Factor 1/3*g**2 + v*g**3 + 0 - 1/3*g**4 - 1/3*g.
-g*(g - 1)**2*(g + 1)/3
Determine d so that -33*d**2 - 54*d**5 - 128*d - 383*d**2 + 20*d**3 - 270*d**4 - 524*d**3 = 0.
-4/3, -1, 0
Solve 20*z**3 - 2*z**4 + 4*z**5 - 12*z**3 - 10*z**3 = 0.
-1/2, 0, 1
Let h(s) be the first derivative of s**4/16 - s**3/4 - s**2/8 + 3*s/4 + 13. Factor h(n).
(n - 3)*(n - 1)*(n + 1)/4
Let y = 2031/4 + -507. Solve -y*x**2 - 9/4 - 3*x = 0 for x.
-3, -1
Let f(n) = -n**2 + n + 1. Let o(r) = 2*r**2 - 4*r - 1. Let q be 4*1 + (-2 - 1). Let x(s) = q*o(s) + 3*f(s). Factor x(w).
-(w - 1)*(w + 2)
Solve 0 + 0*w**2 - 3/2*w + 3/2*w**3 = 0.
-1, 0, 1
Let r(a) be the second derivative of a**9/45360 + a**8/10080 + a**7/7560 + a**4/6 - a. Let m(g) be the third derivative of r(g). Factor m(p).
p**2*(p + 1)**2/3
Let t be 26/(-91) - (-37)/7. Let m(u) be the third derivative of 0 + 0*u - 1/15*u**3 - u**2 - 1/150*u**t - 1/30*u**4. Find j such that m(j) = 0.
-1
Suppose 4*a + 20 = 9*a. Factor 12/11*n**3 - 8/11 - 2/11*n**a + 24/11*n - 26/11*n**2.
-2*(n - 2)**2*(n - 1)**2/11
Let i = -62 - -64. Let c(q) be the second derivative of 0*q**5 + 0*q**3 - 1/63*q**7 - 1/45*q**6 + 0*q**i + 0*q**4 + 0 + q. Factor c(a).
-2*a**4*(a + 1)/3
Let g(u) be the second derivative of -u**5/140 + u**4/84 + 20*u. Factor g(y).
-y**2*(y - 1)/7
Let v be 4/10 - (-90)/25. Let 3*t**v - 6*t**3 + 3*t**2 - 6*t**4 + 6*t + 0*t**4 = 0. Calculate t.
-2, -1, 0, 1
Let g be (-2)/(44/(-7)) - 6/(-33). Factor 1/4*l - g + 1/4*l**2.
(l - 1)*(l + 2)/4
Let w(u) = u**3 - 24*u**2 + 65*u - 37. Let z(r) = -12*r**2 + 32*r - 18. Let h(v) = 2*w(v) - 5*z(v). Factor h(b).
2*(b - 1)**2*(b + 8)
Suppose -c = c. Suppose -5*l + 2*p + 29 - 6 = c, 26 = 2*l - 5*p. Factor 2/7*v**l + 0*v**2 - 2/7*v + 0.
2*v*(v - 1)*(v + 1)/7
Let s(x) = -2*x**2 + x + 3. Let z(m) = 3*m**2 + 0*m + 0*m - 5 - 5*m + 3*m. Let u(h) = 10*s(h) + 6*z(h). Let u(y) = 0. Calculate y.
-1, 0
Suppose -4 = 8*v - 9*v. Let h(i) be the third derivative of 1/10*i**5 + 0 + 0*i + 0*i**3 + 1/6*i**v + 2*i**2. Factor h(b).
2*b*(3*b + 2)
Suppose 0 = 27*t - 19*t - 24. Factor -3/5*b - 3/5 + 3/5*b**t + 3/5*b**2.
3*(b - 1)*(b + 1)**2/5
Let l be -1*(0 - -2)/(-2). Let r be 1 - 1/(l - 2). Factor -s**4 - 2*s**3 - 3*s**4 - 2*s**r + 2*s + 6*s**4.
2*s*(s - 1)**2*(s + 1)
Let 20 - 15 + 14 + 4*q**3 + 5 - 4*q - 24*q**2 = 0. Calculate q.
-1, 1, 6
Suppose 0 = -i - 0 + 2. Let b(w) be the second derivative of 0*w**i + 1/42*w**4 - 1/49*w**7 - 1/70*w**5 - w + 0 - 1/21*w**6 + 0*w**3. Factor b(u).
-2*u**2*(u + 1)**2*(3*u - 1)/7
Let w(f) be the third derivative of f**6/30 - f**5/20 - 3*f**4/8 - f**3/3 + 20*f**2. Factor w(q).
(q - 2)*(q + 1)*(4*q + 1)
Factor 0*k - 2*k - 24*k**3 - 26*k**3 + 46*k**2 + 6*k.
-2*k*(k - 1)*(25*k + 2)
Suppose -a - 18 = -4*a. Let o be (-16)/a - (-76)/19. Suppose 0 + 8/3*f**5 - 2/3*f**2 + 14/3*f**4 + 0*f + o*f**3 = 0. Calculate f.
-1, 0, 1/4
Let y(z) = -z**2 + 1. Let w(r) = -r**2 - 3*r + 4. Let c(s) = w(s) - 2*y(s). Let p be c(2). Factor -13*q + p + 27*q**2 - 23*q**3 + 7*q**4 + 6 - 4.
(q - 1)**3*(7*q - 2)
Let y(m) = 8*m**4 + 14*m**3 - 8*m**2 - 2. Let x(p) = -33*p**4 - 55*p**3 + 33*p**2 + 9. Let c(j) = 4*x(j) + 18*y(j). Factor c(f).
4*f**2*(f + 3)*(3*f - 1)
Factor 2/11*p**5 + 0 - 6/11*p**3 + 0*p**4 + 4/11*p**2 + 0*p.
2*p**2*(p - 1)**2*(p + 2)/11
Let p = -1 - -3. Let m be 2*1*(3 - p). What is q in -q**2 + 0*q**2 - m*q + 2*q**3 + q**2 = 0?
-1, 0, 1
Let n(t) be the first derivative of t**2 + 0*t - 1/2*t**4 + 2 - 2/3*t**3 + 2/5*t**5. Factor n(q).
2*q*(q - 1)**2*(q + 1)
Let s be -10*(-4)/21 - (-228)/(-171). Factor 4/7 + s*r**2 - 8/7*r.
4*(r - 1)**2/7
Suppose 5*a - 2 - 3 = -v, 3*a - 3*v - 21 = 0. Factor -2*q - 9*q**3 - a*q**4 + 3*q**4 - q + 2*q**4 + 9*q**2.
3*q*(q - 1)**3
Let v be (-5)/(35/14) - -4. What is u in u**3 + 1/2*u**v + 0*u + 0 + 1/2*u**4 = 0?
-1, 0
Let d(l) = 2*l**3 + 32*l**2 + 29*l - 15. Let x be d(-15). Factor 0*m + 1/5*m**2 + x - 1/5*m**3.
-m**2*(m - 1)/5
Let l = 5 + -3. Factor 4*a**3 + l*a**4 + 2*a**3 + a**2 + 2*a**2 + a**4.
3*a**2*(a + 1)**2
Let k be (-2 - -5)*(-1 + 2). Suppose w**2 - 8*w + w**k + w**2 - 2*w**4 + 7*w = 0. What is w?
-1, 0, 1/2, 1
Let y(n) = 5*n**4 + 16*n**3 - 6*n**2 - 60*n + 41. Let o(i) = -i**3 + i**2 - 1. Let r(g) = 4*o(g) - y(g). Determine m so that r(m) = 0.
-3, 1
Suppose 0 = 7*p - 6 + 6. Let j(f) be the first derivative of -1/6*f**4 - 2/9*f**3 + 1/9*f**6 + p*f + 2/15*f**5 + 0*f**2 + 3. Factor j(s).
2*s**2*(s - 1)*(s + 1)**2/3
Suppose 3 = 2*t - 1. Factor 3*f**2 + 3*f + 3*f**3 + 3*f**4 - 5*f**3 - 1 - 5*f**t - f**5.
-(f - 1)**4*(f + 1)
Let k be ((-3)/(-7))/(1/2). Determine j, given that -10/7*j - k*j**3 + 2*j**2 + 2/7 = 0.
1/3, 1
Let r(l) be the third derivative of 0*l - 1/120*l**6 + 1/30*l**5 - 1/3*l**3 + 1/24*l**4 - 3*l**2 + 0. Determine y, given that r(y) = 0.
-1, 1, 2
Suppose -5 + 3 = 4*n - 5*g, -2*n - 4*g + 12 = 0. Factor -2*v - v - 9*v**3 + 7*v**2 + n*v + 3*v.
-v*(v - 1)*(9*v + 2)
Find r, given that 10/13*r**2 + 4/13*r + 8/13*r**3 + 2/13*r**4 + 0 = 0.
-2, -1, 0
Let n(d) be the first derivative of d**5/110 + d**4/66 - d**3/33 - d**2/11 + 4*d + 5. Let b(m) be the first derivative of n(m). Suppose b(s) = 0. What is s?
-1, 1
Let d(p) be the second derivative of 2*p + 0 + 0*p**4 - 1/80*p**5 + 1/168*p**7 + 0*p**6 + 0*p**3 + 0*p**2. Factor d(u).
u**3*(u - 1)*(u + 1)/4
Determine b so that -1/4*b**4 - 1/12 - b**2 + 1/2*b + 5/6*b**3 = 0.
1/3, 1
Let n(w) = -3*w**2 + 4*w - 3. Let k = -16 - -10. Let s(f) = -7*f**2 + 9*f - 7. Let x(t) = k*s(t) + 15*n(t). Find m such that x(m) = 0.
1
Let l(a) be the first derivative of -a**6/60 + a**4/12 + a**2/2 - 3. Let n(g) be the second derivative of l(g). Factor n(b).
-2*b*(b - 1)*(b + 1)
What is n in 36*n + 61*n**2 + 34*n**2 + 29*n - 20*n**2 - 10 = 0?
-1, 2/15
Let c(a) be the first derivative of a**3/3 + a**2/2 - 4. Factor c(b).
b*(b + 1)
Let a(v) be the third derivative of -2*v**2 + 0*v**4 + 0*v + 0 - 1/360*v**6 + 0*v**3 + 1/180*v**5. Factor a(j).
-j**2*(j - 1)/3
Suppose 3*w - 4*j = 11, -4*j + 65 - 4 = 5*w. Let 18*f**4 - 12*f**5 - 27*f**3 - 3*f**4 + w*f**5 + 21*f**2 - 6*f = 0. What is f?
0, 1, 2
Suppose 0*x - 12 = 3*x, -14 = -b + 3*x. Let r(k) be the first derivative of -1/14*k**4 + 0*k**b + 2 + 0*k - 2/21*k**3. Suppose r(h) = 0. What is h?
-1, 0
Let f(b) be the third derivative of -b**7/3780 - b**6/360 - b**5/90 + 7*b**4/24 + 4*b**2. Let g(z) be the second derivative of f(z). Factor g(y).
-2*(y + 1)*(y + 2)/3
Factor -6*l**3 - 2*l**2 + 8/3 + 16/3*l.
-2*(l - 1)*(3*l + 2)**2/3
Let w be (-2 + (-8)/2)*(-9)/189. Determine i, given that 0 - w*i + 2/7*i**2 = 0.
0, 1
Let a = 17 - 17. Let f(j) be the second derivative of -j + 1/4*j**4 + 1/20*j**5 + 1/2*j**3 + 1/2*j**2 + a. Determine g so that f(g) = 0.
-1
Let k(r) be the third derivative of 3*r**2 + 0*r**3 + 0*r + 0 - 1/210*r**5 + 1/84*r**4. Solve k(v) = 0.
0, 1
Let n be 232/396 + (-48)/132. Determine s so that 0*s**2 + n - 4/9*s - 2/9*s**4 + 4/9*s**3 = 0.
-1, 1
Let k(c) be the third derivative of -1/4*c**3 + 4*c**2 + 0*c - 7/240*c**5 - 23/96*c**4 + 0. Factor k(f).
-(f + 3)*(7*f + 2)/4
Let i(w) be the third derivative of 0*w**4 - 3*w**2 - 1/60*w**6 - 1/30*w**5 + 0*w + 0*w**3 + 0. Factor i(h).
-2*h**2*(h + 1)
Let f(s) = -s**3 + s**2 + s. Let p(b) = -3*b**3 - 30*b**2 - 15*b + 10. Let x(j) = -6*f(j) - 3*p(j). Factor x(n).
3*(n + 1)*(n + 5)*(5*n - 2)
Let q(l) be the third derivative of -l**8/84 + 4*l**7/105 + l**6/5 - 8*l**5/15 - 5*l**4/6 + 4*l**3 - 21*l**2. Find w such that q(w) = 0.
-2, -1, 1, 3
Let p(z) be the third derivative of -3*z**6/260 - 11*z**5/390 - z**4/78 - 10*z**2. What is s in p(s) = 0?
-1, -2/9, 0
Let d(j) be the first derivative of -3*j**4/16 - 5*j**3/2 - 51*j**2/8 - 6*j - 41. Factor d(w).
-3*(w + 1)**2*(w + 8)/4
Let x(a) be the first derivative of -2*a**3/3 + 12*a**2/5 - 8*a/5 - 23. What is d in x(d) = 0?
2/5, 2
Factor -4/5*t**4 - 32/5*t**2 + 16/5*t + 4*t**3 + 0.
-4*t*(t - 2)**2*(t - 1)/5
Let k(f) be the first derivative of f**6/60 + f**5/5 + f**4 + 8*f**3/3 + f**2 + 3. Let b(d) be the second derivative of k(d). Factor b(a).
2*(a + 2)**3
Let x = -2/27 + 11/27. Let y(j) be the second derivative of -1/18*j**3 + 2*j - 1/36*j**4 + 0 + x*j**2. Factor y(o).
-(o - 1)*(o + 2)/3
Let c = 329 - 9869/30. Let f(r) be the second derivative of c*r**5 + 1/189*r**7 + 0*r**2 + 1/45*r**6 + 1/54*r**4 + 0 