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Let i(g) = -5*g**5 + 36*g**4 - 45*g**3 + 24*g**2 - 10*g - 22. Let x(y) = -y**5 + 7*y**4 - 9*y**3 + 5*y**2 - 2*y - 4. Let c(s) = 2*i(s) - 11*x(s). Factor c(d).
d*(d - 2)*(d - 1)**3
Let i(p) be the third derivative of 0 - 2/3*p**3 - p**2 - 2/5*p**5 + 0*p + 7/6*p**4. What is j in i(j) = 0?
1/6, 1
Let p(c) be the first derivative of c**5/120 - 7*c**4/24 + 49*c**3/12 - 3*c**2/2 + 14. Let s(j) be the second derivative of p(j). Factor s(o).
(o - 7)**2/2
Suppose -7*r = -5*y - 3*r + 24, -4*y + 4*r + 16 = 0. Factor 137*d**2 - y*d + 137*d**2 - 278*d**2.
-4*d*(d + 2)
Let f be (5/(-7) + 1)*(4 + 3). Factor -6*b + 2*b - b**2 + 6*b + 2*b**f.
b*(b + 2)
Let l(a) be the third derivative of a**8/1008 + a**7/315 - a**6/72 - a**5/18 + a**4/18 + 4*a**3/9 - 24*a**2 - a. Solve l(u) = 0 for u.
-2, -1, 1, 2
Factor 7/4*b**2 + 13/4*b - 1/2.
(b + 2)*(7*b - 1)/4
Factor 2/3*y**4 - 10/3*y**3 + 0 + 14/3*y**2 - 2*y.
2*y*(y - 3)*(y - 1)**2/3
Let f(m) be the third derivative of 5*m**6/48 + 3*m**5 + 455*m**4/16 + 245*m**3/6 + 31*m**2. Factor f(a).
5*(a + 7)**2*(5*a + 2)/2
Let z(w) be the third derivative of w**7/210 - w**6/30 + w**5/12 - w**4/12 - 148*w**2 - 3*w. Factor z(i).
i*(i - 2)*(i - 1)**2
Let d(p) be the first derivative of -5*p**6/24 + 5*p**4/8 - 5*p**2/8 - 354. Find t such that d(t) = 0.
-1, 0, 1
Let h(n) be the third derivative of -n**10/302400 + n**8/40320 - 7*n**5/30 + 13*n**2. Let t(v) be the third derivative of h(v). Factor t(j).
-j**2*(j - 1)*(j + 1)/2
Let l(u) be the first derivative of -u**4/66 + u**3/33 - 3*u - 4. Let i(n) be the first derivative of l(n). What is j in i(j) = 0?
0, 1
Let -49/4*n**2 + 0*n + 0 - 15/4*n**4 + 1/4*n**5 + 63/4*n**3 = 0. What is n?
0, 1, 7
Let u(m) be the first derivative of 1/15*m**2 - 4/15*m - 1 - 1/30*m**4 + 4/45*m**3. Factor u(n).
-2*(n - 2)*(n - 1)*(n + 1)/15
Let q(h) be the third derivative of h**5/20 - 31*h**4/24 - 11*h**3/3 + 456*h**2. Factor q(a).
(a - 11)*(3*a + 2)
Suppose p - 3*l = -4, -3*p + 8*p + 5*l - 20 = 0. Let d be 3*(28/(-3))/(-7). Factor -d*a**p - 5*a - 4*a + 7*a**2.
3*a*(a - 3)
Suppose -5 = -4*g + 5*z, -2*g + 6*z + 5 = z. Suppose g = 3*h - 3 - 6. Factor -6*x**2 - 2*x**2 - 7*x**h + 3*x**3 + 2*x**4 + 16*x.
2*x*(x - 2)**2*(x + 2)
Let y(q) = -35*q**2 + 4700*q - 8960. Let t(s) = -s**2 + 127*s - 242. Let r(h) = -75*t(h) + 2*y(h). Let r(k) = 0. What is k?
2, 23
Let s(p) = -2*p + 1. Let i be s(-2). Suppose -i*w = -9 - 6. What is k in -8 + 15 + 25 + 196*k**w + 240*k + 504*k**2 = 0?
-2, -2/7
Let p(n) be the third derivative of 0*n**3 - 3/80*n**6 + 0 + 1/140*n**7 - 1/16*n**4 - 2*n**2 + 3/40*n**5 + 0*n. Factor p(k).
3*k*(k - 1)**3/2
Factor y + 8/9 + 1/9*y**2.
(y + 1)*(y + 8)/9
Let r(n) be the second derivative of 1/42*n**7 + 1/3*n**4 + 0*n**2 + 1/10*n**5 - 2/15*n**6 - 37*n + 0 - 1/2*n**3. Suppose r(c) = 0. What is c?
-1, 0, 1, 3
Let h(n) be the second derivative of 5/36*n**4 + 0 + 1/60*n**5 - 15*n + 7/18*n**3 + 1/2*n**2. Factor h(c).
(c + 1)**2*(c + 3)/3
Let n = 202 + -194. Let g(j) = j**3 - 8*j**2 + 2*j - 14. Let r be g(n). Suppose -3/4*w**r + 3/4 + 1/4*w**3 - 1/4*w = 0. What is w?
-1, 1, 3
Suppose -4*y + 2 = -30. Suppose -y = -h - 2. Factor 5*u**5 + 5*u**4 - 8*u**3 + h*u**5 + 4*u - u**4 - 7*u**5 + 4 - 8*u**2.
4*(u - 1)**2*(u + 1)**3
Let s(d) be the third derivative of 0*d**3 + 5/24*d**4 + 0*d - 5/32*d**6 + 1/42*d**7 + 0 + 1/4*d**5 - 19*d**2. Suppose s(o) = 0. Calculate o.
-1/4, 0, 2
Let u(v) be the first derivative of 1/12*v**3 + 7 + 0*v + 1/16*v**4 + 0*v**2. Suppose u(p) = 0. What is p?
-1, 0
Let k(h) be the first derivative of 3/5*h**5 + 9/2*h**4 + 8*h**3 - 27*h + 28 - 9*h**2. Find u, given that k(u) = 0.
-3, -1, 1
Let o(p) be the second derivative of 27/20*p**5 - 1/6*p**7 + 6*p**2 + 10/3*p**3 + 19/30*p**6 + 14*p - 71/12*p**4 + 0. Determine w, given that o(w) = 0.
-2, -2/7, 1, 3
Let k(f) be the first derivative of -1/11*f**4 + 1/11*f**2 + 2/33*f**3 + 0*f - 4. Suppose k(q) = 0. Calculate q.
-1/2, 0, 1
Let k(l) = -l**2 + 96*l + 1152. Let s(g) = g**2 - 192*g - 2304. Let q(o) = -10*k(o) - 6*s(o). Factor q(p).
4*(p + 24)**2
Let y be (-4)/70*((-4)/36)/((-3)/(-126)). Factor 8/15*k**4 - 2/3*k**3 + 0 - 2/15*k**5 + 0*k + y*k**2.
-2*k**2*(k - 2)*(k - 1)**2/15
Let m(v) be the second derivative of -1/80*v**5 + 0 - 21*v + 1/24*v**3 + 1/120*v**6 + 0*v**2 - 1/48*v**4. Factor m(q).
q*(q - 1)**2*(q + 1)/4
Let j(l) = -80*l - 158. Let a be j(-2). Let 0*z + 8/7*z**3 - 2/7*z**a - 6/7*z**4 + 0 = 0. What is z?
0, 1/3, 1
Let z be (1/(-1) - -2) + 1. Factor 3*x**2 - z - 5*x**2 + x**2 - x**2 + 4*x.
-2*(x - 1)**2
Suppose 971 = 2*l + 961. Let q(m) be the third derivative of 0 + 0*m + 0*m**3 - 4*m**2 + 0*m**l + 1/168*m**4 - 1/840*m**6. Factor q(i).
-i*(i - 1)*(i + 1)/7
Let m be ((-450)/115 + 3)*(1 - (-26)/(-14)). Find j such that 6/23 - 2/23*j - 18/23*j**2 - 4/23*j**4 + m*j**3 = 0.
-1/2, 1, 3
Let c(p) = 30*p**3 + 84*p**2 + 93*p + 36. Let i(z) = -z**4 - 30*z**3 - 85*z**2 - 94*z - 36. Let u(y) = -2*c(y) - 3*i(y). Solve u(s) = 0 for s.
-6, -2, -1
Let g = 3386 + -3383. Factor 0*d + 0*d**g - 2/5*d**2 + 4/5*d**5 + 0 + 6/5*d**4.
2*d**2*(d + 1)**2*(2*d - 1)/5
Let b(w) = -9*w + 54. Let a be b(6). Suppose -5*s = 4*q - 4 + 17, a = 4*q + 4*s + 8. Determine o so that 8*o - 22/3*o**q + 5/2*o**4 + 0*o**2 + 8/3 = 0.
-2/3, -2/5, 2
Let t(n) be the third derivative of 3*n**7/455 - n**6/156 - 2*n**5/195 - 10*n**2 + 9. Factor t(f).
2*f**2*(f - 1)*(9*f + 4)/13
Let h(f) = -f**2 + 35*f - 253. Let p(a) = 2*a**2 - 71*a + 505. Let n(d) = -7*h(d) - 3*p(d). Factor n(y).
(y - 16)**2
Suppose -675*i = -655*i - 67 + 27. Determine u, given that -u**i + 1/3*u**3 + 4/3 + 0*u = 0.
-1, 2
Factor 254/9 + 256/9*n + 2/9*n**2.
2*(n + 1)*(n + 127)/9
Let u(g) = -g**2 + 2286*g + 11458. Let q be u(-5). Let 2/3*r**5 + 4/3*r**4 + 0*r + 0 - 4/3*r**2 - 2/3*r**q = 0. What is r?
-2, -1, 0, 1
Let a(f) = 4*f**2 + 7*f + 4. Let u(t) = 9*t**2 + 13*t + 8. Let l(v) = -5*a(v) + 2*u(v). Solve l(i) = 0 for i.
-4, -1/2
Let k(x) = 26*x + 26*x + 24*x - 52 - 72*x. Let v be k(14). Factor v*q**2 - 4/5*q**4 + 0 - 4/5*q**3 - 12/5*q.
-4*q*(q - 1)**2*(q + 3)/5
Let n(j) be the first derivative of -j**8/840 - j**7/105 - j**6/90 + j**5/15 + j**4/4 + 6*j**3 + 1. Let v(f) be the third derivative of n(f). Factor v(u).
-2*(u - 1)*(u + 1)**2*(u + 3)
Let r(b) be the first derivative of -b**6/8 + 15*b**4/8 - 5*b**3 + 45*b**2/8 - 3*b + 41. Factor r(h).
-3*(h - 1)**4*(h + 4)/4
Let w(a) = 4*a**5 + 9*a**4 + 7*a**3 - 10*a**2 + 5*a. Let d(y) = 5*y**5 + 10*y**4 + 7*y**3 - 10*y**2 + 6*y. Let i(x) = 5*d(x) - 6*w(x). What is k in i(k) = 0?
-2, 0, 1, 5
Let x(a) be the first derivative of 5*a**2 - a**2 - 4*a**3 - 4*a - 19 - a**4 - 10*a**2. Determine n, given that x(n) = 0.
-1
Let k(t) = 4*t**4 - 22*t**3 - 119*t**2 - 168*t - 72. Let x(i) = -14*i**4 + 64*i**3 + 356*i**2 + 504*i + 216. Let s(n) = -10*k(n) - 3*x(n). Factor s(m).
2*(m + 1)**2*(m + 6)**2
Let a(d) be the third derivative of -5*d**8/336 + d**7/42 + 5*d**6/24 + d**5/4 + 7*d**2. Let a(i) = 0. What is i?
-1, 0, 3
Factor -8 - 16*m**3 + 3*m**3 - 2*m + 5*m**2 + 6*m**3 + 2*m**3 + 4*m**3.
-(m - 4)*(m - 2)*(m + 1)
Let t(r) be the first derivative of 13*r**6/2 - 6*r**5 - 12*r**4 + 10*r**3 + 9*r**2/2 - 377. Solve t(o) = 0.
-1, -3/13, 0, 1
Suppose 162*y = -56*y. Find a, given that -10/7*a**3 - 2/7*a + y + 12/7*a**2 = 0.
0, 1/5, 1
Let f(v) be the second derivative of 5*v**4/48 + 25*v**3/12 + 125*v**2/8 + 84*v. Suppose f(x) = 0. Calculate x.
-5
Let l(h) be the third derivative of -h**6/60 + h**5/2 - 59*h**4/12 + 15*h**3 - 2*h**2 + 121*h. Let l(a) = 0. Calculate a.
1, 5, 9
Suppose -7 - 89 = -48*k. Let t(a) be the first derivative of 1/20*a**4 - 1/5*a**3 + 1/5*a**k + 7 + 0*a. Factor t(u).
u*(u - 2)*(u - 1)/5
Let j(c) = 8*c + 5*c**3 + 3*c**3 + c**3 + 8 + 18*c**2 - c**2. Let r(x) = 6*x**3 + 11*x**2 + 5*x + 5. Let o(p) = -5*j(p) + 8*r(p). Factor o(f).
3*f**2*(f + 1)
Let b(d) be the second derivative of -d**7/42 - d**6/10 - d**5/20 + d**4/4 + d**3/3 + 6*d - 6. Find n such that b(n) = 0.
-2, -1, 0, 1
Suppose 11331 = y + 11326. What is x in -1/5*x**2 + 2*x - y = 0?
5
Let r = -31 + 33. Suppose 10*d - 208 = r*d. Suppose 21*x**2 - d - 25*x**2 - 10 - 24*x = 0. What is x?
-3
Let b(w) = 7*w + 37. Let a be b(-5). Let p(x) be the first derivative of -6 - 1/18*x**6 - 8/3*x**a + 25/9*x**3 + 4/3*x - 19/12*x**4 + 7/