Let x(r) = -7*r**3 + 44*r**2 - 143*r + 97. Let q(n) = -n**3 - n - 1. Let m(a) = 3*q(a) - x(a). Let m(i) = 0. What is i?
1, 5
Let d(v) be the third derivative of -v**6/80 + 7*v**5/40 - 7*v**4/16 - 15*v**3/4 - 2*v**2 - 209. Factor d(f).
-3*(f - 5)*(f - 3)*(f + 1)/2
Let b be (1/2)/((-2)/(-12)). Suppose -5*z = 2*k - 12, -b*z + 1 = 5*k - 10. Find m, given that -5 - 3*m**z - 6*m**2 + 6*m + 4 + 4*m**3 = 0.
1/4, 1
Let s(c) = -1 + 2*c + c - 2 + 0*c. Let g be s(2). Factor 0*k**g + 3*k**3 + 0*k - k**3 - 2*k.
2*k*(k - 1)*(k + 1)
Suppose 8*i - 11 = 5. Find a such that -32*a**5 + i*a - a**3 + 3*a**4 - 3*a**2 + 65*a**5 - 34*a**5 = 0.
-1, 0, 1, 2
Let d(k) be the third derivative of -k**9/15120 + k**7/1260 - k**5/120 + 7*k**4/24 + 16*k**2. Let n(y) be the second derivative of d(y). Factor n(g).
-(g - 1)**2*(g + 1)**2
Let m be 0/((6 + (-5 - -3))*1). Solve -1/3*p**2 + 1/3*p**3 + m*p + 0 = 0 for p.
0, 1
Let n(s) be the third derivative of s**8/26880 + s**7/10080 - 5*s**4/24 - s**3/6 - 12*s**2 + 2*s. Let r(f) be the second derivative of n(f). Factor r(o).
o**2*(o + 1)/4
Let v = 9072 + -9070. Factor 3*g**v - 3/2*g**4 - 3/2*g**3 + 0 + 0*g.
-3*g**2*(g - 1)*(g + 2)/2
Factor 1172/5*i**3 + 828*i**2 + 2/5*i**5 - 2430*i + 1350 + 86/5*i**4.
2*(i - 1)**2*(i + 15)**3/5
Let a(c) be the second derivative of c**6/120 - 3*c**5/40 + c**4/4 - c**3/3 + 3*c. Let o(z) be the second derivative of a(z). Suppose o(m) = 0. What is m?
1, 2
Let v(c) be the second derivative of c**7/2 + 41*c**6/2 + 4269*c**5/20 - 1185*c**4/4 - 225*c**3 - 314*c. Determine z so that v(z) = 0.
-15, -2/7, 0, 1
Let i(h) = -313*h + 942. Let x be i(3). Factor 5/2*v - 13/2*v**x + 3/2*v**4 + 11/2*v**2 - 3.
(v - 3)*(v - 1)**2*(3*v + 2)/2
Let u = 8910 + -8908. Determine a, given that 36/5 + 6/5*a**3 + 48/5*a**u + 78/5*a = 0.
-6, -1
Let n(c) = 3*c**5 - c**3 + c**2 - c - 1. Let f(b) = 13*b**5 - 8*b**4 + 17*b**3 - 18*b**2 + 4*b - 4. Let d(p) = 5*f(p) - 20*n(p). Factor d(j).
5*j*(j - 4)*(j - 2)*(j - 1)**2
Let c(n) = 49*n**2 - 3*n - 2. Let t be c(-1). Let d = -50 + t. Suppose 2/3*y**3 + 0*y**2 + d*y**4 - 1/3*y + 0 - 1/3*y**5 = 0. What is y?
-1, 0, 1
Let r(c) be the third derivative of -25*c**8/3528 - 11*c**7/441 - 19*c**6/1260 + 23*c**5/630 + 2*c**4/63 - 4*c**3/63 - 131*c**2. Let r(w) = 0. What is w?
-1, 2/5
Suppose 4*j = -183 - 25. Let a be -8*(3 - j/(-16)). Factor -4/5*y**3 + 1/5*y**a + 0 + 0*y.
-y**2*(4*y - 1)/5
Suppose 4*d + 983 = 979, -4*q + 15 = -3*d. Factor 4/21*g**2 + 26/21*g**q + 0 + 0*g.
2*g**2*(13*g + 2)/21
Let v(j) be the second derivative of -j**4/96 - 25*j**3/6 - 625*j**2 - 243*j. Factor v(w).
-(w + 100)**2/8
Factor 5*a**3 + 96*a**2 - 74*a + 326*a - a**3.
4*a*(a + 3)*(a + 21)
Let p(i) = 5*i**4 - 4*i**3 - 27*i**2 - 38*i - 14. Let y(z) = -6*z**4 + 3*z**3 + 26*z**2 + 37*z + 13. Let h(b) = -7*p(b) - 6*y(b). Let h(o) = 0. Calculate o.
-5, -2, -1
Let v(f) be the second derivative of -3/80*f**5 + 1/20*f**6 + 0*f**2 + 0*f**4 - 1/56*f**7 + 0 + 2*f + 0*f**3. Suppose v(q) = 0. Calculate q.
0, 1
What is p in 15/2*p + 5/2*p**4 - 15/2*p**3 + 0 - 5/2*p**2 = 0?
-1, 0, 1, 3
Suppose -y = 2*d - 22, -3*y = 3*d + 11 - 47. Let 16*w**2 - 95*w**2 - 8*w**3 + 37*w**2 - d*w = 0. Calculate w.
-5, -1/4, 0
Let b(l) = -24*l**3 + 76*l**2 - 68*l + 24. Let c(q) = q**4 + 47*q**3 - 154*q**2 + 136*q - 48. Let i(m) = 9*b(m) + 4*c(m). Factor i(s).
4*(s - 3)*(s - 2)*(s - 1)**2
Let c(x) be the third derivative of -x**6/1200 - 7*x**5/600 + 3*x**4/40 + 207*x**2. Factor c(g).
-g*(g - 2)*(g + 9)/10
Let l = 28 - -16. Find x such that 5*x**3 - 32*x**2 - 10 + 0*x**3 - 19*x + 12*x**2 + l*x = 0.
1, 2
Suppose -2*d - 5*m - 80 = -51, -d + 4*m = -31. Factor 0 - 1/5*b**d + 2/5*b**2 - 1/5*b**4 + 0*b.
-b**2*(b - 1)*(b + 2)/5
Let f(u) be the third derivative of u**6/200 - u**5/50 - 7*u**4/40 - 2*u**3/5 - 7*u**2 + 1. Solve f(g) = 0 for g.
-1, 4
Let y = -125 + 125. Let x(u) be the third derivative of 1/3*u**3 + y*u + 0 + 1/30*u**5 + 1/6*u**4 - 8*u**2. Find c, given that x(c) = 0.
-1
Let l(r) be the third derivative of r**7/420 + 7*r**6/240 + r**5/24 - 7*r**4/48 - r**3/2 + 2*r**2 - 111. Factor l(c).
(c - 1)*(c + 1)**2*(c + 6)/2
Let n(o) be the first derivative of -o**7/2100 + o**6/900 + o**5/300 - o**4/60 - 5*o**3/3 + 8. Let a(j) be the third derivative of n(j). Factor a(y).
-2*(y - 1)**2*(y + 1)/5
Let z be (-92)/(-24) - (-2)/12. Suppose 0 = z*j - 8. Factor 10*s**j + 3*s**3 + 5*s**2 - 9*s**2.
3*s**2*(s + 2)
Let r be 148/185*(-5)/(-2). Suppose 2/5*h + 9/5*h**r + 7/5*h**3 + 0 = 0. What is h?
-1, -2/7, 0
Let t(g) be the second derivative of -5*g**4/24 - 5*g**3/6 + 15*g**2/4 + 33*g + 2. Factor t(h).
-5*(h - 1)*(h + 3)/2
Let r(c) be the first derivative of c**5/30 - c**4/12 - c**3/6 + c**2/3 + 2*c/3 + 35. Solve r(p) = 0 for p.
-1, 2
Let o be -2 + (7 - (-1 - -3)). Suppose 0 = -4*a + 6*a - 3*y + 5, -3*a + 40 = 5*y. Factor -2*s**3 + a*s**2 - o*s**2 + s + 3*s.
-2*s*(s - 2)*(s + 1)
Suppose b = -5*u + 10, -5*b = -3*u - 3 + 9. What is k in 4*k + 0*k**2 - 8 + 6*k**2 + 0 - 2*k**u = 0?
-2, 1
Let z be -18 + 0 - (0 - -2). Let i be 3/z*-4*5. Solve 6*r**2 + 4*r - 2*r + 0*r**2 + 2*r**i - 3*r**4 + r**2 = 0 for r.
-1, -1/3, 0, 2
Let b(i) = -4*i**2 + i - 1. Let n(w) = -26*w**2 - 114*w - 124. Let u(q) = -6*b(q) + n(q). Let u(r) = 0. Calculate r.
-59, -1
Let s(d) be the second derivative of -1/30*d**5 + d**3 + 3*d**2 + 7*d + 0 - 1/6*d**4. Let x(c) be the first derivative of s(c). Factor x(q).
-2*(q - 1)*(q + 3)
Factor 4*b**2 - 179*b**3 - 2*b**4 - 199*b**3 + 50*b**4 + 348*b**3 - 22*b**5.
-2*b**2*(b - 1)**2*(11*b - 2)
Let j(z) = 4*z**2 + 348*z - 359. Let b(c) = -3*c**2 - 231*c + 239. Let h(k) = -7*b(k) - 5*j(k). Factor h(v).
(v - 122)*(v - 1)
Let t(m) = -16*m - 16. Let q(s) = -s**2 + 18*s + 19. Let c(b) = -2*q(b) - 3*t(b). Factor c(j).
2*(j + 1)*(j + 5)
Factor -49/4*x + 9 + 7/2*x**2 - 1/4*x**3.
-(x - 9)*(x - 4)*(x - 1)/4
Let a(q) be the first derivative of -q**5 - 25*q**4/2 - 115*q**3/3 - 35*q**2 - 501. Factor a(u).
-5*u*(u + 1)*(u + 2)*(u + 7)
Let s(v) be the first derivative of -2*v**3/33 - 8*v**2/11 + 96*v/11 + 112. Factor s(f).
-2*(f - 4)*(f + 12)/11
Let p(m) = 52*m**4 + 12*m**3 - 76*m**2 - 4*m + 32. Let g(j) = -34*j**4 - 8*j**3 + 51*j**2 + 3*j - 22. Let v(z) = -8*g(z) - 5*p(z). Factor v(n).
4*(n - 1)**2*(n + 1)*(3*n + 4)
Let m(u) be the second derivative of -3*u**5/20 - 9*u**4/4 - 7*u**3 - 9*u + 1. What is z in m(z) = 0?
-7, -2, 0
Let c(d) be the third derivative of -d**7/630 + d**6/45 - 2*d**5/15 - 5*d**4/24 + 2*d**2. Let r(w) be the second derivative of c(w). Factor r(y).
-4*(y - 2)**2
Let k(s) be the third derivative of s**6/2340 - s**5/780 - s**4/78 + 15*s**3/2 + 50*s**2. Let h(c) be the first derivative of k(c). Factor h(b).
2*(b - 2)*(b + 1)/13
Let h(c) = c**3 - 21*c**2 + 20*c + 3. Let a be h(20). Factor -12 - 6 + 26 - 16*u**2 - 4*u + 3*u**a + 9*u**3.
4*(u - 1)**2*(3*u + 2)
Suppose 12 - 35*k**2 - 4 + 5*k**3 + 7*k**4 - 2*k**5 + 12 + 8*k**4 - 3*k**5 = 0. Calculate k.
-1, 1, 2
Let n(u) be the third derivative of -u**10/37800 - u**9/6300 - u**8/2800 - u**7/3150 + u**4/2 - 5*u**2. Let b(y) be the second derivative of n(y). Factor b(z).
-4*z**2*(z + 1)**3/5
Suppose 2*q = 2*x - 2*q + 16, 5*q = 2*x + 21. Let s be (4/(-6))/(x/(-6)). Find d, given that -11*d + 37*d**s - 7*d**3 - 10*d + 6 - 2*d**3 - 13*d**2 = 0.
2/3, 1
Let k(h) be the third derivative of 1/18*h**4 + 0 + 0*h**5 - 3*h**2 + 1/9*h**3 - 1/90*h**6 - 1/315*h**7 + 0*h. Suppose k(r) = 0. Calculate r.
-1, 1
Suppose 2*b = -7 + 17. Solve 125*v**2 - 8*v**4 - 61*v**3 - 37*v**4 + b*v**5 + 136*v**3 = 0 for v.
-1, 0, 5
Factor -3/2*v - 3/4*v**2 + 9/4.
-3*(v - 1)*(v + 3)/4
Let d = -14538 - -14538. Factor -1/2*q**2 + 7/2*q + d.
-q*(q - 7)/2
Let h = 2069/5 - 4133/10. Find v, given that -h*v**2 - 2 + 5/2*v = 0.
1, 4
Let x(r) be the third derivative of 7*r**6/4140 - r**5/115 - r**4/69 + 5*r**3/3 + 11*r**2. Let n(d) be the first derivative of x(d). Factor n(v).
2*(v - 2)*(7*v + 2)/23
Factor -3/5 + 0*f - 3/5*f**4 + 6/5*f**2 + 0*f**3.
-3*(f - 1)**2*(f + 1)**2/5
Let s(j) = 3*j - 63. Let v be s(21). Let c be 3/(9/(-3))*v. Solve 8*p + 33/2*p**3 - 20*p**2 + 1/2*p**5 + c - 5*p**4 = 0.
0, 1, 4
Find v, given that -1365*v**3 + 4*v**2 + 32*v - 20 + 4 + 1357*v**3 = 0.
-2, 1/2, 2
Let a(q) be the second derivative of q**5/10 - 3*q**4/2 + 23*q**3/3 - 15*q**2 - 1