*4/30 + 4*i**3/15 - 4*i**2/5 + 4*i. Find u such that r(u) = 0.
2
Let k(n) be the third derivative of n**7/840 + n**6/360 - n**5/60 - 5*n**3/3 + 6*n**2. Let d(o) be the first derivative of k(o). Solve d(s) = 0 for s.
-2, 0, 1
Let q(s) = 8*s**2 - 22*s - 6. Let l(t) = -4*t**2 + 11*t + 3. Let z be 3/(-2)*(-104)/12. Let j(h) = z*l(h) + 6*q(h). Suppose j(m) = 0. Calculate m.
-1/4, 3
Let l be (-360)/(-35) + 2/(-7). What is j in 12*j**3 + 7*j**2 + 6*j - 3*j**4 - 12*j**2 - l*j**2 = 0?
0, 1, 2
Let w(o) be the first derivative of 0*o**2 - 3 + 1/15*o**4 + 0*o - 2/75*o**5 - 2/45*o**3. Factor w(c).
-2*c**2*(c - 1)**2/15
Solve 1/4*g**5 + 1/2*g**3 - 3/4*g - 1/2*g**2 - 1/4 + 3/4*g**4 = 0 for g.
-1, 1
Let a(z) be the first derivative of -3 - 21/5*z**5 - 2*z**3 - 27/4*z**4 + 0*z + 0*z**2. What is x in a(x) = 0?
-1, -2/7, 0
Suppose -2*g = 5*d - 212, -2*g + 172 = 4*d + 2*g. Let o = -122/3 + d. Factor 10/3*c**2 + o*c + 0 - 14/3*c**3.
-2*c*(c - 1)*(7*c + 2)/3
Let s(m) be the second derivative of 4*m**5/25 + 11*m**4/15 + 2*m**3/3 - 4*m**2/5 - 21*m. Factor s(d).
4*(d + 1)*(d + 2)*(4*d - 1)/5
Let t be ((-2)/2)/((-2)/8). Factor 2*o**t + 0 - 25*o**2 + 28*o**3 + 2*o**5 - 4 - 7*o**2 - 14*o**4 + 18*o.
2*(o - 2)*(o - 1)**4
Let o be 235/141*2/20*9. Factor 9/4*q**2 + o - 15/4*q.
3*(q - 1)*(3*q - 2)/4
Let -2*p**3 - 4 + 6*p + 0*p**3 + 3*p**3 - 3*p**3 = 0. Calculate p.
-2, 1
Let v(t) be the third derivative of -t**8/20160 + t**7/7560 + t**4/24 + t**2. Let j(d) be the second derivative of v(d). Let j(i) = 0. What is i?
0, 1
Find h, given that 0*h + 0*h**2 - 1/2*h**3 + 0*h**4 + 0 + 1/2*h**5 = 0.
-1, 0, 1
Find u, given that -1/4 + 1/4*u**2 - 1/4*u + 1/4*u**3 = 0.
-1, 1
Let c(t) be the second derivative of -10*t**4/21 - t**3/21 + t**2/7 + 22*t. Solve c(f) = 0.
-1/4, 1/5
Let b(f) be the third derivative of -f**7/735 + f**5/210 + 2*f**2. Determine z, given that b(z) = 0.
-1, 0, 1
Let f be 2*-3*(-2)/12. Let p be f - (3/(-3) - 0). Factor 0*t**p - 5*t**3 + t**2 - 3*t**2.
-t**2*(5*t + 2)
Suppose 20 = -2*h + 7*h - 2*j, 2*h + 4*j = -16. Let a be (-9)/(-3)*h/3. Find l such that -l**a - 2*l**2 + 0 + 6*l - 3 + 0 = 0.
1
Let -2/7*q**5 + 4/7*q**3 - 2/7 - 2/7*q - 2/7*q**4 + 4/7*q**2 = 0. Calculate q.
-1, 1
Let t(v) = -v - 5. Let z be t(-9). Let l = 2/7 + 3/14. Factor 1/4 - 1/2*a**3 - l*a**2 + 1/4*a**5 + 1/4*a**z + 1/4*a.
(a - 1)**2*(a + 1)**3/4
Let o(q) be the second derivative of q**7/70 - q**6/40 - 3*q**5/20 + q**4/8 + q**3 - q**2 + 2*q. Let t(n) be the first derivative of o(n). Factor t(z).
3*(z - 2)*(z - 1)*(z + 1)**2
Suppose -k = -4*k - 3. Let x be 0 + 0 + (-2)/k. Solve 4*p**5 + 4*p**4 - 2*p**5 - 2*p**2 - x*p + 0*p**4 - 2*p**2 = 0.
-1, 0, 1
Let v(w) be the third derivative of w**8/840 + w**7/105 + w**6/30 + w**5/15 + w**4/12 + w**3/2 - 4*w**2. Let z(p) be the first derivative of v(p). Factor z(k).
2*(k + 1)**4
Let h(v) be the second derivative of 3*v**5/20 + v**4 + 3*v**3/2 - 4*v. Factor h(x).
3*x*(x + 1)*(x + 3)
Let f = -558 - -561. Factor o + 1/3*o**f - 1/3 - o**2.
(o - 1)**3/3
Let s(v) = -v + 10. Let m be s(7). Suppose 0 = 2*q, -l = -2*l - m*q + 2. Factor 1/2*p**4 - 1/2*p**l + 0*p + 0 + 0*p**3.
p**2*(p - 1)*(p + 1)/2
Let 9/2*c**3 + 0 - 3*c**2 + 0*c + 9/2*c**4 - 3*c**5 = 0. What is c?
-1, 0, 1/2, 2
Find y such that 2/9*y**3 + 0 - 2/3*y**2 + 4/9*y = 0.
0, 1, 2
Let z = 359/18 + -39/2. Let d(w) be the first derivative of 1 + 1/12*w**4 + 2/3*w**2 + 0*w + z*w**3. Let d(g) = 0. Calculate g.
-2, 0
Let q be 1 + 1*-4*(-4)/48. Suppose -4*f + 25 = f, -2 = 4*b - 2*f. Let -8/3*v**2 - 10/3*v + b*v**3 + q = 0. Calculate v.
-1, 1/3, 2
Factor 9*s**4 - 39/2*s**3 - 6*s + 18*s**2 - 3/2*s**5 + 0.
-3*s*(s - 2)**2*(s - 1)**2/2
Let t(l) be the third derivative of l**6/420 - l**5/105 + l**4/84 - 7*l**2. Factor t(k).
2*k*(k - 1)**2/7
Let v(l) = -l**3 + 2*l**2 - 3*l. Let r be v(2). Let q be (-2)/r - (1 + -1). Find g, given that 1/3*g**4 + 1/3*g**5 - 1/3*g**3 + 0 - q*g**2 + 0*g = 0.
-1, 0, 1
Let o(t) = 2*t**3 - 8*t**2 + 2*t. Let b(h) be the second derivative of h**5/5 - 4*h**4/3 + 5*h**3/6 + 5*h. Let v(n) = -6*b(n) + 11*o(n). Factor v(d).
-2*d*(d - 2)**2
Suppose -12*s - 10*s**2 + 17*s + 30*s + 20 = 0. Calculate s.
-1/2, 4
Let x(u) be the third derivative of -u**5/30 + u**4/6 + u**3/2 - u**2. Let q(h) = -1. Let j(p) = 3*q(p) - x(p). Factor j(s).
2*(s - 3)*(s + 1)
Let r(u) be the second derivative of u**5/80 + u**4/12 + 5*u**3/24 + u**2/4 - u. Determine a, given that r(a) = 0.
-2, -1
Let v = 0 + 4. What is q in v*q**4 - 2*q + 3*q**2 - q + 3*q**3 - 7*q**4 = 0?
-1, 0, 1
Let t(b) = b**4 + b + 1. Let p(w) = -10*w**4 + 8*w**3 - w**2 + 5*w + 5. Let n(h) = 2*p(h) - 10*t(h). Find k, given that n(k) = 0.
0, 1/5, 1/3
Find v such that -3*v**2 - 12/7*v + 3/7*v**4 + 0 - 6/7*v**3 = 0.
-1, 0, 4
Let x(l) be the first derivative of l**4/4 + 5*l**3/3 + 4*l + 5. Let u be x(-5). Let 2/3*c**3 + 0 - 2/3*c**u + 0*c**2 + 0*c = 0. What is c?
0, 1
Factor -5*d - 5*d**3 + 5*d**2 + 0*d**3 + 5*d**2.
-5*d*(d - 1)**2
Suppose 3*q = -5*q + 32. Let v(g) be the first derivative of 4/3*g**3 + 0*g + g**2 + 1/2*g**q + 3. Find l such that v(l) = 0.
-1, 0
Suppose -5 - 3 = -4*p. Solve f**p + 11*f**2 + 2*f**3 + 16 + 20*f + 4*f = 0.
-2
Let v(o) = o**3. Let j(h) = -h**5 + 2*h**4 + 5*h**3 - 2*h**2 + h. Let w(z) = -j(z) + 5*v(z). Factor w(t).
t*(t - 1)**3*(t + 1)
Let c be (1 + 17)*4/8. Suppose -2*w + 3*o = o - 6, -2*o = 3*w - c. Factor -4*x**2 - 2*x**3 + 0*x**3 - x**w - x.
-x*(x + 1)*(3*x + 1)
Let r(o) be the second derivative of 3/80*o**5 - 3*o - 1/120*o**6 + 1/24*o**3 - 1/16*o**4 + 0 + 0*o**2. What is d in r(d) = 0?
0, 1
Let k(q) be the first derivative of 4*q**5/5 + 2*q**4 - 4*q**2 - 4*q + 6. Factor k(g).
4*(g - 1)*(g + 1)**3
Let t(f) be the third derivative of f**6/720 - f**5/60 + f**4/16 + 4*f**2. Solve t(k) = 0 for k.
0, 3
Let l(q) be the first derivative of -q**4/16 - q**3/4 + q**2/2 - 5. Factor l(g).
-g*(g - 1)*(g + 4)/4
Let b = 1195/4 - 297. Factor -1/2 - b*v**2 + 9/4*v.
-(v - 1)*(7*v - 2)/4
Let c(x) = -7*x**5 + 9*x**4 - 2*x**3 + 5*x**2 + 5. Let n(a) = 3*a**5 - 4*a**4 + a**3 - 2*a**2 - 2. Let o(y) = -2*c(y) - 5*n(y). Factor o(d).
-d**3*(d - 1)**2
Factor w + 2*w + w - 5*w**3 + w**3 + 40*w**2 - 40.
-4*(w - 10)*(w - 1)*(w + 1)
Find o, given that 1/4*o**2 + 1/2*o + 0 = 0.
-2, 0
Let q = -102 - -409/4. Solve -q*u**2 + 1/4*u + 0 = 0 for u.
0, 1
Suppose -2 = -4*l + 2*b + 8, 6 = 2*l - 2*b. Find t, given that -2*t - t - 2*t + 2*t - 3*t**l = 0.
-1, 0
Let r = 20 - 19. Let x(t) = -9*t**3 + 3*t**2 - 6*t. Let n(s) = s**3 + s. Let u(z) = r*x(z) + 6*n(z). Find b such that u(b) = 0.
0, 1
Let i = 890/3 - 296. Factor 2/3*a**4 + 0 + 0*a + 0*a**3 - i*a**2.
2*a**2*(a - 1)*(a + 1)/3
Let f(b) = b**3 + b**2 - 2*b + 2. Let k be f(2). Suppose 3*w = 2*g + k, -5*g - 2 = -4*g. Factor 2/5*j**3 + 0*j + 0 - 1/5*j**w.
j**2*(2*j - 1)/5
Let m(y) = -8*y**3 - y**2 + 37*y + 25. Let x(p) = 20*p**3 + 2*p**2 - 92*p - 62. Let i(b) = -12*m(b) - 5*x(b). Let i(t) = 0. Calculate t.
-1, 5/2
Let j(y) be the first derivative of -y**5/20 + 3*y**4/16 - y**3/4 + y**2/8 - 6. Factor j(u).
-u*(u - 1)**3/4
Let f = 54/5 - 643/60. Let r(b) be the first derivative of 1/8*b**2 - f*b**3 + 2 + 1/2*b. Let r(n) = 0. What is n?
-1, 2
Let g(b) be the first derivative of b**4 - 4*b**3 + 6*b**2 - 4*b - 2. Solve g(y) = 0.
1
Let b(r) = -2*r**2 - 10*r + 3. Let t be b(-5). Let -3/2*s**4 + 0*s**t + 3/2*s**2 + 0*s + 0 = 0. Calculate s.
-1, 0, 1
Let w(g) = g + 1. Let k(x) = 6*x + 17. Let n(r) = -k(r) + 4*w(r). Let p be n(-9). Suppose -q**3 + 5*q - p*q - q**2 = 0. Calculate q.
-1, 0
Let l(a) be the third derivative of 11*a**7/5880 - a**6/1260 - 2*a**3/3 - 6*a**2. Let d(s) be the first derivative of l(s). Solve d(c) = 0 for c.
0, 2/11
Let g(s) = -4*s**2 + 7*s - 5. Suppose 5*n - 8 = 17. Let u(z) = 3*z**2 - 6*z + 4. Let f(l) = n*u(l) + 4*g(l). Factor f(i).
-i*(i + 2)
Let j(v) = -3*v**4 - 18*v**3 - 39*v**2 - 24*v. Let s(m) = 6*m**4 + 36*m**3 + 79*m**2 + 49*m. Let b(l) = 13*j(l) + 6*s(l). Find d such that b(d) = 0.
-3, -2, -1, 0
Let n(r) be the first derivative of -r**8/420 - r**7/70 - r**6/90 + r**5/10 + r**4/3 + 8*r**3/3 + 7. Let q(i) be the third derivative of n(i). Factor q(j).
-4*(j - 1)*(j + 1)**2*(j + 2)
Let n(c) be the second derivative of c**5/50 + c**4/3 + 3*c**3/5 + 12*c. Factor n(r).
2*r*(r + 1)*(r + 9)/5
Let f(v) be the t