2
Let k(n) = -1 - 6*n + n**2 + 9*n - 1. Let q be k(-4). Factor -1 - 1 + g**3 + 2*g - 3*g**3 + 2*g**q + 0*g**2.
-2*(g - 1)**2*(g + 1)
Let m(t) be the first derivative of t**5/40 + t**4/24 - t**3/6 - 6*t + 23. Let w(y) be the first derivative of m(y). Let w(u) = 0. What is u?
-2, 0, 1
Let p(j) = -10*j**3 - 70*j**2 - 648*j - 578. Let o(g) = 14*g**3 + 70*g**2 + 649*g + 578. Let a(c) = -4*o(c) - 6*p(c). Factor a(f).
4*(f + 1)*(f + 17)**2
Let b be 7 - -1 - (-2077)/(-268). Let h(i) = i**2 - 4. Let g be h(-3). Factor -b*k**g + 0*k + 0*k**2 + 1/2*k**4 + 0 - 1/4*k**3.
-k**3*(k - 1)**2/4
Factor 4*i**2 + 36 - 3 + 8 - 9 + 36*i.
4*(i + 1)*(i + 8)
Let q(l) be the third derivative of -l**5/120 - 14*l**4/3 - 3136*l**3/3 + l**2 + 33. Suppose q(i) = 0. What is i?
-112
Solve -23*d**2 - 92*d + 62*d**2 - 6*d + 19*d**3 + 2*d**4 + 7*d**3 + 31*d**2 = 0.
-7, 0, 1
Let k(t) be the first derivative of 2/15*t**3 + 0*t**2 - 1/30*t**4 + 6 + 6*t - 3/50*t**5. Let g(i) be the first derivative of k(i). Factor g(m).
-2*m*(m + 1)*(3*m - 2)/5
Let l(c) be the second derivative of 6*c**4 + 2*c**2 + 13*c - 11/2*c**3 + 0 - 4/5*c**5. Find s such that l(s) = 0.
1/4, 4
Let v(h) be the third derivative of h**6/900 + 4*h**5/75 + 7*h**4/60 - 46*h**3/45 - 2*h**2 + 336*h. Factor v(k).
2*(k - 1)*(k + 2)*(k + 23)/15
Suppose b - 1 - 3 = 0. Let f be (b + -10)*2/(-6). Factor -3*m**f + 5*m + 7*m**2 + 36 - 29*m.
4*(m - 3)**2
Let a be ((-4)/(-6))/(26/39). Let h be (a + 14)/5 - 2/(-2). Determine f so that 2/5*f**h + 0*f - 2/5*f**3 + 2/5*f**5 + 0 - 2/5*f**2 = 0.
-1, 0, 1
Let k = 51 - -19. Let s = k + -279/4. Factor 3/4*z**2 + 1/4*z**3 + s + 3/4*z.
(z + 1)**3/4
Let o(m) be the second derivative of m**5/100 + 29*m**4/60 + 13*m**3/2 - 45*m**2/2 + 29*m. Factor o(q).
(q - 1)*(q + 15)**2/5
Let m = -7065/2 - -3534. Let -1/2*b**2 + m + b = 0. Calculate b.
-1, 3
Factor 135/4*p + 15*p**2 - 5/4*p**3 + 35/2.
-5*(p - 14)*(p + 1)**2/4
Let z = -41/90 - -5/9. Let s(k) be the second derivative of -1/2*k**3 + 1/2*k**2 - z*k**6 + 1/42*k**7 + 1/6*k**4 + 0 + 1/10*k**5 + 6*k. Factor s(a).
(a - 1)**4*(a + 1)
Let z(l) be the third derivative of l**5/150 + l**4/30 - l**3/5 + 30*l**2 - 2. Factor z(q).
2*(q - 1)*(q + 3)/5
Let g be (-301)/215 + 127/80. Let w(o) be the second derivative of 3/80*o**5 + 4*o + 0 + 3/8*o**3 - g*o**4 - 3/8*o**2. Find a such that w(a) = 0.
1
Factor -1/2*q**3 + 0 + 1/4*q**4 + 0*q**2 + 0*q.
q**3*(q - 2)/4
Let q(r) be the second derivative of r**4/18 + 8*r**3/9 - 16*r**2 - 3*r + 3. Factor q(o).
2*(o - 4)*(o + 12)/3
Let u(z) be the third derivative of -z**5/12 + 5*z**4/3 - 35*z**3/6 + 5*z**2 + 111*z. Factor u(g).
-5*(g - 7)*(g - 1)
Let c(p) = 6*p - 4*p + 0*p - 14. Let q be c(8). Factor 0 + 0*d + 2/3*d**4 + 0*d**q + 0*d**3.
2*d**4/3
Let x(y) be the first derivative of 3/2*y**2 - 4*y**3 + 2*y + 7/4*y**4 - 6. Factor x(i).
(i - 1)**2*(7*i + 2)
Determine k, given that 74*k + 60*k + 916*k**2 - 32 - 44*k + 127 - 921*k**2 = 0.
-1, 19
Let k(m) = -14*m + 2*m**2 + 0*m**2 + 9 - 23 + 0*m**2. Let g be k(8). Factor -3/4*y**5 + 0 + 3/4*y**3 - 3/4*y**4 + 0*y + 3/4*y**g.
-3*y**2*(y - 1)*(y + 1)**2/4
Find l such that 24/7*l**3 + 2/7*l**2 - 24/7*l + 8/7*l**4 + 8/7 = 0.
-2, 1/2
Let f(a) be the third derivative of -a**6/320 - a**5/20 + 11*a**4/64 + 9*a**3/8 + 4*a**2 - 2. Let f(y) = 0. Calculate y.
-9, -1, 2
Let v(f) be the first derivative of -f**3/21 - 8*f**2/7 - 15*f/7 + 51. Factor v(m).
-(m + 1)*(m + 15)/7
Suppose 2/3 + 16/21*d + 2/21*d**2 = 0. Calculate d.
-7, -1
Let a(q) be the second derivative of q**7/840 + q**6/240 + q**5/240 + 7*q**2/2 - 36*q. Let n(t) be the first derivative of a(t). What is b in n(b) = 0?
-1, 0
Suppose -25*p - 53*p = 0. Factor 0*v**4 + 0*v**2 + p - 1/2*v**3 + 1/4*v + 1/4*v**5.
v*(v - 1)**2*(v + 1)**2/4
Let 17*b**2 - 4 - 73*b - 12*b**5 - 22*b**4 + 9*b**2 + 18*b**3 + 67*b = 0. What is b?
-2, -1, -1/3, 1/2, 1
Let q(k) be the third derivative of k**7/210 - k**6/120 - k**5/10 + k**4/6 + 4*k**3/3 + 5*k**2 + 9*k. Suppose q(h) = 0. What is h?
-2, -1, 2
Let b(u) be the first derivative of -5/2*u**4 + 0*u**2 + 0*u + u**5 + 7 + 0*u**3. Solve b(d) = 0 for d.
0, 2
Let w be ((-12)/108)/(2/(-4)). Find z, given that 0*z + 0 - 2/9*z**2 + w*z**3 = 0.
0, 1
Let c(x) be the second derivative of -189*x**5/20 + 125*x**4/2 - 122*x**3 - 12*x**2 - 2*x + 21. What is h in c(h) = 0?
-2/63, 2
Let y(l) = l**4 + l**2 + 1. Let m(c) = 9*c**4 + 5*c**3 - 6*c**2 + 4. Let n be -2 + 0 + (-36)/(-6). Let u(d) = n*y(d) - m(d). Suppose u(a) = 0. Calculate a.
-2, 0, 1
Let s(k) be the second derivative of k**7/3780 - k**6/1080 - k**4/2 + 10*k. Let y(f) be the third derivative of s(f). Let y(b) = 0. Calculate b.
0, 1
Let f(c) be the first derivative of c**3/15 - 7*c**2/10 + 2*c - 318. Solve f(d) = 0 for d.
2, 5
Let f(m) be the third derivative of 0*m - 1/15*m**5 - 2/21*m**7 + 3*m**2 + 0*m**3 + 0 - 1/3*m**4 + 4/15*m**6. Factor f(x).
-4*x*(x - 1)**2*(5*x + 2)
Suppose 14 = -5*p + 224. Let q be 5/(-56) - p/(-112). Let 0 + q*u + 6/7*u**2 + 2/7*u**4 + 6/7*u**3 = 0. What is u?
-1, 0
Let y(w) = -w**3 - 25*w**2 - 50*w - 6. Let x be y(-2). Factor -845/2 - 5/2*k**x + 65*k.
-5*(k - 13)**2/2
Let t be (0/3)/2 - -6. Let f be 7/3 - t/18. Factor -4 + 2*m**2 - 6*m**f - 4 + 9*m + 3*m.
-4*(m - 2)*(m - 1)
Suppose 1162 = -19*v + 12*v. Let t = v + 170. Solve 21/5*b**2 + 3*b**3 + 9/5*b + 3/5*b**t + 0 = 0.
-3, -1, 0
Suppose 7*c - 229 - 380 = 0. Let i = c + -87. Determine w, given that 2/5*w**5 + 0*w**4 + 0 + 0*w**2 - 2/5*w**3 + i*w = 0.
-1, 0, 1
Let z be (-12)/8*8*1/(-6). Let h(q) be the first derivative of z + 0*q + 1/8*q**2 - 1/16*q**4 + 0*q**3. Factor h(n).
-n*(n - 1)*(n + 1)/4
Let t = 26 + -16. Suppose -1 + 4*x**3 + 1 - 8*x**4 + 14*x**5 - t*x**5 = 0. Calculate x.
0, 1
Let o(s) = -2*s**3 - 17*s**2 - 24*s - 5. Let w(u) = -9*u**3 - 25*u**2 - 8*u**2 - 94*u - 26*u - 24 - 51*u**2. Let n(t) = -21*o(t) + 4*w(t). Factor n(z).
3*(z + 1)**2*(2*z + 3)
Let 0 + 32/3*t**4 - 20*t**3 - 32/3*t**2 - 4/3*t + 64/3*t**5 = 0. Calculate t.
-1, -1/4, 0, 1
Let a be 203/(-21) + 2*1/(-6). Let p be ((-7)/(-7))/(a/(-4)). Factor 0*k**2 + 4/5*k**4 + 0 + 0*k + p*k**3 + 2/5*k**5.
2*k**3*(k + 1)**2/5
Factor -121/3 + 77/6*h + 1/6*h**3 + 10/3*h**2.
(h - 2)*(h + 11)**2/6
Let o be ((-21)/28)/(((-18)/(-596))/3). Let w = o + 75. Factor 0 - 2*v - 2*v**2 - w*v**3.
-v*(v + 2)**2/2
Let m = -40183/15 - -2679. Factor -2/15*p**5 + 2/15*p**4 - 2/15*p**2 + m*p**3 + 0 + 0*p.
-2*p**2*(p - 1)**2*(p + 1)/15
Suppose -136*y + 10*y + 252 = 0. Factor 2/9*k**3 - 2/3 - 10/9*k - 2/9*k**y.
2*(k - 3)*(k + 1)**2/9
Factor -2*w**2 + 757*w**3 + 17*w**2 - 762*w**3.
-5*w**2*(w - 3)
Let c(n) be the first derivative of -5*n**6/6 + 18*n**5/5 - n**4 - 6*n**3 + 9*n**2/2 + 350. Let c(a) = 0. What is a?
-1, 0, 3/5, 1, 3
Let k be ((-1220)/366)/(10/(-8)). What is u in 2 - k*u + 2/3*u**2 = 0?
1, 3
Let d(c) be the second derivative of 0*c**5 + 0 + 1/80*c**6 + 0*c**3 + 0*c**2 - 1/32*c**4 - 19*c. Solve d(m) = 0 for m.
-1, 0, 1
Let y(m) = 6*m**4 + 162*m**3 + 237*m**2 + 45*m - 15. Let g(c) = -c**4 - 23*c**3 - 34*c**2 - 6*c + 2. Let a(n) = -15*g(n) - 2*y(n). Factor a(f).
3*f**2*(f + 3)*(f + 4)
Let n be (-33)/(-132) + (32825/76 - 1). Solve n*u**4 + 6912/19*u**2 + 12288/19*u**3 + 1728/19*u + 162/19 = 0 for u.
-3/8
Suppose 3 = -3*p - 3*r, -5 = 2*p + 4*r + 7. Factor 6*d**3 - d**4 + 12*d + 7*d**4 + 4 + 13*d**2 + d**4 - 6*d**p.
(d + 1)**2*(d + 2)**2
Let d(b) be the first derivative of 245*b**6/6 - 224*b**5 - 645*b**4/4 + 620*b**3/3 - 50*b**2 - 58. Let d(s) = 0. What is s?
-1, 0, 2/7, 5
Find x such that 5/9*x**2 - 1/9 - 8/9*x**4 - 1/9*x + 1/9*x**3 + 4/9*x**5 = 0.
-1/2, 1
What is b in -144 - 7*b**4 - 284*b + 1/4*b**5 - 208*b**2 - 66*b**3 = 0?
-2, 36
Let m(x) be the first derivative of -5*x**3/3 + 45*x**2 - 405*x + 11. Factor m(z).
-5*(z - 9)**2
Let k(n) be the first derivative of 136*n**3/3 + 9*n**2 - 4*n + 119. Determine f, given that k(f) = 0.
-1/4, 2/17
Let l = -5/843 + 7873/843. Suppose -8/3*k**2 + 4/3*k**3 - 16/3 - l*k = 0. What is k?
-1, 4
Let w(c) be the second derivative of -c**7/63 + 8*c**6/45 - 2*c**5/5 - c**4/9 + 13*c**3/9 - 2*c**2 + 76*c. Let w(p) = 0. What is p?
-1, 1, 6
Let y = 7 + -7. Let u = -2/145 + 304/1015. Factor y*o**3 + 0*o - u*o**4 + 2/7*o**2 + 0.
-2*o**2*(o - 1)*(o + 1)/7
Let k(t) be the third derivative of -t**6/140 - 3*t**5/70 +