1, 2
Let b(r) be the second derivative of -r**5/30 + r**4/36 + 5*r**3/18 + r**2/3 - 6*r. Suppose b(u) = 0. What is u?
-1, -1/2, 2
Determine y, given that 8*y**3 - y**4 + 5*y - 3*y**2 + 2*y**4 - 9*y**3 - 2 = 0.
-2, 1
Let q(s) = -5*s**2 + 19*s - 29. Let k(u) = -11*u**2 + 39*u - 57. Let m(p) = -3*k(p) + 7*q(p). Factor m(t).
-2*(t - 4)**2
Let m(a) be the third derivative of a**8/1344 + a**7/140 + 7*a**6/240 + a**5/15 + 3*a**4/32 + a**3/12 - 4*a**2. Let m(p) = 0. What is p?
-2, -1
Let q = 2/20331 + 1734898/142317. Let r = q + -34/3. Factor r*c**2 + 2*c + 4/7.
2*(c + 2)*(3*c + 1)/7
Let s be 0*(-3)/9*-1. Factor s*b**3 + 3*b**2 - b**3 - 4*b**2.
-b**2*(b + 1)
Let d be (-12)/18 + 22/6. Determine u so that -10*u**5 + 23/2*u**d - 2*u**2 - 1 - 9/2*u + 6*u**4 = 0.
-1/2, -2/5, 1
Let q(l) be the second derivative of -7*l**5/15 - 13*l**4/36 + 13*l**3/18 - l**2/3 - 16*l. Factor q(t).
-(t + 1)*(4*t - 1)*(7*t - 2)/3
Let w = 292/447 + 2/149. Let t(s) be the second derivative of -w*s**3 + s**2 + 0 + s + 1/6*s**4. Suppose t(z) = 0. What is z?
1
Let j(c) be the third derivative of c**8/720 - c**7/336 + c**6/360 - c**5/60 - 2*c**2. Let m(z) be the third derivative of j(z). Factor m(b).
(4*b - 1)*(7*b - 2)
Suppose -3*f - 2*f = -10. Let d be (7 - f) + -2 - 1. Solve -2*v**3 + 10 + d*v**4 - 10 = 0 for v.
0, 1
Let m(z) be the third derivative of z**2 - 3/20*z**5 + 1/4*z**4 + 0*z + 0*z**3 - 1/8*z**6 + 0. Suppose m(l) = 0. What is l?
-1, 0, 2/5
Factor 0*n + 0 - 2/5*n**4 + 0*n**2 + 4/5*n**3.
-2*n**3*(n - 2)/5
Let w(z) = -6*z**4 + 22*z**3 - 50*z**2 + 50*z - 14. Let q(g) = -g**4 - g**3 + g**2 + g + 1. Let x(u) = -2*q(u) + w(u). Factor x(f).
-4*(f - 2)**2*(f - 1)**2
Suppose j - 9 = -2*j + 5*l, -j + 5*l + 3 = 0. Find x such that j*x**2 + 6 - 5*x + x - 5*x = 0.
1, 2
Let x = -5 - -10. Let n(v) be the third derivative of -1/18*v**4 - 1/90*v**x + 0*v + 0 + 1/45*v**6 + 1/105*v**7 + v**2 + 0*v**3. Factor n(o).
2*o*(o + 1)**2*(3*o - 2)/3
Suppose 8 = -10*a + 18. Let v be a - 1 - 0/(-4). Factor 1/2*r**4 + v*r + 0 + 3/2*r**3 + r**2.
r**2*(r + 1)*(r + 2)/2
Let j(h) = -20*h + 23. Let i(l) = -7*l + 8. Let n(w) = -17*i(w) + 6*j(w). Let f be n(0). Factor -1 + 6*z**2 - z - 2*z**2 - 3*z**f + z**3.
(z - 1)*(z + 1)**2
Let a(w) be the second derivative of 2*w**7/21 + 4*w**6/5 + 11*w**5/5 + 2*w**4/3 - 8*w**3 - 16*w**2 + w. Solve a(s) = 0 for s.
-2, -1, 1
Let g be ((-3)/(-3))/(21/350*2). Determine m so that g*m**2 - 4/3 - 25/3*m**3 + 4/3*m = 0.
-2/5, 2/5, 1
Let h(b) be the second derivative of -b**6/75 + b**5/25 - b**4/30 - 4*b. Factor h(t).
-2*t**2*(t - 1)**2/5
Let x(u) be the first derivative of -u**3/2 + 21*u**2/8 - 9*u/4 + 1. Factor x(b).
-3*(b - 3)*(2*b - 1)/4
Let r = 83 + -77. Let c(i) be the third derivative of 7/240*i**r + 0*i - 1/6*i**3 - 7/48*i**4 - i**2 + 0 + 1/60*i**5. Factor c(b).
(b - 1)*(b + 1)*(7*b + 2)/2
Let m(c) be the second derivative of -c**6/540 + c**4/36 + c**3/3 + c. Let q(o) be the second derivative of m(o). Solve q(u) = 0.
-1, 1
Let q = 167 - 163. Let g(s) be the first derivative of 2 + 2/9*s**3 - 1/3*s - 1/15*s**5 + 0*s**q + 0*s**2. Solve g(i) = 0.
-1, 1
Let a(i) = i**3 + 9*i**2 - 2*i - 9. Let f be a(-9). Let z = f - 6. Factor 2*g**z + 6*g - g**4 - g**4 - 8*g**3 + g**2 - 3*g**2 + 4.
-2*(g - 1)*(g + 1)**2*(g + 2)
Factor -14/5 + 4/5*m**2 + 26/5*m.
2*(m + 7)*(2*m - 1)/5
Let z = 2 + 1. Factor 0 + 1 + o**2 + o + 0 - z*o.
(o - 1)**2
Suppose -1/2*z**3 - 1 + 1/2*z + z**2 = 0. What is z?
-1, 1, 2
Let y(n) be the first derivative of 5*n**6/6 + 4*n**5 + 15*n**4/4 - 20*n**3/3 - 10*n**2 + 13. Let y(k) = 0. What is k?
-2, -1, 0, 1
Let -4/7*z**5 + 0 - 4/7*z**3 + 0*z + 8/7*z**4 + 0*z**2 = 0. What is z?
0, 1
Let c be -4*3/4*-1. Suppose q - 4*a + 12 = 0, 5*q + 5*a = 55 - 15. Solve i**q + 5 - 4 + 2*i**c + 0 - i**5 - 2*i**2 - i = 0 for i.
-1, 1
Suppose -14 = 5*n - 7*n. Let h be (-5)/n - (-2 + 1). Let -2/7*i**3 + 2/7 + h*i - 2/7*i**2 = 0. What is i?
-1, 1
Suppose 10 = -w - 8. Let r be (4/(-16))/(w/32). Let -34/9*b**2 - 26/9*b**3 - 2/3*b + r + 2/3*b**4 + 8/9*b**5 = 0. Calculate b.
-1, 1/4, 2
Let r(m) be the third derivative of -m**7/420 + m**6/60 - m**5/30 - m**3/2 - m**2. Let i(y) be the first derivative of r(y). Factor i(c).
-2*c*(c - 2)*(c - 1)
Factor 4*z**4 + 160*z**3 - 3*z**2 - 112*z**3 + 47*z**2.
4*z**2*(z + 1)*(z + 11)
Let t be (-13 - -13)/(2/(3 + -1)). Let w(h) be the third derivative of h**2 + 1/8*h**3 + 1/80*h**5 + 1/16*h**4 + t + 0*h. Find j such that w(j) = 0.
-1
Let y be 4 - ((-7197)/(-1800))/1. Let g(t) be the third derivative of 0*t**3 - y*t**6 + 0*t**4 - 2*t**2 + 0*t + 0 - 1/300*t**5. Factor g(w).
-w**2*(w + 1)/5
Let u(m) = -3*m**2 + 51*m + 3. Let r be u(17). Factor 5/4*c - 1/4*c**r + 1/2 + 3/4*c**2 - 1/4*c**4.
-(c - 2)*(c + 1)**3/4
Suppose -2*y + 4*y - 4*i = -604, y = 5*i - 290. Let o = -2166/7 - y. Factor o*p**3 - 2*p**4 + 2/7*p**2 + 0*p + 0 + 8/7*p**5.
2*p**2*(p - 1)**2*(4*p + 1)/7
Let p(y) be the third derivative of -y**7/420 + y**6/80 + y**5/24 - y**4/16 - y**3/3 + 10*y**2. Factor p(i).
-(i - 4)*(i - 1)*(i + 1)**2/2
Let k(z) be the third derivative of 0*z + 1/132*z**6 + 4/1155*z**7 + 4*z**2 + 1/330*z**5 + 0 + 0*z**3 + 0*z**4. Determine u, given that k(u) = 0.
-1, -1/4, 0
Suppose 5*m - 2 = -3*r, -2*r + 0*r + m + 23 = 0. Suppose 4*p - 13 = k + p, 3*p = 3*k + r. Determine h so that 2*h**k - h + 5 + 5*h - 3 = 0.
-1
Let s(h) = -2*h**4 - 10*h**3 - 17*h**2 - 9*h + 3. Let v(d) = 6*d**4 + 30*d**3 + 50*d**2 + 26*d - 8. Let k(y) = -8*s(y) - 3*v(y). Factor k(a).
-2*a*(a + 1)**2*(a + 3)
Suppose -2*w - 12 = 4*k - 0, 4*w - 4*k - 12 = 0. What is c in 2 - c - 2 - c**2 + w = 0?
-1, 0
Solve 3053 - 3053 + 4*m**2 - 8*m = 0 for m.
0, 2
Let z(v) be the third derivative of 1/4*v**5 + 3*v**2 + 0 + 3/2*v**4 + 0*v + 2*v**3. Factor z(s).
3*(s + 2)*(5*s + 2)
Suppose 2*b = 3*s - b - 9, -b = -2*s + 5. What is t in 4 - 2*t - 2*t + s*t**2 - 2 = 0?
1
Factor h**3 - 66 - 5*h**2 + 120 - 58 + 8*h.
(h - 2)**2*(h - 1)
Factor -8*f**4 + 38*f**2 - 12*f**3 - 19*f + 3*f + 4*f**5 - 6*f**2.
4*f*(f - 2)*(f - 1)**2*(f + 2)
Let a(z) be the second derivative of z**7/252 - z**6/36 + 3*z**5/40 - 7*z**4/72 + z**3/18 + 15*z. Find h, given that a(h) = 0.
0, 1, 2
Let b = 23 - 159/7. Solve 4/7 + 2/7*f - b*f**2 = 0 for f.
-1, 2
Let u = -1027/9540 - -6/53. Let n(o) be the third derivative of 0 + 0*o**3 + 1/72*o**4 + u*o**5 + 0*o + 2*o**2. Factor n(j).
j*(j + 1)/3
Suppose 4*c - 5*l - 23 = 0, 4*c = 5*c + 5*l + 13. Let f = 2967 - 20687/7. Let 78/7*d**c + f*d**3 + 30/7*d + 30/7*d**4 + 4/7 = 0. What is d?
-1, -2/5, -1/3
Factor -1/2*k**2 - 3*k - 5/2.
-(k + 1)*(k + 5)/2
Suppose -s - s + 2 = 5*q, 0 = -q - 5*s - 18. Let 2*c**q - 2/3*c**3 + 0 - 4/3*c = 0. Calculate c.
0, 1, 2
Let f = -9315/4 - -2317. Let s = f - -12. Let -s*o**3 + 1/4*o**5 + 1/4*o**2 - 1/4*o**4 + 0*o + 0 = 0. Calculate o.
-1, 0, 1
Let g(j) be the second derivative of -j**6/720 - j**5/120 - j**4/48 + j**3/6 + 3*j. Let t(p) be the second derivative of g(p). Suppose t(z) = 0. What is z?
-1
Let z(r) be the first derivative of r**6/30 - 3*r**5/10 + r**4 - 4*r**3/3 + 5*r + 3. Let l(t) be the first derivative of z(t). Factor l(a).
a*(a - 2)**3
Let h(w) = 2*w. Let a be h(1). Factor a + 2*u**5 + 4*u - 2*u - 4*u**3 - 2.
2*u*(u - 1)**2*(u + 1)**2
Let b(v) = 3*v**4 + 7*v**3 - 5*v**2 - 5. Let d(j) = -2*j**4 - 4*j**3 + 3*j**2 + 3. Let a(c) = -6*b(c) - 10*d(c). Factor a(u).
2*u**3*(u - 1)
Let g(r) be the first derivative of -r**3 - 6*r**2 - 12*r + 7. Factor g(j).
-3*(j + 2)**2
Let f be 6/4 - (-24)/(-80). Let a(q) be the first derivative of 2 - 1/3*q**3 + f*q**2 - 4/5*q. Let a(c) = 0. Calculate c.
2/5, 2
Suppose -7*t**5 - 1/4*t**3 - 59/2*t**2 + t + 85/4*t**4 + 2 = 0. What is t?
-1, -1/4, 2/7, 2
Let g = 3 + -1. Let f be g + (0 - (0 - 0)). Factor -2*m + 2*m + 2*m**2 - f.
2*(m - 1)*(m + 1)
Let o(j) be the second derivative of j**7/14 - j**6/5 + j**4/2 - j**3/2 - 9*j. Factor o(k).
3*k*(k - 1)**3*(k + 1)
Let l(s) be the third derivative of s**8/2240 + s**4/12 + 7*s**2. Let a(t) be the second derivative of l(t). Factor a(r).
3*r**3
Let p(r) be the first derivative of -r**5/15 - r**4/6 + r**2/3 + r/3 + 6. Factor p(x).
-(x - 1)*(x + 1)**3/3
Suppose 0 + 3/2*u**5 + 27/2*u**3 + 21/2*u**2 + 3*u + 15/2*u**4 = 0. Calculate u.
-2, -1, 0
Let z(w) = 4*w - 46. Let s be z(12). Suppose 2/3*t - 1/3*t**s - 1/3