/7
Let a(y) be the first derivative of -y**6/360 + y**5/120 + 2*y**3/3 + 2. Let v(z) be the third derivative of a(z). Factor v(n).
-n*(n - 1)
Let -1/4*j**5 - 1/2*j**3 + 3/4*j**4 + 0*j + 0*j**2 + 0 = 0. Calculate j.
0, 1, 2
Let w(p) be the first derivative of 4*p**2 - 1 + 8*p + 2/3*p**3. Factor w(f).
2*(f + 2)**2
Let u(z) = -20*z**2 + 56*z - 36. Let h(s) = s + 1. Let x(d) = 12*h(d) + u(d). Determine q, given that x(q) = 0.
2/5, 3
Let u(o) = -2*o**4 - 10*o**3 + 14*o**2 - 10*o + 4. Suppose 4*z - 9 = -5. Let a(x) = -x**4 - x**2 + x. Let d(h) = z*u(h) - 4*a(h). Factor d(c).
2*(c - 2)*(c - 1)**3
Suppose 7*d - 4*d + 5 = 4*u, 5*d - 3 = u. Let o = -90 + 90. Factor o*v + 1/3*v**3 + 0 + 0*v**u.
v**3/3
Let y(j) be the second derivative of -j**4/54 - 8*j**3/27 - 16*j**2/9 + 3*j. Solve y(h) = 0.
-4
Let g(v) be the first derivative of -1/9*v**3 - 1 + 0*v**2 + 1/3*v. What is j in g(j) = 0?
-1, 1
Factor -x**4 - 2*x**5 - x**4 - 4*x + 4*x**5 + 5*x**3 + 10*x**2 - 11*x**3.
2*x*(x - 1)**3*(x + 2)
Let l(a) be the first derivative of -15*a**4/4 - 10*a**3/3 + 23. Factor l(q).
-5*q**2*(3*q + 2)
Suppose -10*x + 32 = -2*x. Let c be -1 - -6 - (5 + -2). Factor -1/3*n**x + 0 + n**c - 2/3*n + 0*n**3.
-n*(n - 1)**2*(n + 2)/3
Let i be (-196)/(-231) + 4/(-22). Let u(z) be the first derivative of 2 - i*z**3 + 2*z**2 - 4*z**4 + 0*z - 2*z**5. Determine r so that u(r) = 0.
-1, 0, 2/5
Let w = 45 - 89/2. Factor 1/2*k**2 + 0 - w*k.
k*(k - 1)/2
Let j(d) be the first derivative of d**4/6 - d**2 + 6*d + 5. Let q(r) be the first derivative of j(r). Factor q(w).
2*(w - 1)*(w + 1)
Suppose 48 = 6*x - 2*x. Let h be 9/x*(-12)/(-18). Factor -1/2 - w + h*w**4 + 0*w**2 + w**3.
(w - 1)*(w + 1)**3/2
Suppose 22 = -t - 5*q, 2*t - 2*q = -0*q + 16. Factor -1/2*s - 1/4*s**t + 3/4*s**2 + 0.
-s*(s - 2)*(s - 1)/4
Let o = 208 - 100. Solve -243*r**3 - 105*r**4 - 15 + o*r - 31*r**2 + 25*r**2 - 9 = 0.
-2, -1, 2/7, 2/5
Let x(h) be the first derivative of 5*h**3/3 + 2*h**2 - h - 30. Factor x(r).
(r + 1)*(5*r - 1)
Let t = -3 + 6. Let a be -2*(-5)/(-10)*-2. Factor -4*x**a + 0*x + 2*x - t*x + 5*x + x**3.
x*(x - 2)**2
Let j(t) be the first derivative of -t**6/6 + 2*t**5/5 - 2*t**3/3 + t**2/2 + 6. Suppose j(b) = 0. Calculate b.
-1, 0, 1
Let w = -219 + 219. Let 1/3*f**5 + w + f**2 + 1/3*f**3 - 2/3*f - f**4 = 0. Calculate f.
-1, 0, 1, 2
Let o be 1 - 0 - (3 - 5). Solve -4/3 - 10*h**o - 3*h**4 - 20/3*h - 37/3*h**2 = 0.
-1, -2/3
Solve -1/2*n - 1/2*n**2 + 0 = 0 for n.
-1, 0
Let f be (-5)/(-4) + (-117)/(-156). Factor 1/2*m**4 - 1/2 - m**3 + 0*m**f + m.
(m - 1)**3*(m + 1)/2
Let s(a) be the first derivative of 7/10*a**2 - 1/5*a + 3 - 4/5*a**3. Factor s(l).
-(3*l - 1)*(4*l - 1)/5
Let f(p) be the third derivative of -p**6/210 - p**5/105 + 2*p**4/21 + 8*p**3/21 + 6*p**2. Factor f(q).
-4*(q - 2)*(q + 1)*(q + 2)/7
Let r(c) be the second derivative of -c**4/90 - c**3/9 - 2*c**2/5 - 16*c. Factor r(f).
-2*(f + 2)*(f + 3)/15
Let -1/2*q**2 - q + 1/2*q**4 + 0 + q**3 = 0. Calculate q.
-2, -1, 0, 1
Let s(p) be the third derivative of -10*p**8/21 - 92*p**7/105 - 2*p**6/5 + p**5/6 + p**4/6 - 8*p**2. Suppose s(r) = 0. What is r?
-1/2, -2/5, 0, 1/4
Determine r so that 15*r - 4*r**2 + 15*r**2 - 7*r**2 - r**2 + 18 = 0.
-3, -2
Suppose 2*f = -2*f + 8. Suppose -2*y + 12 = f*y. Find t such that -y*t**2 + 2*t**3 - 3*t + 2*t**3 - 1 - 5*t**3 = 0.
-1
Let u(y) be the second derivative of 0 + y**2 + 0*y**3 + 0*y**4 - 1/60*y**5 - y. Let f(r) be the first derivative of u(r). Let f(j) = 0. What is j?
0
Suppose 0 = -5*i + 15, -2*i - 3*i = -n - 11. Suppose 0*u = -2*u - 4*g + 4, -n*u + 2*g - 2 = 0. Suppose 0*h + 1/2*h**3 + u - 1/2*h**2 = 0. Calculate h.
0, 1
Let g(j) = 144*j**2 - 168*j + 48. Suppose -4*n + 0*n = 12. Let i(h) = -145*h**2 + 168*h - 48. Let l(z) = n*i(z) - 2*g(z). What is a in l(a) = 0?
4/7
Determine g so that -22 + 5*g**4 - 22 + 80*g**2 + 44 + 40*g**3 = 0.
-4, 0
Determine q so that -4*q**2 - 6 + 4*q + 22 - 8 = 0.
-1, 2
Let v(s) = s. Let r = 12 - 6. Let a(o) = o**2 + o + 2. Let j(y) = r*v(y) + 3*a(y). Find l, given that j(l) = 0.
-2, -1
Let u(h) be the third derivative of 1/3*h**4 + 1/84*h**8 - 1/10*h**6 + 0*h + 1/15*h**5 - 2/105*h**7 + 0*h**3 + 0 + 10*h**2. Determine n, given that u(n) = 0.
-1, 0, 1, 2
Let r be (-3)/20*(-6)/27. Let g(v) be the third derivative of 1/6*v**4 + v**2 - 1/6*v**5 + 0*v + 1/21*v**7 + 0*v**3 - r*v**6 + 0. Factor g(k).
2*k*(k - 1)*(k + 1)*(5*k - 2)
Let o(v) = -v**2 + 10*v + 3. Let y be o(10). Suppose 0 = 2*s + 2*r - 10, -y*s + 21 = 4*r + 3. Factor 4*b**4 + 0*b**2 + 2*b - 2*b**s - 2*b**2 - 2*b**5.
-2*b*(b - 1)**3*(b + 1)
Let d(y) be the third derivative of y**7/1260 + y**6/360 - y**5/30 + 5*y**4/24 + 6*y**2. Let a(h) be the second derivative of d(h). Factor a(q).
2*(q - 1)*(q + 2)
Let q be (15/(-25))/((-16)/20). Factor 0 - 3/4*o**2 + q*o.
-3*o*(o - 1)/4
Suppose -4*b + 13 = 5. Solve 0*r**2 - 4 + 2*r - 4*r**2 + 0*r**2 + 6*r**b = 0 for r.
-2, 1
Let n(q) be the first derivative of q**3/9 - q**2/6 - 2*q/3 + 4. What is c in n(c) = 0?
-1, 2
Suppose 2*v = 4, -3*m - 8 = -4*m - 4*v. Factor 0*q + 2/5*q**2 + 2/5*q**3 + m.
2*q**2*(q + 1)/5
Suppose -4*c + 7*c = 60. Let 2*j + c - j**2 - 21 + 0*j = 0. Calculate j.
1
Let j(s) = s**2 + 6*s. Let r be j(-6). Let i(m) be the third derivative of 0*m + 1/24*m**4 + r + m**2 + 1/20*m**5 + 0*m**3. Factor i(t).
t*(3*t + 1)
Let p(h) be the second derivative of -1/70*h**5 - 4/21*h**3 + 0*h**2 - 2/21*h**4 + 3*h + 0. Suppose p(c) = 0. What is c?
-2, 0
Let w(u) = u**4 + u**3 + u**2. Suppose 6 = -0*i + i. Let q(k) = -5*k**3 + 3*k**2 + k - i*k**2 - 5*k**4 - k**5 - 2*k**4. Let v(b) = -q(b) - 5*w(b). Factor v(s).
s*(s - 1)*(s + 1)**3
Let o(u) be the third derivative of 5*u**8/336 + u**7/42 - u**6/24 - u**5/12 + 36*u**2. Factor o(y).
5*y**2*(y - 1)*(y + 1)**2
Let n(q) be the third derivative of -q**6/40 + q**5/20 + q**4/2 - 2*q**3 + 18*q**2. Find d, given that n(d) = 0.
-2, 1, 2
Suppose -4 = -4*g - 4*p, -3*g + 2*g = -4*p - 16. Suppose -2*m - 8 = -g*m. Determine y so that -2/3*y**2 - 2*y**m + 0*y + 0 + 6*y**5 - 10/3*y**3 = 0.
-1/3, 0, 1
Let l = -3 - -3. Suppose -v - 5*u = -2*v + 7, -4*v + 3*u + 11 = l. Factor -2*s**3 + 1/2*s**v + 2*s - 1/2.
-(s - 1)*(s + 1)*(4*s - 1)/2
Let u = -67 - -203/3. Let 2*v**3 - 8/3*v + 0*v**2 + 0 - u*v**4 = 0. Calculate v.
-1, 0, 2
Suppose 3*b + 27 = -3*z, -2*z + 2*b - 3 = -b. Let v = -3 - z. Factor 0*g**4 - 2*g**3 - v*g**2 + 2*g**5 + 2*g**4 + g**2.
2*g**2*(g - 1)*(g + 1)**2
Let u(g) be the second derivative of g**4/4 - g**3 - 9*g**2/2 + 17*g. Factor u(n).
3*(n - 3)*(n + 1)
Solve -8/15*b**3 - 2/15*b**4 - 2/15 - 4/5*b**2 - 8/15*b = 0.
-1
Let w(a) be the first derivative of -3/2*a**2 + 1/3*a**3 - 3 + 1/5*a**5 + 3/4*a**4 - 2*a. Factor w(t).
(t - 1)*(t + 1)**2*(t + 2)
Solve 1/7*i**5 + 25/7*i**2 + i**4 + 16/7*i + 19/7*i**3 + 4/7 = 0 for i.
-2, -1
Let w(k) = 6*k**2 + 6*k + 4. Let d be ((-9)/6)/((-6)/8). Let b(a) = -2*a + a + a**d - 1 - 2*a**2. Let y(u) = -4*b(u) - w(u). Find r such that y(r) = 0.
-1, 0
Suppose 2*d - 4*t = -12 + 4, -2*t + 22 = 2*d. Suppose 2*h + 96 = 4*q, -q - 5*h - d = -2*q. Factor 4*y**2 - 16 + y**2 - 8*y + q*y**3 + 6*y**4 + 23*y**2.
2*(y + 1)*(y + 2)**2*(3*y - 2)
Factor 2/3*h**2 - 1/6*h**5 + 2/3*h**4 + 0 - h**3 - 1/6*h.
-h*(h - 1)**4/6
Let o(s) = s**3 - 16*s**2 - 15*s - 10. Let z(h) = 9*h**3 - 129*h**2 - 120*h - 81. Let n(t) = -33*o(t) + 4*z(t). Factor n(a).
3*(a + 1)**2*(a + 2)
Let b = 181/4 + -45. Let p be -1*(2 + 27/(-12)). Factor 1/4*n**2 - b*n**4 + 1/4*n**3 + 0 - p*n.
-n*(n - 1)**2*(n + 1)/4
Let r(d) be the first derivative of 2*d**3/9 - 2*d**2 + 6*d - 21. Factor r(m).
2*(m - 3)**2/3
Suppose 18*p + 90*p**4 - 172*p**4 - 21*p**2 + 85*p**4 = 0. What is p?
-3, 0, 1, 2
Let 0 + 2/9*l**2 + 2/9*l = 0. What is l?
-1, 0
Let z be (38/(-30))/((-12)/20) - -1. What is j in -2/9*j**5 - z*j**3 - 2*j - 4/3*j**4 - 32/9*j**2 - 4/9 = 0?
-2, -1
Let r be (-4182)/14 + 2/(-7). Let z = -889/3 - r. Let 2/3*m + z*m**2 - 4/9 + 14/9*m**3 = 0. What is m?
-1, 2/7
Let d(i) be the second derivative of -7*i**6/300 + 13*i**5/40 - 31*i**4/20 + 8*i**3/3 - 8*i**2/5 + 27*i. Let d(l) = 0. Calculate l.
2/7, 1, 4
Let q(z) be the third derivative of z**7/945 - z**5/270 - 8*z**2. Factor q(h).
2*h**2*(h - 1)*(h + 1)/9
Suppose -10 = -6*t + t. Determine a, given that a**3 - 7*a**2 - t*a**3 + 8*a**2 = 0.
0, 1