**2 + d*w**5 - 2/5 + 6/5*w**4 - 6/5*w + 4/5*w**3 = 0. Calculate w.
-1, 1
Let s = 15 - 11. Let h(l) be the second derivative of -1/3*l**3 + 0 + 0*l**2 + l + 1/6*l**s. Factor h(r).
2*r*(r - 1)
Let v = -5 + 6. Let z be (-4)/(-16) - v/(-4). Factor -3/2*j - 1/2*j**2 + 3/2*j**3 - z + j**4.
(j - 1)*(j + 1)**2*(2*j + 1)/2
Let j = 5 - 21. Let s be 28/j*2/(-7). Find f such that -3/2*f - 1 - s*f**2 = 0.
-2, -1
Let h(k) = -k**4 + 2*k**3 + 4*k**2 + 4*k. Let p(m) = -3*m**4 + 5*m**3 + 13*m**2 + 11*m. Let s(f) = -11*h(f) + 4*p(f). What is i in s(i) = 0?
-4, 0, 2
Let k(i) be the third derivative of i**7/1575 + i**6/450 + i**5/300 + i**4/12 - 2*i**2. Let h(w) be the second derivative of k(w). Factor h(y).
2*(2*y + 1)**2/5
Let d(t) be the second derivative of t**7/3780 + t**6/540 - t**4/27 - t**3/2 - 2*t. Let x(b) be the second derivative of d(b). Determine u, given that x(u) = 0.
-2, 1
Let b be (-48)/(-45) + (-10)/25. Let t(y) be the first derivative of 6*y**2 + 1 + b*y**3 + 18*y. Factor t(s).
2*(s + 3)**2
Find h, given that 3*h + 4 + 1/2*h**2 = 0.
-4, -2
Suppose 3*h + 10 = 22. Let m be -2 - (-2 + h - 9). Determine i so that 14*i**3 - 14*i**m + 5*i**2 + 3*i**4 - i**2 - 7*i**4 = 0.
-1, -2/7, 0, 1
Suppose 4*o + 5 = y + 19, o - 2*y - 7 = 0. Find t such that 0*t - 4/3*t**o + 8/3*t**2 + 4/3*t**5 - 2*t**4 - 2/3 = 0.
-1, -1/2, 1
Suppose 15 = 5*l - 5*j, -l + 4*j + 12 = -0*l. Let -3/2*x**3 - 3*x + l + 9/2*x**2 = 0. What is x?
0, 1, 2
Let j(z) be the first derivative of -z**4/22 + 2*z**3/33 + z**2/11 - 2*z/11 - 19. Let j(g) = 0. Calculate g.
-1, 1
Suppose -5*o = -33 + 13. Factor 13 - 2*y - o*y - 6*y**2 - 17 + 4*y**2.
-2