f**4 + 1. Factor d(p).
4*p*(p - 4)*(p - 2)*(p + 1)
Suppose -41*u = -9*u + 12*u. Let k(t) be the first derivative of 2/35*t**5 + 5 + 2/7*t**4 - 2/21*t**3 + u*t - 4/21*t**6 + 0*t**2. Find s such that k(s) = 0.
-1, 0, 1/4, 1
Let w be (-12)/(-15)*10/4. Let k(a) be the second derivative of 0*a**w - 1/6*a**3 - 1/20*a**5 + 0 - 6*a + 1/6*a**4. Let k(p) = 0. Calculate p.
0, 1
Let a(k) = 17*k**3 + 200*k**2 + 561*k + 12. Let l(w) = 15*w**3 + 200*w**2 + 560*w + 10. Let u(p) = 5*a(p) - 6*l(p). Factor u(b).
-5*b*(b + 3)*(b + 37)
Let l = 17186 - 17183. Factor -14/9*b**l - 4/9*b**2 + 0*b + 0 - 10/9*b**4.
-2*b**2*(b + 1)*(5*b + 2)/9
Suppose -16/11*m**3 + 2*m**2 - 160/11*m**4 + 4/11*m + 0 = 0. What is m?
-1/4, 0, 2/5
Let x(d) = 13*d**2 - 174*d - 159. Let y(s) = -4*s**2 + 58*s + 54. Let a(h) = 4*x(h) + 14*y(h). Let a(b) = 0. What is b?
-1, 30
Let y be ((-6)/15)/((-3)/30). Suppose -f - 4*x + 2*x + 13 = 0, y*f + 2*x - 22 = 0. Factor -f*q**4 + q**5 + 2*q**5 - 2*q**5 + 3 + 2*q**2 - 3*q + 2*q**3 - 2.
(q - 1)**4*(q + 1)
Let s(z) be the third derivative of z**7/945 - 7*z**6/540 - z**5/15 - 15*z**2 + 3. Suppose s(h) = 0. Calculate h.
-2, 0, 9
Factor 19 - 32*d + d**2 + d**2 + 37.
2*(d - 14)*(d - 2)
Let o(q) = 2*q**2 - 7*q - 12. Let w be o(5). Suppose i - w*l - 12 = -3*i, -5*l - 20 = -4*i. Factor 0*t + i - 8/7*t**3 + 2/7*t**4 + 8/7*t**2.
2*t**2*(t - 2)**2/7
Let b(p) be the first derivative of -16*p**3/3 + 58*p**2 + 96*p + 218. Factor b(z).
-4*(z - 8)*(4*z + 3)
Suppose -9*a + 2 = -16. Suppose 2*i - 5*w = 8, a*i + 3*i + 5*w = 20. Find z, given that 6*z**2 + 9*z - 3*z**5 - 9*z**i - 6*z**3 - 8 + 1 + 5 + 5 = 0.
-1, 1
Factor 2/7*w**2 + 53792/7 - 656/7*w.
2*(w - 164)**2/7
Let b(q) = q**2 + 1. Let n(x) = 6 - 2*x**2 - 5*x**3 + 0*x**2 + x**2 + 2*x - 4*x. Let d(i) = -6*b(i) + n(i). Let d(u) = 0. What is u?
-1, -2/5, 0
Factor 29/2 + 1/2*n**2 + 15*n.
(n + 1)*(n + 29)/2
Suppose 3*g + 43 = -2*b, 2*b + g - 4*g + 13 = 0. Let c = 17 + b. Factor 0*z - 6*z**4 + 3*z**5 - 6*z**5 + c*z + 6*z**2.
-3*z*(z - 1)*(z + 1)**3
Let q(t) = 2*t**4 + 4*t**3 - 3*t**2. Let o(f) = 16*f**2 - 14*f**3 + f**3 - 7*f**3 - 4*f**4 - 6*f**4. Let m(c) = 6*o(c) + 28*q(c). Factor m(s).
-4*s**2*(s - 1)*(s + 3)
Let i = 555/8 - 3869/56. Factor 2/7 + 6/7*z**2 + i*z**3 + 6/7*z.
2*(z + 1)**3/7
Let 18/7*s**3 - 24/7*s + 0 - 27/7*s**5 + 108/7*s**2 - 75/7*s**4 = 0. Calculate s.
-2, 0, 2/9, 1
Suppose 13*p = 9*p - 48. Let l be (-21)/(-182)*(20/p + 3). Factor -l*t**2 + 2/13 + 0*t.
-2*(t - 1)*(t + 1)/13
Suppose -3*p - p + 5*k = -21, -4*p - 2*k = -14. Find n, given that n**2 + 6*n**4 + 3*n**5 - p*n**2 - 2*n + n**4 + 0*n**2 + 3*n**3 = 0.
-1, 0, 2/3
Let o be (-3)/2*(-232)/1914. Factor 0 - o*q - 2/11*q**3 + 4/11*q**2.
-2*q*(q - 1)**2/11
Factor 4*y + 0 + 2/3*y**3 + 14/3*y**2.
2*y*(y + 1)*(y + 6)/3
Suppose 0*z + 2*z - 10 = 0. Let h be 3/45*-3 - (-11)/z. Factor -2/7 - 2/7*u**h + 4/7*u.
-2*(u - 1)**2/7
Factor 410/23*d + 72/23*d**3 - 336/23*d**2 - 150/23.
2*(d - 3)*(6*d - 5)**2/23
Let z = -24821/5 - -4965. Solve -z*v**3 + 4/5 + 12/5*v**2 - 12/5*v = 0.
1
Let d(b) = 2*b**3 + 13*b**2 + 12*b + 1. Let g(j) = -j**2 + 1. Let r(w) = 2*d(w) - 2*g(w). Factor r(n).
4*n*(n + 1)*(n + 6)
Let c(m) be the second derivative of m**4/20 - 2*m**3/5 + 9*m**2/10 - 2*m + 13. Factor c(k).
3*(k - 3)*(k - 1)/5
Let n(r) = -453*r + 456. Let t be n(1). Determine w, given that -3/4*w**2 - 1/2*w + 0 - 1/4*w**t = 0.
-2, -1, 0
Let a = -217287/4 - -54324. Factor -3/2*z - 3/4*z**2 + a.
-3*(z - 1)*(z + 3)/4
Let b(w) be the third derivative of -17/15*w**7 + 7/24*w**8 - 4/3*w**4 - 4/3*w**3 + 23/30*w**5 + 0*w + 0 + 67/60*w**6 - 28*w**2. Factor b(m).
2*(m - 1)**3*(7*m + 2)**2
Suppose 3*i = 2*b + 2 + 14, 2*i - 4 = 3*b. Suppose g + g + i = 5*j, j = 5*g - 3. Suppose -1 - 2 + 1 + 3*q**j + q = 0. What is q?
-1, 2/3
Let m be (-32 + 34)*(1 - 0). Let c(d) be the second derivative of -6*d - 5/6*d**4 - 4*d**m - 8/3*d**3 + 0 - 1/10*d**5. Solve c(z) = 0 for z.
-2, -1
Factor -3/5*t**3 - 2*t**2 + 0 + 4/5*t**4 + 8/5*t + 1/5*t**5.
t*(t - 1)**2*(t + 2)*(t + 4)/5
Let j = -2955 - -20687/7. Determine b so that 0 - 10/7*b**3 - 6/7*b + 2*b**2 + j*b**4 = 0.
0, 1, 3
Let c(d) = 4*d**4 - 34*d**3 - 3*d**2 - 6*d. Let w(o) = 44*o**4 - 376*o**3 - 32*o**2 - 64*o. Let l(j) = -32*c(j) + 3*w(j). Determine i so that l(i) = 0.
0, 10
Suppose 160 = 4*x + 5*r, -12*x - 4*r = -11*x - 29. Let f be (-16)/(-72) - (-17)/x. Find i, given that f*i**5 + 0*i**2 - 3/5*i**4 + 0*i + 0 + 0*i**3 = 0.
0, 1
Let u(x) = 9*x - 716. Let m be u(80). Let o(g) be the second derivative of -g - m*g**3 + 8*g**2 + 0 + g**4 - 1/10*g**5. Factor o(c).
-2*(c - 2)**3
Let c(q) be the second derivative of -q**4/96 - 3*q**3/16 - q**2/2 + 416*q. Factor c(l).
-(l + 1)*(l + 8)/8
Suppose -2*l = -g + 13, 5 = 5*g + 4*l + l. Suppose 5*j + g = 420. Factor 64*y - 15*y**2 + 28 + j*y**2 - 12 + 20*y**3.
4*(y + 1)*(y + 2)*(5*y + 2)
Let y = 484/185 - 8/37. Let l(c) be the first derivative of 6/5*c**2 - 1/5*c**3 - y*c - 5. Solve l(x) = 0.
2
Let c be 500/325 - 18/(-39). Let x(d) be the first derivative of -8 + 3/14*d**c - 1/7*d**3 + 6/7*d. Suppose x(m) = 0. Calculate m.
-1, 2
Factor 19396 - 4*q**2 - 12*q - 19396.
-4*q*(q + 3)
Let h(q) be the first derivative of 2*q**3/3 + 8*q**2 + 30*q + 191. Let h(i) = 0. Calculate i.
-5, -3
Let j(f) = f**3 + 6*f**2 - 9*f - 10. Let i = -10 + 3. Let r be j(i). Suppose -4*k**2 - 9*k + 0*k**5 - 3*k**3 + 13*k + 4*k**r - k**5 = 0. What is k?
-1, 0, 1, 2
Factor 4/7*a - 6/7*a**2 + 2/7.
-2*(a - 1)*(3*a + 1)/7
Suppose -3*j - 8 = -j. Let p = j - -6. Find x such that -5*x + 2*x + 2*x**p + 4*x + x**3 = 0.
-1, 0
Factor 0*a**2 - 4/3*a**3 + 4/3*a - 2/3*a**4 + 2/3.
-2*(a - 1)*(a + 1)**3/3
Let y be (-1)/(-2)*(-4 - -28). Let l be 0*(-4)/y*3. Solve 0 - 2/5*g**3 - 2/15*g**5 + 2/5*g**4 + l*g + 2/15*g**2 = 0 for g.
0, 1
Let m(y) be the first derivative of 22 + 0*y + 2/27*y**3 + 1/6*y**2. Factor m(l).
l*(2*l + 3)/9
Let t(c) = 49*c - 4689. Let x be t(97). Factor -8*a**2 + x*a + 1/3*a**3 - 512/3.
(a - 8)**3/3
Let z = 478/5 - 95. Let m(w) be the first derivative of -4*w - 6*w**2 - 1/4*w**4 + 1/6*w**6 - 11/3*w**3 + 2 + z*w**5. Factor m(b).
(b - 2)*(b + 1)**3*(b + 2)
Let f(i) be the first derivative of 7*i**4 + 16*i + 2/3*i**6 + 4/3*i**3 - 4*i**5 - 16*i**2 - 18. Suppose f(c) = 0. What is c?
-1, 1, 2
Let r(f) be the first derivative of f**5/4 + 5*f**4/2 - 5*f**3/12 - 5*f**2 + 260. Factor r(l).
5*l*(l - 1)*(l + 1)*(l + 8)/4
Let a be (-26)/7 + 15/(-4)*824/(-515). Factor 80/7*u**2 - 12/7*u**3 - 2/7*u**5 - 50/7*u + 0 - a*u**4.
-2*u*(u - 1)**2*(u + 5)**2/7
Let t(a) be the second derivative of a**5/90 + 5*a**4/27 + 23*a**3/27 + 14*a**2/9 - 109*a. Let t(p) = 0. What is p?
-7, -2, -1
Let z = 0 - -6. Let d be -6 - -11 - 4 - (-10)/z. Determine f, given that -6*f**3 - 4*f**2 - d*f**4 - 2/3*f + 0 = 0.
-1, -1/4, 0
Factor -12/7 + 1/7*u**3 + 3/7*u**2 - 4/7*u.
(u - 2)*(u + 2)*(u + 3)/7
Let n(y) = -3*y**4 - 9*y**3 - 11*y**2 + 9*y + 15. Let j(q) = q**4 - q**3 - q**2 - q + 1. Let p = 10 + -11. Let k(h) = p*j(h) - n(h). Factor k(u).
2*(u - 1)*(u + 2)**3
Let z = 11/26 - -49/130. Let m(h) = 4*h**2 + 35*h - 6. Let p be m(-9). Solve -2/5*y**5 - z*y**2 + 4/5*y**4 + 0*y**p + 2/5*y + 0 = 0 for y.
-1, 0, 1
Let u(x) be the second derivative of 0*x**3 + 0*x**2 + 1/6*x**5 + 3*x + 0*x**4 + 5/126*x**7 + 0 - 1/6*x**6. Factor u(h).
5*h**3*(h - 2)*(h - 1)/3
Let y = -250573 + 2258563/9. Let s = -378 + y. Let 2/9*w**3 - s*w + 2/9*w**2 + 0 = 0. Calculate w.
-2, 0, 1
Let b be 22/24 + 2/(-8). Suppose -2/3*q**4 + 2/3*q - 2/3*q**3 + 0 + b*q**2 = 0. What is q?
-1, 0, 1
Let a(f) be the second derivative of -3*f**5/160 + f**4/8 + 3*f**3/16 - 27*f**2/8 - 39*f. Determine j, given that a(j) = 0.
-2, 3
Let d(b) = 2*b**2 + 2*b - 8. Let g be d(-3). Suppose -2*a = g*a - 24. What is w in -1/6*w**5 - 1/6*w**3 + 0*w - 1/3*w**a + 0*w**2 + 0 = 0?
-1, 0
Let t be (-88)/120*-5 + 0/1. Suppose -5*n + 24 = -1. Let -4/3*j**3 + t*j + 2/3 - 16/3*j**4 - 7/3*j**n + 14/3*j**2 = 0. Calculate j.
-1, -2/7, 1
Let v = 129/4 + -32. Let z(t) be the second derivative of -v*t**3 + 1/24*t**4 + 4*t + 1/2*t**2 + 0. What is s in z(s) = 0?
1, 2
Let r(z) = -7*z - 44. Let u be r(-7). Let k(p) be the third derivative of 1/96*p**4 - 3*p**2 + 0 + 1/480*p**6 + 0*p**3 - 1/120*p**u + 0*p. Solve k(d) = 0.
0, 1
Let x(z) be the third derivative of -z**8/