= 0.
0, 1, 2, 5
Let t(b) = 1. Let q(n) = n**2 + 29*n - 34. Let l(d) = q(d) + 4*t(d). Let l(s) = 0. Calculate s.
-30, 1
Let k(f) be the first derivative of -f**3/12 - 3*f**2/4 - 2*f + 210. Let k(x) = 0. What is x?
-4, -2
Let h(w) be the third derivative of -1/72*w**4 + 1/60*w**5 - 1/6*w**3 + 0*w + 1/360*w**6 + 20*w**2 + 0. Let h(r) = 0. What is r?
-3, -1, 1
Let d be (-12)/4 + (-513)/(-63). Factor 108/7 + d*m + 3/7*m**2.
3*(m + 6)**2/7
Let u(x) be the third derivative of -x**6/90 - 2*x**5/15 - 2*x**4/3 + x**3/3 - 4*x**2. Let d(n) be the first derivative of u(n). Let d(i) = 0. What is i?
-2
Let c(u) be the second derivative of -u**5/80 + u**4/16 + u**3/6 - 139*u. Factor c(t).
-t*(t - 4)*(t + 1)/4
Let j(d) = 45*d**3 + 55*d**2 + 394*d + 401. Let a(z) = 8*z**3 + 9*z**2 + 66*z + 67. Let b(n) = -34*a(n) + 6*j(n). Solve b(s) = 0 for s.
-2, 16
Suppose 0 = 3*n + n - 8. Suppose 5*q - 3*u = -5, -5*q - n + 32 = 4*u. Factor -f**2 - 9 + 5*f + 4*f - 5*f + q*f.
-(f - 3)**2
Let d(k) be the first derivative of k**4/2 + 2*k**2 + k + 17. Let w(q) = -q**3 - 5*q - 2. Let b(t) = 4*d(t) + 5*w(t). Determine f, given that b(f) = 0.
-1, 2
Let o be 18/8 - 10/40. Suppose -o*x - 2*l = 0, 5*x = -l - 2*l + 4. Determine d, given that 3*d**4 - 4*d**2 + 9*d**x + d**2 - 5*d**2 + d - 5*d**3 = 0.
-1/3, 0, 1
Let f(z) be the second derivative of z**7/105 + z**6/25 - z**5/50 - 7*z**4/30 + 4*z**2/5 + 18*z + 14. Solve f(b) = 0.
-2, -1, 1
Let m(i) = 2*i**2 + 1. Let k(w) = 36*w**2 - 52*w + 20. Let g(a) = -k(a) + 20*m(a). Let g(c) = 0. Calculate c.
-13, 0
Let k(d) = -2*d**2 - 35*d + 253. Let o be k(-23). Suppose 2/7 + 3/7*j - 4/7*j**3 + 1/7*j**5 - 2/7*j**2 + o*j**4 = 0. What is j?
-1, 1, 2
Let h be 98/5 - 2736/144. Let 18/5*g + h*g**2 - 21/5 = 0. Calculate g.
-7, 1
Determine o, given that 0*o + 2/3*o**3 + 0 + 1/6*o**2 = 0.
-1/4, 0
Let s(u) = u + 23. Let b be s(16). Let i = -37 + b. Suppose d**5 + 0*d**i + 9/4*d**4 + 0*d + 0 + 1/2*d**3 = 0. What is d?
-2, -1/4, 0
Let b(g) = g**2 + 4*g - 9. Let x be b(-6). Solve -45*p**x - 3*p**2 - 6*p + 22*p**3 + 26*p**3 = 0 for p.
-1, 0, 2
Suppose 24 = 5*t + 2*k, -67*k = -4*t - 65*k + 12. Let u(d) be the second derivative of 0*d**3 + 1/36*d**4 + 0 - 2/3*d**2 - t*d. Factor u(a).
(a - 2)*(a + 2)/3
Let i = 7/285 + 806/1995. Let z = -5 + 9. Factor -4/7*k - 1/7*k**z + i*k**2 + 2/7*k**3 - 4/7.
-(k - 2)**2*(k + 1)**2/7
Let j be -1 - (20/5 - 24). Factor -8 + 1 + j*c**2 + 16*c + 3 + c**2.
4*(c + 1)*(5*c - 1)
Let w(s) be the second derivative of -s**4/24 - 7*s**3/12 - 3*s**2 + 46*s. Find m such that w(m) = 0.
-4, -3
Let q = 32 - 14. Factor 5*h + q*h**3 - 24*h**3 - 2*h + 3*h**5.
3*h*(h - 1)**2*(h + 1)**2
Let u be -9*(28 - 6939/243). Solve 24*x**u + 0 - 2/3*x**2 + 2/3*x**4 - 76/3*x**3 + 4/3*x = 0 for x.
-1, -1/4, 0, 2/9, 1
Let h = 185 + -3697/20. Let v(o) be the second derivative of 0*o**2 - 4*o + 1/2*o**3 + 0 + h*o**5 - 1/2*o**4. Determine s so that v(s) = 0.
0, 1
Let k(i) be the third derivative of 1/100*i**5 + 319/350*i**7 + 2/5*i**3 + 47/40*i**6 + 15*i**2 + 0*i + 121/560*i**8 - 4/5*i**4 + 0. Let k(d) = 0. What is d?
-1, 2/11
Suppose 3*n - 4*k = 38, 4*k + 4 = -2*n - 4. Let d = -8 - -11. Suppose -5*w**3 - d*w**2 - n*w - 3*w**2 + 3*w**3 + 0*w**2 - 2 = 0. Calculate w.
-1
Let g(z) be the second derivative of 0 - z**3 + 0*z**4 + 3/10*z**5 + 1/10*z**6 - 3/2*z**2 + 9*z. Factor g(p).
3*(p - 1)*(p + 1)**3
Suppose -3*g + 14 = -2*l + 5, -g - l = -3. Let d(h) be the third derivative of 0 + 1/15*h**5 - 1/3*h**4 + 0*h**g + 0*h - 8*h**2. What is f in d(f) = 0?
0, 2
Let w = -16/3993 + 1363/7986. Factor -2/3 + 5/6*z - w*z**2.
-(z - 4)*(z - 1)/6
Let y(p) be the third derivative of 45*p**2 + 0*p + 5/6*p**3 + 1/12*p**5 + 0 - 5/12*p**4. Factor y(t).
5*(t - 1)**2
Let x(w) be the second derivative of -13*w + 0 - 1/150*w**5 + 2/15*w**2 - 1/45*w**4 + 1/45*w**3. Factor x(u).
-2*(u - 1)*(u + 1)*(u + 2)/15
Find c, given that -4/3*c**2 - 1/3*c**3 + 2 - 1/3*c = 0.
-3, -2, 1
Let u = 5/22 - 2/33. Let m(c) = c**3 - 21*c**2 + 22*c - 38. Let w be m(20). Factor u*n + 1/6*n**w - 1/3.
(n - 1)*(n + 2)/6
Let 3/7*z**2 + 270/7 - 141/7*z = 0. Calculate z.
2, 45
Let h be (-36)/(-16) - (-6)/(-24). Suppose 7 - 17 = -3*n - h*b, 4*n - b = 6. Solve 1/2 - 1/2*f**4 + f + 0*f**n - f**3 = 0.
-1, 1
Determine t, given that 15/2 + 7*t - 1/2*t**2 = 0.
-1, 15
Factor -54 + 1/3*d**4 + 17/3*d**3 - 39*d + 61/3*d**2.
(d - 2)*(d + 1)*(d + 9)**2/3
Factor 270*u**2 + 14 + 3*u**3 - 339*u**2 + 35 + 20 - 3*u.
3*(u - 23)*(u - 1)*(u + 1)
Let j(a) = -1. Let r(c) be the first derivative of c**3/3 - c**2 + 3*c - 20. Let u(b) = 6*j(b) + 2*r(b). Factor u(z).
2*z*(z - 2)
Let q(s) = 7*s. Let x(r) = 8*r - 1. Let b(d) = 6*q(d) - 5*x(d). Let w be b(-1). Factor 0 + 3/4*t**w - 3/4*t**4 + 0*t - 3/2*t**5 + 0*t**2.
-3*t**3*(t + 1)*(2*t - 1)/4
Let w(o) be the first derivative of o**4/10 + 28*o**3/15 + 43*o**2/5 + 12*o - 151. Factor w(a).
2*(a + 1)*(a + 3)*(a + 10)/5
Let h(b) be the second derivative of b**4/6 + 2*b**3/3 + 976*b. Let h(l) = 0. What is l?
-2, 0
Suppose 5*a - 3*a = 10. Let q(z) = 2*z**2 - 7*z + 9. Let l be q(a). Factor -l + 4*r + 8 - r**2 - 12*r.
-(r + 4)**2
Suppose -m - 3*g + 5*g = -5, -18 = -5*m + 3*g. Suppose -m*a = 2*a - 10. Factor 0*d + 0 - 4/7*d**a + 10/7*d**3 + 2*d**4.
2*d**2*(d + 1)*(7*d - 2)/7
Let a(o) be the first derivative of 2*o**6/9 - 4*o**5/3 - 13*o**4/3 - 28*o**3/9 + 756. Determine c, given that a(c) = 0.
-1, 0, 7
Let a(x) be the third derivative of 1/3*x**5 - 4/3*x**3 - 1/15*x**6 + 0*x - 2*x**2 + 0 - 1/6*x**4. Find b such that a(b) = 0.
-1/2, 1, 2
Let b(r) = 3*r**4 - r**3 - 4*r**2 + r - 1. Let j(t) = -29*t**4 + 367*t**3 + 1050*t**2 + 907*t + 251. Let u(n) = -b(n) + j(n). Solve u(q) = 0 for q.
-1, -3/4, 14
Let x be 40/(-80) + -33*(-2)/4. Suppose x = 9*s - 2. Factor 1/4*n**4 - 3/4*n**3 + 0 + 0*n + 1/2*n**s.
n**2*(n - 2)*(n - 1)/4
Let k(y) be the third derivative of -1/270*y**5 - 1/54*y**4 + 0*y - 1/27*y**3 - 15*y**2 + 0. Factor k(i).
-2*(i + 1)**2/9
Factor -35/2*y + 18 - 1/2*y**2.
-(y - 1)*(y + 36)/2
Let c(w) be the first derivative of -w**5 + 5*w**4/4 + 25*w**3/3 + 15*w**2/2 - 37. Determine f so that c(f) = 0.
-1, 0, 3
Let j be 40/(-16)*(-44)/10. Factor 1 + 2 + 4 - j + 4*l**2.
4*(l - 1)*(l + 1)
Let t(d) be the third derivative of d**6/300 - 12*d**5/25 + 144*d**4/5 - 4608*d**3/5 + 4*d**2 + 14*d. Determine c so that t(c) = 0.
24
Let o(u) = -20*u**5 - 39*u**4 + 16*u**3 + 42*u**2 - 6*u - 3. Let d(f) = -f**5 - f**4 + f**3 - 2*f + 1. Let x(n) = 5*d(n) - o(n). Find r such that x(r) = 0.
-2, -1, -2/3, 2/5, 1
Suppose l + 3*q - 17 = 0, 6*l - 15 = l - q. Let k(n) be the second derivative of -1/30*n**4 + 1/5*n**3 + 0 - 5*n + 0*n**l. Factor k(z).
-2*z*(z - 3)/5
Let 2*a**5 - 7/2*a**3 + 3/2*a - 1/2*a**2 + 0 + 1/2*a**4 = 0. What is a?
-1, 0, 3/4, 1
Let b(x) be the first derivative of -1/2*x**2 + 1 - 7/30*x**5 + 0*x + 0*x**3 - 1/6*x**4. Let a(p) be the second derivative of b(p). Factor a(i).
-2*i*(7*i + 2)
Let t be 2/((-7)/((-42)/8)) - 1. Suppose 4*n = -4*k + 8*n, -21 = -4*k - 3*n. Factor -5/4*f**4 + 5/4*f**2 + 0 + t*f**k - 1/2*f.
-f*(f - 1)*(f + 1)*(5*f - 2)/4
Let n(d) be the first derivative of -d**5/40 + d**4/6 - 23*d - 20. Let f(q) be the first derivative of n(q). Factor f(k).
-k**2*(k - 4)/2
Suppose 3*j = -5*d + 8*j, -2*d + 5*j - 6 = 0. Find a, given that 5 + 3 + 4*a - 12*a**d + 53*a**4 - 49*a**4 - 4*a**3 = 0.
-1, 1, 2
Suppose 4*w - 3*m = 6, -w + 4*m - 11 = -2*w. Let r(g) = g**3 + g**2 + 3. Let y be r(0). Determine t, given that 5*t**3 - 2*t + 0*t - w*t**y = 0.
-1, 0, 1
Let r be (-4)/(-10)*(-310)/(-372)*15. Let s(h) be the third derivative of 0 + 1/84*h**4 + 1/105*h**r + 0*h**3 + 1/420*h**6 + 12*h**2 + 0*h. Factor s(t).
2*t*(t + 1)**2/7
Factor -2*u**5 - 56/5*u**4 + 0 - 96/5*u**3 + 32/5*u - 32/5*u**2.
-2*u*(u + 2)**3*(5*u - 2)/5
Let i = 8 + -117/14. Let m = i - -6/7. Factor k**2 - m*k + 0 - 1/2*k**3.
-k*(k - 1)**2/2
Suppose -13*b = -20*b + 7329. What is t in 5*t**4 + 505*t**4 + 612*t**2 + 108*t - 61*t**5 + 136*t**5 + b*t**3 = 0?
-3, -2/5, 0
Suppose 5*m = 2*y + 30, 4*m = 6*m + 4*y - 36. Suppose -5*h + 41 - 6 = 0. Factor m*d**2 - 4*d - h*d**2 + 3*d.
d*(d - 1)
Factor -520/9*q + 16/3 - 294*q**3 + 686/9*q**4 + 644/3*q**2.
2*(q - 3)*(7*q - 2)**3/9
Let j = 11703/25 + -468. Let l(z) be the first derivative of -1/10*z**6 + 3/5*z - 3 - 3/10