- 27/7*a**2 - 3/7*a**4 - 6/7.
-3*(a + 1)**3*(a + 2)/7
Let w be (-1 + 2)*1 + 2. Find o such that -4*o**5 - o**4 - 2*o**3 + 3*o**2 + 4*o**w + 3*o**2 + 2*o - 5*o**4 = 0.
-1, -1/2, 0, 1
Let f(t) be the first derivative of -3/20*t**5 + 3/2*t**2 + 3*t - 1/4*t**4 + 1/2*t**3 + 1. Let j(r) be the first derivative of f(r). Factor j(g).
-3*(g - 1)*(g + 1)**2
Let r(x) be the first derivative of 91125*x**4 - 16200*x**3 + 1080*x**2 - 32*x + 41. Find z, given that r(z) = 0.
2/45
Let y = 1 - -1. Factor a**y + 1 + 3 - 3 - 2*a.
(a - 1)**2
Let v(a) be the second derivative of -a**6/60 + a**5/5 - a**4 + 8*a**3/3 - a**2/2 - 3*a. Let c(w) be the first derivative of v(w). Factor c(i).
-2*(i - 2)**3
Factor -2/9*z + 1/3*z**2 - 1/9*z**3 + 0.
-z*(z - 2)*(z - 1)/9
Let x(p) be the second derivative of 0*p**2 + 0 + 1/4*p**4 + 3*p + 1/10*p**5 + 1/6*p**3. Suppose x(i) = 0. Calculate i.
-1, -1/2, 0
Suppose -k + 14 = 5*t, -k - 3*k - 19 = -5*t. Let y(q) be the first derivative of -2*q**2 - 2 - 8/3*q - 2/3*q**t - 1/12*q**4. Solve y(l) = 0.
-2
Suppose -1/4 + 1/4*y**2 + 1/4*y - 1/4*y**3 = 0. What is y?
-1, 1
Factor 1/6*v**4 - 1/3*v - 1/6*v**2 + 1/3*v**3 + 0.
v*(v - 1)*(v + 1)*(v + 2)/6
Solve -1/4*b**3 - 3/2*b**2 - 2 - 3*b = 0.
-2
Let l(y) = 3*y**2 - 10*y - 5. Let b be l(4). Solve 0 - 1/3*c**2 + 0*c + 1/3*c**b = 0 for c.
0, 1
Let y(j) be the second derivative of -j**7/7560 - j**6/2160 + j**5/180 + j**4/12 - 3*j. Let z(m) be the third derivative of y(m). Factor z(t).
-(t - 1)*(t + 2)/3
Let l(v) be the second derivative of v**9/45360 - v**8/5040 + v**7/1512 - v**6/1080 + v**4/4 - 3*v. Let a(w) be the third derivative of l(w). Factor a(t).
t*(t - 2)*(t - 1)**2/3
Let v(h) = -7*h**3 - 9*h**2 - 2. Let a(f) = -f + 1. Let q(o) = -2*a(o) - v(o). Let q(w) = 0. What is w?
-1, -2/7, 0
Let n(y) = y**3 + 7*y**2 - y - 1. Let a(o) = -o**3 - 15*o**2 + 3*o + 2. Let z(d) = 2*a(d) + 5*n(d). Factor z(r).
(r + 1)**2*(3*r - 1)
Suppose 0 = -5*c - 0 + 5. Let q(n) be the first derivative of n**4 - 4/3*n**3 + 0*n - c + 0*n**2 - 1/5*n**5. Find f, given that q(f) = 0.
0, 2
Let r(t) = t**3 - 8*t**2 - 2*t - 10. Let l be r(8). Let w = l - -26. Factor -4/3*o**3 + 2*o**2 + w*o - 2/3.
-2*(o - 1)**2*(2*o + 1)/3
Suppose 2*z = 5*k - 39, 3*z - 6*z - 41 = -5*k. Suppose 3*x = k*x - 20. Determine y, given that -9/4*y**x + y + 0 + 3*y**4 - 3*y**2 + 5/4*y**3 = 0.
-1, 0, 2/3, 1
Suppose -6*r + 10 = -r. Factor -4*m + r*m - 2*m**2 - 2*m.
-2*m*(m + 2)
Let n(c) = c**3 - 3*c**2 - 2*c - 5. Let w be n(4). Solve 2/3*b**2 - 2/3*b**w - 2/3 + 2/3*b = 0.
-1, 1
Suppose 8*m = -3*m. Let a(c) be the first derivative of 3 + 0*c**2 + m*c - 1/4*c**4 + 2/9*c**3. Determine z, given that a(z) = 0.
0, 2/3
Suppose 10 = -3*q + 13. Let h be q/2*-2*0. Factor h - 6/13*r**2 + 4/13*r.
-2*r*(3*r - 2)/13
Let p(x) = -7*x**4 - 16*x + 23*x**4 - 5*x**2 + 5*x**3 - 2 - 11*x**2 - 9. Let k(r) = -3*r**4 - r**3 + 3*r**2 + 3*r + 2. Let d(u) = 11*k(u) + 2*p(u). Factor d(z).
-z*(z - 1)*(z + 1)**2
Let y(o) be the first derivative of -o**2 + 18*o + 5. Let s be y(8). Factor 1/2*m**4 - m + 0*m**s + m**3 - 1/2.
(m - 1)*(m + 1)**3/2
Let h(n) be the first derivative of -n**5/20 - n**4/8 + 2*n**2 + 4. Let u(g) be the second derivative of h(g). Factor u(z).
-3*z*(z + 1)
Suppose 0*d - 4*d + 8 = 0. Let i be (3 + -7)*d/(-4). Factor -2 + 5*r**4 - 5*r**3 - 3*r**2 + 3*r + 4*r - i*r**3.
(r - 1)**2*(r + 1)*(5*r - 2)
Suppose -1 = 4*m - 5*m. Let c be (1 + (-4)/4)/m. Find s, given that 0 + 0*s**2 + c*s - 2/9*s**5 - 4/9*s**4 - 2/9*s**3 = 0.
-1, 0
Let l = 7/17 + 13/51. Let 2/3*t**2 - 1/3*t**3 - l + 1/3*t = 0. What is t?
-1, 1, 2
Let f(k) = -k**2 - k + 2. Let u be f(0). Let o = 365 + -3281/9. Suppose 0 + o*z**u - 2/9*z**5 + 0*z**3 + 2/9*z - 4/9*z**4 = 0. Calculate z.
-1, 0, 1
Let q(t) = -4*t**2 - 51*t - 147. Let d(b) = 20*b**2 + 256*b + 736. Let i(p) = -3*d(p) - 16*q(p). Find f, given that i(f) = 0.
-6
Find v, given that -5 - 5*v**3 - 24*v + 10*v - v - 15*v**2 = 0.
-1
Let g(h) = h**2 + 9*h + 18. Let x be g(-8). Suppose -11*s - x = -16*s. Factor 0*v - 1/4*v**s + 1/4.
-(v - 1)*(v + 1)/4
Let b(g) = -g**3 - 7*g**2 + 2*g - 4. Let f be b(-8). Let h be f/10 - (-10)/(-25). Factor 4*w - w**3 + 4*w**h + 2*w**3 - w**5 - 4*w**2 - 4*w**3.
-w*(w - 2)**2*(w - 1)*(w + 1)
Factor c + 3*c**5 + 34*c**3 - 36*c**2 + 11*c + 5*c**3 - 18*c**4.
3*c*(c - 2)**2*(c - 1)**2
Let g(d) be the first derivative of -4*d**3/3 + 4*d**2 - 18. Factor g(k).
-4*k*(k - 2)
Let m(r) be the first derivative of -1/8*r**2 + 0*r - 1/16*r**4 - 2 - 1/6*r**3. Factor m(f).
-f*(f + 1)**2/4
Let a(j) = -15*j**3 - 35*j**2. Let u(c) = -c**3 - c**2 + c. Let k(t) = a(t) - 20*u(t). Factor k(m).
5*m*(m - 4)*(m + 1)
Let y(p) be the second derivative of 0 + 1/63*p**7 + 0*p**2 + 2*p + 0*p**4 + 2/45*p**6 + 0*p**3 + 1/30*p**5. Suppose y(c) = 0. What is c?
-1, 0
Factor 0*v + 1/3*v**2 - 1/2*v**3 + 1/6*v**4 + 0.
v**2*(v - 2)*(v - 1)/6
Let j(q) be the second derivative of 1/210*q**7 - 1/50*q**5 + 8*q + 0*q**6 + 0 + 0*q**2 + 1/30*q**3 + 0*q**4. Find l, given that j(l) = 0.
-1, 0, 1
Suppose y + 0 = 8. Let k be 3 + y/(-12) + -2. Factor -2*t**2 - 4*t - k*t**3 - 8/3.
-(t + 2)**3/3
Suppose 5*d - 5*i - 35 = 0, 4*i = 2*d - 4 - 16. Suppose -k**d - k - 1 - 6*k**2 + k**2 + 7*k**2 + 2*k**3 - k**5 = 0. Calculate k.
-1, 1
Let w(s) be the third derivative of s**6/180 + s**5/90 - s**4/18 + 5*s**2. Let w(u) = 0. Calculate u.
-2, 0, 1
Let c(d) be the third derivative of -2*d**2 + 3/8*d**4 + 0*d + 0 - 1/3*d**3 - 7/60*d**5. Solve c(h) = 0 for h.
2/7, 1
Let u(r) be the second derivative of r**6/285 - 7*r**5/190 + 3*r**4/19 - 20*r**3/57 + 8*r**2/19 - 5*r. What is m in u(m) = 0?
1, 2
Let u(t) be the third derivative of 0*t - 1/12*t**3 - 1/120*t**5 + 0 - 1/24*t**4 - 2*t**2. Factor u(i).
-(i + 1)**2/2
Suppose -13*i + 8 = -9*i. Let d(k) be the second derivative of -2*k - 1/4*k**4 - 1/9*k**3 + 0*k**i + 0. Let d(h) = 0. Calculate h.
-2/9, 0
Let h(f) = 2*f - 12. Let x be h(9). Factor -y**3 - x*y**2 + 3*y**3 + y**3.
3*y**2*(y - 2)
Let s = -1 + -1. Let a(m) = -m**3 + 4*m + 3. Let u be a(s). Solve -4*p**3 + 13*p**u + 4*p - p**3 - 2 + 14*p**2 = 0 for p.
-1, 1/4
Let b(f) be the first derivative of 3 + 1/12*f**4 + 1/6*f**2 + 0*f - 2/9*f**3. Factor b(t).
t*(t - 1)**2/3
Let p be 4 - 1/(-1 - 0). Suppose 0 = -3*d - 2*h + 5*h + 6, p*d + h + 2 = 0. What is f in 0*f**2 + 0*f**3 + 0*f + d + 1/2*f**5 - 1/2*f**4 = 0?
0, 1
Factor 1/3*s + 0 + 1/3*s**2.
s*(s + 1)/3
Let s = -17 + 15. Let i = s - -2. Factor 1/2*y + i + 1/2*y**2.
y*(y + 1)/2
Suppose 13*g - 8*g = 75. Let m be (-3)/g - 21/(-30). Factor -m - 7/4*u**2 + 9/4*u.
-(u - 1)*(7*u - 2)/4
Let t(n) be the second derivative of 5/12*n**3 + 2*n - 7/24*n**4 + 0 + 1/2*n**2. Factor t(f).
-(f - 1)*(7*f + 2)/2
Let a be (126/24)/(3/8). Find o such that 6*o - a*o**4 - 4*o**2 - 18*o**3 - 6*o = 0.
-1, -2/7, 0
Suppose -i - m - 38 = -6*i, 0 = -4*i + m + 30. Suppose 3*l - i = 13. Let w**2 - 3*w**4 - l*w**2 - 9*w**3 - 1 + 1 = 0. Calculate w.
-2, -1, 0
Let t = 16402/1141 - -32/163. Let t*o**2 - 8/7 + 32/7*o + 56*o**4 - 74*o**3 = 0. Calculate o.
-1/4, 2/7, 1
Factor 0*g - 2/3 + 2/3*g**2.
2*(g - 1)*(g + 1)/3
Let x = 8 + -15/2. Let y be 6/15 + (-6)/15. Solve x*f**2 - 1/2*f + y = 0 for f.
0, 1
Let n(z) be the first derivative of 2*z**6/3 + 28*z**5/5 + 15*z**4 + 52*z**3/3 + 8*z**2 - 26. Factor n(u).
4*u*(u + 1)**3*(u + 4)
Let u = 12 + -7. Let -r**5 - 2*r**4 + 4*r**u - r**3 - 4*r**5 = 0. What is r?
-1, 0
Suppose 87*o + 1 = 88*o. Suppose 0*s + o - 1/4*s**2 = 0. Calculate s.
-2, 2
Solve 31*d + 0 + 6*d**2 + 10 - 15*d = 0.
-5/3, -1
Suppose 9*r - 3*k = 4*r - 3, -r - 3 = -3*k. Factor r*l**3 - 4/3*l**5 + 8/3*l**4 + 4/3*l + 0 - 8/3*l**2.
-4*l*(l - 1)**3*(l + 1)/3
Let c(y) be the third derivative of 0*y + 0 - 1/3*y**3 + 0*y**4 - 7*y**2 + 1/30*y**5. Factor c(l).
2*(l - 1)*(l + 1)
Let f(a) be the second derivative of a**4/42 - a**3/21 + 3*a. Factor f(g).
2*g*(g - 1)/7
Let b = 5 + -3. Factor 8*w**b - 7 + 2 - 10*w + 1 + 6*w**2.
2*(w - 1)*(7*w + 2)
Let a(u) be the first derivative of -2*u**3/27 + u**2/9 + 3. Determine o so that a(o) = 0.
0, 1
Let v(l) be the second derivative of 7*l**5/20 - 17*l**4/3 + 155*l**3/6 + 25*l**2 - 7*l. Suppose v(g) = 0. Calculate g.
-2/7, 5
Let r = -3881191/12222 + 2858/9. Let u = r + 199641/6790. Factor -231/5*d**3 - 12/5*d + 0 + 96/5*d**2 + u*d**4.
3*d*(d - 1)*(