 Let k(t) be the second derivative of 0 + j*t**4 - 1/18*t**3 + 2*t + 0*t**2. Factor k(u).
u*(u - 1)/3
Let v(p) be the first derivative of p**8/224 - p**6/80 - p**2 - 10*p + 35. Let s(o) be the second derivative of v(o). Factor s(n).
3*n**3*(n - 1)*(n + 1)/2
Let r(f) be the first derivative of f**7/189 + 2*f**6/135 + f**5/90 - 21*f - 18. Let q(n) be the first derivative of r(n). Solve q(s) = 0 for s.
-1, 0
Let n(t) = 4*t**5 + 4*t**4 - 12*t**3 - 24*t**2 - 10*t. Let o(g) = 13*g**5 + 13*g**4 - 35*g**3 - 71*g**2 - 29*g. Let u(p) = 14*n(p) - 4*o(p). Factor u(h).
4*h*(h - 3)*(h + 1)**2*(h + 2)
Let l(t) be the first derivative of t**6/15 - 38*t**5/75 + 3*t**4/2 - 98*t**3/45 + 8*t**2/5 - 8*t/15 - 114. Let l(i) = 0. What is i?
1/3, 1, 2
Let y(s) be the first derivative of -s**5/40 + 7*s**3/24 + 3*s**2/8 - 36. Let y(k) = 0. Calculate k.
-2, -1, 0, 3
Let u = -813 - -818. Let a(w) be the first derivative of -u + 0*w + 4/9*w**3 + 0*w**2 + 1/6*w**4. Factor a(s).
2*s**2*(s + 2)/3
Let c be (14 + (-94)/8)*4/18. Factor 0 + 1/2*y**2 + c*y.
y*(y + 1)/2
Solve 0*j + 2/7*j**2 - 1/7*j**5 + 0 + 4/7*j**4 - 5/7*j**3 = 0 for j.
0, 1, 2
Suppose 42 + 63 = 5*p. Let b(s) = 3*s - p*s**2 - 7*s**2 + 19*s**2. Let m(o) = o**3 + 19*o**2 - 7*o. Let k(j) = 7*b(j) + 3*m(j). Suppose k(c) = 0. What is c?
0, 2
Let w(n) = 7*n**5 - 2*n**4 + 4*n**3 - 6*n**2 - 6*n - 6. Let k(u) = u**5 - u**4 - u**2 - u - 1. Let h(z) = 30*k(z) - 5*w(z). Determine t so that h(t) = 0.
-2, 0
Factor 0 - 2/7*w - 1/7*w**3 + 3/7*w**2.
-w*(w - 2)*(w - 1)/7
Let j(r) be the second derivative of -1/5*r**3 + 0 + 1/30*r**4 - 3*r + 2/5*r**2. Factor j(d).
2*(d - 2)*(d - 1)/5
Let p(w) be the first derivative of 4*w**3/9 - 143*w**2/6 - 12*w + 832. Find q such that p(q) = 0.
-1/4, 36
Let t = -223 - -232. Suppose -3*y + 3 = -t. Factor 8/11*v**3 - 10/11*v**2 + 4/11*v + 0 - 2/11*v**y.
-2*v*(v - 2)*(v - 1)**2/11
Let g be (-123)/(-533) - (-252)/91. Suppose 3*q**4 - 2/3 - 11/3*q**g + 11/3*q - 7/3*q**2 = 0. What is q?
-1, 2/9, 1
Let c(s) = 3*s**3 - 3*s**2 - 165*s + 165. Let p(o) = -3*o**3 + 4*o**2 + 165*o - 166. Let h(f) = 2*c(f) + 3*p(f). Factor h(a).
-3*(a - 8)*(a - 1)*(a + 7)
Factor -124 - 124 + 6*a + 257 + a**2.
(a + 3)**2
Factor 11*p - 53 + 117 + 18*p + 8*p + p**3 + 12*p**2 + 11*p.
(p + 4)**3
Let c(i) = i + 1. Let s(z) be the second derivative of -5*z**4/12 - 2*z**3/3 + z**2/2 - 7*z. Let y(x) = -c(x) + s(x). Suppose y(f) = 0. What is f?
-1, 0
Suppose -5*u**2 - u**2 + 12*u**2 - 5*u - u**2 - 30 = 0. What is u?
-2, 3
Let c = -136 - -141. Solve 10*i + 15*i**2 - 4*i**4 - 5*i**5 - c*i**4 - 6*i**4 - 5*i**3 = 0.
-2, -1, 0, 1
Let a(d) be the third derivative of 0*d**5 + 0*d**4 + 1/420*d**7 + 0 + 16*d**2 + 0*d**3 + 1/240*d**6 + 0*d. Factor a(g).
g**3*(g + 1)/2
Let z(r) be the third derivative of -4/33*r**3 + 1/33*r**4 + 0*r + 0 - 1/330*r**5 - 6*r**2. Factor z(j).
-2*(j - 2)**2/11
Suppose 0 = -5*i + 50 - 30, -8*r + 8 = 2*i. Factor -2/13 + r*s + 2/13*s**2.
2*(s - 1)*(s + 1)/13
Let h(z) be the third derivative of -7*z**8/288 - 59*z**7/180 - 209*z**6/240 + 121*z**5/40 + z**2 - 33. Factor h(m).
-m**2*(m - 1)*(7*m + 33)**2/6
Let v be (100/(-825))/(14/(-77)). Find m such that v*m - 8/15*m**2 - 4/15 + 2/15*m**3 = 0.
1, 2
Suppose 4*j = 17 + 39. Solve 2*s**4 - 2*s**2 + 2*s**4 - j*s**3 - 6*s**2 + 10*s**3 = 0.
-1, 0, 2
Suppose 4*y = 2*s - 14, -5*s + 0*y + 13 = y. Let i(v) = -45*v**3 + 117*v**2 + 66*v + 12. Let j(d) = d**3 - d**2 - d + 1. Let f(x) = s*j(x) - i(x). Factor f(o).
3*(o - 3)*(4*o + 1)**2
Let b(a) be the third derivative of -a**6/900 + a**5/75 - a**4/20 + 11*a**3/6 + 12*a**2. Let t(k) be the first derivative of b(k). Factor t(g).
-2*(g - 3)*(g - 1)/5
Let b(l) = 48*l**2 - 5 + 4*l - 3 - 49*l**2. Let i(d) = -1. Let g(o) = b(o) - 5*i(o). Determine z, given that g(z) = 0.
1, 3
Solve 97/3*n - 4/3*n**2 - 8 = 0 for n.
1/4, 24
Let u(f) be the first derivative of f**5/30 - 11*f**4/24 + 17*f**3/9 - 2*f**2 + 27. Determine x, given that u(x) = 0.
0, 1, 4, 6
Let m = -14 + 20. Let o = m + -3. Factor 3*c**5 + 3*c**4 - o*c**3 + 0*c**3 - 5*c**2 + 2*c**2.
3*c**2*(c - 1)*(c + 1)**2
Let m be (-1)/(-2) - (-2859)/(-1474). Let x = 135/67 - m. Let 14/11*f**2 - x*f - 12/11 = 0. Calculate f.
-2/7, 3
Let m(u) be the second derivative of -u**8/224 - u**7/504 + 5*u**6/144 + u**5/12 - 7*u**4/6 + 10*u. Let b(r) be the third derivative of m(r). Factor b(p).
-5*(p - 1)*(2*p + 1)*(3*p + 2)
Let g(u) be the third derivative of 1/60*u**6 + 0 + 0*u**4 + 12*u**2 + 0*u - 4/3*u**3 + 1/10*u**5. Determine a, given that g(a) = 0.
-2, 1
Factor -26/9*k**2 - 22/9 + 2/9*k**3 + 46/9*k.
2*(k - 11)*(k - 1)**2/9
Let j(o) be the first derivative of o**4/34 - 2*o**3/17 - o**2/17 + 6*o/17 + 72. Let j(h) = 0. Calculate h.
-1, 1, 3
Suppose -5*d - 5*n + 3 = -2, -3*d = 2*n - 5. Factor -2*u**2 + 1676 - 1676 + 2*u**d.
2*u**2*(u - 1)
Factor -495*z**2 - 112 + 765*z + 7 + 60*z**3 - 325*z + 7*z**4 + 13*z**4.
5*(z - 3)*(z + 7)*(2*z - 1)**2
Solve 2*p - 2*p**3 + 7*p**3 + p**5 - 8*p**3 - p**2 + p**4 = 0 for p.
-2, -1, 0, 1
Let j(u) = -u**2 - 2*u + 1. Let i(z) = z**2 + z - 1. Suppose 2*n - 8*n = 6. Let b(l) = n*j(l) - 2*i(l). Solve b(f) = 0 for f.
-1, 1
Let a(n) be the third derivative of -5/8*n**4 + 3/20*n**5 + 0 - n**3 + 5*n**2 + 0*n. Factor a(i).
3*(i - 2)*(3*i + 1)
Factor -6*t**5 + 3*t**5 - 278*t**2 + 266*t**2 + 9*t**4.
-3*t**2*(t - 2)**2*(t + 1)
Let s = -14668/7 + 2106. Let l = s - 356/35. Factor -l*f**4 + 0*f**3 + 0*f - 2/5 + 4/5*f**2.
-2*(f - 1)**2*(f + 1)**2/5
Suppose -4*f + 7 = -5. Let a be 11 + (6 - -4 - 2 - 6). Factor -10*x - x**3 + a*x - 2*x**f.
-3*x*(x - 1)*(x + 1)
Let l = 429 - 3859/9. Determine r so that 2/9*r**2 - 2/9*r**3 - l + 2/9*r = 0.
-1, 1
Let x(u) = 3*u - 3. Let y be x(4). Factor -3*j**2 + j**4 - 4*j**4 - y*j**3 + 15*j**3.
-3*j**2*(j - 1)**2
Let q(o) be the second derivative of o**8/560 + 2*o**7/315 + o**6/180 + o**4 - 3*o. Let f(n) be the third derivative of q(n). Let f(a) = 0. Calculate a.
-1, -1/3, 0
Let r(c) be the second derivative of -c**4/36 - 2*c**3/9 - 2*c**2/3 - c - 12. Find f such that r(f) = 0.
-2
Let p(z) be the first derivative of 0*z**2 - 1/6*z**4 - 3 + 0*z**3 + z. Let i(h) be the first derivative of p(h). Factor i(n).
-2*n**2
Let x(d) = 12*d**3 - 40*d**2 + 12*d + 12. Let u(a) = -11*a**3 + 37*a**2 - 13*a - 13. Let c(b) = 4*u(b) + 3*x(b). Solve c(y) = 0.
-1/2, 2
Let j(o) be the first derivative of -2*o**5/5 + 2*o**4 - 2*o**3 - 4*o**2 + 8*o - 39. Factor j(a).
-2*(a - 2)**2*(a - 1)*(a + 1)
Let f(c) = -20*c**2 + 215*c + 12321. Let l(n) = -3*n**2 - n. Let b(g) = -5*f(g) + 35*l(g). Solve b(w) = 0 for w.
-111
Let y(s) = -4*s**4 + 8*s**3 + s**2 + 5*s - 5. Let x(k) = -12*k**4 + 24*k**3 + 4*k**2 + 16*k - 16. Let z(o) = 5*x(o) - 16*y(o). Solve z(c) = 0 for c.
0, 1
Let a(z) be the third derivative of 5/24*z**3 + 0*z + 1/48*z**5 + 0 + 7*z**2 + 5/48*z**4. What is x in a(x) = 0?
-1
Suppose 0 = 3*b + 26 + 25. Let t = b - -21. Let t*v**3 - 2*v**2 - 3*v**3 - 2*v**3 = 0. Calculate v.
-2, 0
Let x(r) be the second derivative of -r**5/15 - 65*r**4/36 - 136*r**3/9 - 32*r**2/3 - 12*r + 3. Factor x(v).
-(v + 8)**2*(4*v + 1)/3
What is l in 288 - 4*l + 17*l - 281 - 2*l**2 = 0?
-1/2, 7
Let k be (9/(-6))/((-3)/4). Factor t**2 - 1 - 2*t - 5*t**2 + 5*t**k - 2*t**2.
-(t + 1)**2
Let z be (-2)/(-7)*(-95)/76*(-112)/50. What is p in 22/5*p - 24/5*p**2 - z - 18/5*p**3 = 0?
-2, 1/3
Factor -1/2*o**2 + 13/4*o - 3/2.
-(o - 6)*(2*o - 1)/4
Let o be (-51)/(-85)*2*(0 + 1). Factor -o - 1/5*f**2 + f.
-(f - 3)*(f - 2)/5
Let m(w) be the second derivative of -w**2 + 3*w**3 - 5*w + 5/3*w**4 + 0. Let m(u) = 0. Calculate u.
-1, 1/10
Let q be (-10)/24 - ((-390)/30 - (-37)/3). Let -9 - q*a**3 + 11/4*a**2 - 6*a = 0. What is a?
-1, 6
Let o(k) be the third derivative of -k**5/120 + 17*k**4/24 - 16*k**3/3 + 3*k**2 - 6*k. Factor o(y).
-(y - 32)*(y - 2)/2
Let m(c) be the second derivative of 21*c**5/20 - 31*c**4/2 + 95*c**3/2 + 300*c**2 - 319*c. Factor m(b).
3*(b - 5)**2*(7*b + 8)
Let d be (54/(-50))/(15 + 1530/(-100)). Find i such that 12/5*i**2 + 0 - d*i - 2/5*i**3 = 0.
0, 3
Let q(s) be the first derivative of -s**5/12 + 5*s**4/6 - 5*s**3/2 - 9*s**2/2 - 12. Let w(t) be the second derivative of q(t). Find a, given that w(a) = 0.
1, 3
Let x + 2*x + 0*x - 5 - 3*x**3 + 9*x**2 + 23 - 27*x**2 = 0. What is x?
-6, -1, 1
Suppose -6*h 