-2*(v - 1)*(v + 1)**2/5
Let w(c) be the first derivative of c**4/38 + 20*c**3/57 + 32*c**2/19 + 64*c/19 - 22. Factor w(z).
2*(z + 2)*(z + 4)**2/19
Let l(w) = -w**2 - 10*w + 2. Let k be l(4). Let m be (-2)/(-9) + (-204)/k. Find j such that -44/7*j**3 + 16/7*j**2 + 36/7*j**m + 6/7*j - 4/7 - 10/7*j**5 = 0.
-2/5, 1
Suppose 15/2*i**4 + 0 + 45/2*i**2 - 25*i**3 - 5*i = 0. Calculate i.
0, 1/3, 1, 2
Let i = 15 + -9. Let x = i + -3. Let 0 - 3/4*j**x + 0*j - 1/2*j**2 + 5/4*j**4 = 0. What is j?
-2/5, 0, 1
Suppose g - 4*g = -6. Factor 4 + 3*c**2 - 12*c + 0*c**2 + 0*c**g + 8.
3*(c - 2)**2
Suppose -3*q + 6 = 3*q. Let q - x**2 + 1 + 1 - 2*x = 0. Calculate x.
-3, 1
Let q be (2/(-3))/(2/(-9)). Factor q*m**2 + 3*m**3 + m + m**2 - 4*m**4 - 4*m**3.
-m*(m - 1)*(m + 1)*(4*m + 1)
Let d = 131/70 - 13/10. Suppose 0*j - 2/7 - d*j**3 + 6/7*j**2 = 0. Calculate j.
-1/2, 1
Let i = -10 + 13. Factor 7*v - 7*v + 2*v**i - 6*v**3 - 12*v**2.
-4*v**2*(v + 3)
Let v be 16/(-6)*(-6)/4. Factor -5*l**3 - 4*l**5 - 6*l**3 + 15*l**3 + v*l**4 - 4*l**2.
-4*l**2*(l - 1)**2*(l + 1)
Let d(r) = r**2 + r + 3. Let v be d(0). Suppose v*f - 3*f + 3*f**2 + 11*f**3 - 8*f**3 = 0. What is f?
-1, 0
Let m(f) be the first derivative of 2*f**5/5 + f**4 - 2*f**3 - 4*f**2 + 8*f - 6. Factor m(c).
2*(c - 1)**2*(c + 2)**2
Let y = 622 + -617. Determine k, given that 1/2*k + 2*k**2 + 3*k**3 + 1/2*k**y + 2*k**4 + 0 = 0.
-1, 0
Let c(b) be the third derivative of 0*b - 77/100*b**5 + 0 - 4/5*b**4 - 2/5*b**3 - 49/200*b**6 + 2*b**2. Factor c(w).
-3*(w + 1)*(7*w + 2)**2/5
Let t(m) be the third derivative of 1/300*m**5 + m**2 + 0*m + 1/120*m**4 + 0*m**3 + 0. Factor t(p).
p*(p + 1)/5
Let c(x) = -10*x**4 + 23*x**3 - 6*x**2 - x + 2. Let a(m) = 69*m**4 - 162*m**3 + 42*m**2 + 6*m - 15. Let k(f) = 2*a(f) + 15*c(f). What is o in k(o) = 0?
-1/4, 0, 1
Let q(g) be the third derivative of -g**7/4200 - g**6/1800 + 5*g**3/6 + g**2. Let p(i) be the first derivative of q(i). Factor p(y).
-y**2*(y + 1)/5
Determine o so that o + 3*o + 2*o**5 - 3*o - 4*o**3 + o = 0.
-1, 0, 1
Factor -s**2 - 18*s + 0*s**2 + 2*s**2 + 17*s.
s*(s - 1)
Suppose -15 = -4*k - k. Let y be (165/(-54) + k)*-4. Suppose 0 + y*z**2 + 0*z = 0. Calculate z.
0
Let u(y) = -y**3 + y + 1. Let k(m) = 8*m**3 - 6*m**2 + 2*m + 6. Let t(r) = -k(r) - 10*u(r). Factor t(v).
2*(v - 2)*(v + 1)*(v + 4)
Let s = 6 + -3. Factor -4*b**s + 2*b**3 - 2*b**2 + 0*b - b + b**3.
-b*(b + 1)**2
Let -20/7*x + 4/7*x**2 + 16/7 = 0. What is x?
1, 4
Let w(d) be the second derivative of -d**6/135 + 2*d**5/45 - 5*d**4/54 + 2*d**3/27 - 8*d. What is i in w(i) = 0?
0, 1, 2
Let k(l) = -6*l - 15. Let v be k(-6). Let f = 71/3 - v. Factor f + 2/3*j**4 + 4*j**3 + 26/3*j**2 + 8*j.
2*(j + 1)**2*(j + 2)**2/3
Let y = -2/95 - -196/285. Factor 2/3*p + y*p**5 - 8/3*p**4 + 4*p**3 - 8/3*p**2 + 0.
2*p*(p - 1)**4/3
Let b be (-98)/(-60) + (-2)/15. Factor -21/4*h - 9/4*h**3 + 6*h**2 + b.
-3*(h - 1)**2*(3*h - 2)/4
Let o = 52 + -47. Find r, given that -2/5*r**2 + 0*r + 0 - 1/5*r**3 + 4/5*r**4 + 3/5*r**o = 0.
-1, 0, 2/3
Let f(b) = 9*b**2 + 13*b - 9. Let j(m) = 2*m**2 + 3*m - 2. Let y(z) = 6*f(z) - 26*j(z). Find t, given that y(t) = 0.
-1, 1
Suppose 44*d = 48*d - 8. Let s(n) be the first derivative of -1/26*n**4 + 0*n**3 + 2/65*n**5 + 0*n**d + 0*n - 4. Determine t, given that s(t) = 0.
0, 1
Let z(k) be the second derivative of k**4/6 + 4*k. Let z(g) = 0. What is g?
0
Factor -15*n**2 - 3*n**3 + n**5 - 5*n**4 + 6*n**4 + 10*n**2 - 2*n.
n*(n - 2)*(n + 1)**3
Let o = 25/24 + -3/8. Let b(g) be the first derivative of -1/3*g**6 - 2/5*g**5 + 1/2*g**4 + o*g**3 + 2 + 0*g + 0*g**2. Factor b(c).
-2*c**2*(c - 1)*(c + 1)**2
Let y(k) = 210*k**3 + 895*k**2 + 1190*k + 420. Let r(c) = 15*c**3 + 64*c**2 + 85*c + 30. Let p(g) = -85*r(g) + 6*y(g). Find i such that p(i) = 0.
-3, -1, -2/3
Let h be (-2 - -4)/1*1. Suppose 1 = h*g - 3. Factor -4*y**2 + g - 2*y**3 + 2*y**2 - y + 3*y.
-2*(y - 1)*(y + 1)**2
Factor 0 + 8/13*y**2 + 2/13*y**3 + 8/13*y.
2*y*(y + 2)**2/13
Factor -3*s**3 + s**3 - 2*s**3 + 2*s**2 + 2*s**4.
2*s**2*(s - 1)**2
Let q be 10/4*(-7)/(175/(-20)). Factor 0 + 0*h - 1/3*h**5 - 1/3*h**q + 1/3*h**3 + 1/3*h**4.
-h**2*(h - 1)**2*(h + 1)/3
Factor 0*r + 0*r**2 - 2/7*r**4 + 0*r**3 - 2/7*r**5 + 0.
-2*r**4*(r + 1)/7
Factor -49 + 49 - b**2 - 20*b**3 - 5*b**4 + 20*b + 6*b**2.
-5*b*(b - 1)*(b + 1)*(b + 4)
Suppose 0 = -3*q + 230 + 226. Let z = 1070/7 - q. Find u, given that -16/7*u**4 + 0*u + 2*u**3 + 0 - 4/7*u**2 + z*u**5 = 0.
0, 2/3, 1
Let m(h) be the first derivative of 4*h**4 - 5 + 4/5*h**5 + 64*h - 32/3*h**3 - 16*h**2 - 1/3*h**6. Factor m(z).
-2*(z - 2)**3*(z + 2)**2
Let r(x) be the first derivative of 0*x**4 + 2/5*x**5 + 0*x + 1/6*x**6 - 2 - 2/3*x**3 - 1/2*x**2. Solve r(p) = 0 for p.
-1, 0, 1
Let g(j) be the first derivative of j**5/10 + 3*j**4/8 - j**2 + 8. Let g(k) = 0. What is k?
-2, 0, 1
Let i = -4 + 7. Let d = -143/5 - -29. Determine x so that -d*x**2 + 0 - 2/5*x**i + 0*x = 0.
-1, 0
Let -1/4 - 1/4*r**4 + 0*r + 1/2*r**2 + 0*r**3 = 0. What is r?
-1, 1
Let y = 6 + -4. Suppose 5*d - 5*v - 22 = -2, y = d + v. Suppose 3*i**4 + 5*i - 4*i**5 + 1 - 10*i**4 + i**5 - 2*i**d + 6*i**2 = 0. Calculate i.
-1, -1/3, 1
Let -9*m**2 + 0*m**4 + 8*m**3 + 0*m**4 - 5*m + 5*m**4 + 4 - 3*m = 0. What is m?
-2, -1, 2/5, 1
Let w(x) = -x**3 - 27*x**2 + 29*x + 32. Let p be w(-28). Let d(t) be the first derivative of 3 - 11/3*t**3 - 4*t**2 - 3/4*t**p + 4*t. Solve d(u) = 0 for u.
-2, 1/3
Factor -2*m**3 + 3/2*m**2 - 2 + 2*m + 1/2*m**4.
(m - 2)**2*(m - 1)*(m + 1)/2
Suppose -3*v + v = -2. Let 2*i**2 + 5 - v - 4*i - 2 = 0. Calculate i.
1
Let b(s) be the third derivative of -s**7/42 + s**6/15 - s**5/60 - s**4/12 - 11*s**2. Suppose b(m) = 0. What is m?
-2/5, 0, 1
Let u be (-4)/(-6)*(-4 - (-124)/28). Factor 4/7*b - u - 2/7*b**2.
-2*(b - 1)**2/7
Let q(l) = l**2 + 6*l - 216. Let g be q(-18). Factor g + 1/4*j**2 + 1/4*j.
j*(j + 1)/4
Suppose 4*m + 9 = -4*v - 3, 0 = -3*v - 15. Factor -2/5*c**3 + 0*c + 0*c**m + 0 + 2/5*c**4.
2*c**3*(c - 1)/5
Let m(l) be the third derivative of l**5/330 - l**4/66 + l**3/33 - 5*l**2. Factor m(v).
2*(v - 1)**2/11
Suppose 5*i - 5*r = 15, -3*r + r = 8. Let g be i - 6*(-2)/3. Factor f**g - 3*f**4 + 2*f**4 + 5*f**4.
f**3*(4*f + 1)
Suppose o = -3*i - 7 + 25, 32 = 2*o + 4*i. Factor -o*t + 9*t**2 + 3 - 12 + 12*t**3 + 3*t**4 + 3 - 6.
3*(t - 1)*(t + 1)*(t + 2)**2
Factor -4*f**3 + 2 + 2 - 6*f + 5*f**3 - 15*f**3 - 24*f**2.
-2*(f + 1)**2*(7*f - 2)
Suppose 5*w = 2*w + 15. Let b be w/((-10)/(-4))*1. Solve -3*t + 0*t**3 + 0 - 12*t**3 + 5*t - 1 + 11*t**b = 0 for t.
-1/3, 1/4, 1
Let s = -25/74 - -105/37. Suppose s*h**3 - 1 - 3/2*h**4 + 5/2*h**2 - 5/2*h = 0. Calculate h.
-1, -1/3, 1, 2
Suppose -18 = 2*m - 3*m. Let 18 + 0 + m*t - 6*t + 2*t**2 = 0. What is t?
-3
Let p(q) be the third derivative of q**5/20 + q**4/8 + 3*q**2. Factor p(n).
3*n*(n + 1)
Suppose 5*h + 3 = -7. Let x(y) = -y. Let g be x(h). Factor -4/5 + 2/5*a**g + 2/5*a.
2*(a - 1)*(a + 2)/5
Solve 4*g**4 + g**3 - 5*g**4 + 2*g**4 = 0 for g.
-1, 0
Let n = -4/11 + 19/22. Suppose 4*r = -3*i + 3, r - 2*i - 1 = -3*i. Factor 3/4*m**4 + r + 0*m + 1/4*m**3 - n*m**2.
m**2*(m + 1)*(3*m - 2)/4
Let z(p) = -p. Let n(k) = 28*k**2 - 8*k. Let o(b) = n(b) - 12*z(b). Factor o(x).
4*x*(7*x + 1)
Let 9/7*f - 3/7*f**3 + 6/7 + 0*f**2 = 0. What is f?
-1, 2
Let u(x) be the second derivative of 1/10*x**5 + x**3 - 1/2*x**4 - 3*x + 0 - x**2. Determine l, given that u(l) = 0.
1
Let f be (-3)/6 - (-28)/8. Suppose f*k = -0*k + 12. Let -2/11*l**2 - 6/11*l**k + 2/11*l**5 + 0 + 6/11*l**3 + 0*l = 0. Calculate l.
0, 1
Suppose -6*k = -12 - 6. Let n(z) be the third derivative of 0*z + 0*z**k + 1/6*z**4 - z**2 + 1/30*z**5 + 0. Let n(q) = 0. Calculate q.
-2, 0
Let l be 9/(-6)*(-16)/6. Let f(v) be the first derivative of -v - 2 + 2*v**2 - 5/3*v**3 + 1/2*v**l. Factor f(k).
(k - 1)**2*(2*k - 1)
Let z(j) be the first derivative of 2*j**5/55 + j**4/11 + 2*j**3/33 + 1. Factor z(y).
2*y**2*(y + 1)**2/11
Let v(n) be the third derivative of n**6/1620 + n**5/540 - n**3/6 - n**2. Let h(s) be the first derivative of v(s). Suppose h(i) = 0. What is i?
-1, 0
Let f(u) be the third derivative of 0*u**3 - 1/210*u**7 + 0 - 1/24*u**4 + 1/120*u**6 + 1/60*u**5 + u**2 + 0*u. Factor f(g).
-g*(g - 1)**2*(g + 1)
Let v(f) be the first derivative of -2/9*f - 2/45*f**5 - 2 - 4/9*f**3 