e of -1/20*r**4 + 0*r**2 - 5 - 1/10*r**3 + 9*r. Let a(x) be the first derivative of i(x). What is c in a(c) = 0?
-1, 0
Let s = 54 - 52. Let j be s/9 - 210/(-27) - 3. Solve 89 - 2*w**j - 3*w**3 - 4*w**4 + w**3 - 89 = 0.
-1, 0
Let f(a) be the second derivative of 3 + 1/16*a**4 + 23/8*a**3 - 7*a + 33/4*a**2. What is p in f(p) = 0?
-22, -1
Let y(n) be the first derivative of -n**6/2160 + 11*n**5/240 + 50*n**3/3 + 142. Let x(b) be the third derivative of y(b). Factor x(p).
-p*(p - 33)/6
Determine j so that -1/2*j**2 - 117/2 + 59*j = 0.
1, 117
Let h(p) be the first derivative of -15/2*p**4 - 3*p - 24*p**3 + 15*p**5 + 15*p**2 - 192. Determine n so that h(n) = 0.
-1, 1/5, 1
Let f(g) be the first derivative of -g**3/5 - 162*g**2/5 - 8748*g/5 - 1322. Factor f(z).
-3*(z + 54)**2/5
Let m(c) = -7*c - 263. Let s be m(-37). Let w be 11/s - 6*4/(-8). Factor 3/8*k + 5/8*k**2 - w.
(k + 1)*(5*k - 2)/8
Factor -66 + 1/6*n**3 + 218/3*n - 41/6*n**2.
(n - 22)*(n - 18)*(n - 1)/6
Suppose -7*p - 52 = -3*p. Let m = p - -17. Factor -2*b**4 - 2 + 0 + 0*b**m + 0 + 4*b**2.
-2*(b - 1)**2*(b + 1)**2
Let n(d) be the first derivative of d**4/8 + 8*d**3/3 + 55*d**2/4 - 36*d + 1605. Determine i so that n(i) = 0.
-9, -8, 1
Let n be 260008/420 - (-1)/(-15). Let j = n - 616. Factor -70/3*u - 2/3*u**j + 50/3 + 22/3*u**2.
-2*(u - 5)**2*(u - 1)/3
Factor 282 - 6*r**2 + 97*r - 4*r**2 - 2*r**2 + 18*r**2 - 5*r**2.
(r + 3)*(r + 94)
Let u(n) = -13*n**4 + n**3 + n**2 + n - 1. Let g(l) = 237*l**4 + 12*l**3 + 66*l**2 + 54*l + 18. Let j(i) = -g(i) - 18*u(i). Factor j(w).
-3*w*(w + 2)**2*(w + 6)
Let p(s) be the first derivative of s**4/28 + 5*s**3/3 - 151*s**2/7 - 48*s - 196. Let p(x) = 0. What is x?
-42, -1, 8
Let o(h) be the first derivative of -3*h**4 + 16*h**3 - 65*h**2/2 - 34*h + 50. Let k(z) = 2*z**3 - 8*z**2 + 11*z + 6. Let g(n) = 34*k(n) + 6*o(n). Factor g(f).
-4*f*(f - 2)**2
Let o = 1006544/65 - 15483. Let w = -9/13 + o. Factor -4/5 + w*k**2 + 14/5*k.
2*(k + 2)*(4*k - 1)/5
Factor -127*v - 171*v + 117 + 53*v + 78 - 20*v**2.
-5*(v + 13)*(4*v - 3)
Let a be 22 + -20 + 0/(-1). Suppose 2 = -a*n + 6. What is k in 7*k**2 - n*k**2 - 5 + k**2 - k**2 = 0?
-1, 1
Let k(q) = q**3 + 13*q**2 + 10*q + 39. Let z be k(-12). Let x be (-120)/(-126)*z/54. Find d such that 2/3 - x*d + 2/9*d**3 + 2/9*d**2 = 0.
-3, 1
Let c = 277 + -254. Suppose c*r = 5*r. Suppose r - 1/3*n - 1/6*n**2 = 0. What is n?
-2, 0
Let h be -558*(-21)/273 + -22. Factor 578/13*s**2 + 32/13 + h*s.
2*(17*s + 4)**2/13
Suppose 5*a + 2 = 2*h - 231, 5*a = 5*h - 545. Let u = h - 102. Let 36*i**3 - 8*i**2 - 8*i**4 + 16*i**u + 12*i**2 = 0. What is i?
-1/2, 0, 5
Let p be 1/(-4)*(-32)/6. Suppose 102*w + 495 = 495. Factor -8/3*j**2 - 16/9*j - p*j**3 + w - 2/9*j**4.
-2*j*(j + 2)**3/9
Let v be 12/90*912/(22 - 3). Suppose -972/5 - 108/5*c**2 + 48/5*c**4 + 72*c**3 - v*c**5 - 1296/5*c = 0. What is c?
-3/2, 3
Let g(c) be the first derivative of -c**4/22 - 2*c**3/33 + 36*c**2/11 + 72*c/11 + 968. Factor g(x).
-2*(x - 6)*(x + 1)*(x + 6)/11
Let p(w) = -6*w - 71. Let q be p(-11). Let v(d) = -d**4 - d**3 - 2*d. Let u(k) = -5*k**4 + 10*k**3 + 10*k**2 + 5*k. Let g(f) = q*v(f) - u(f). Factor g(c).
5*c*(c - 1)*(c + 1)*(2*c - 1)
Let a(m) be the second derivative of m**7/28 - 2*m**6/5 + 27*m**5/20 - 27*m**3/4 + 6*m + 14. Solve a(d) = 0.
-1, 0, 3
Let j be (((-63)/(-99))/(-7))/((-2)/126). Let n = j - 79/33. Factor -n*r**3 + 16/3*r**2 - 2/3*r - 4/3.
-2*(r - 1)**2*(5*r + 2)/3
Factor -27*g**2 + 8*g**4 - 21 + 101/2*g - 12*g**3 + 3/2*g**5.
(g - 1)**3*(g + 6)*(3*g + 7)/2
Let c(u) be the second derivative of -u**4/6 + 52*u**3/27 - 68*u**2/9 + 4*u + 113. Factor c(t).
-2*(t - 2)*(9*t - 34)/9
Let l(y) be the first derivative of -1/5*y**5 + 0*y - 4/3*y**3 - 8*y**2 - 1/6*y**6 + 3*y**4 - 81. Find m, given that l(m) = 0.
-4, -1, 0, 2
Let u(d) be the first derivative of -d**6/9 + 18*d**5/5 - 16*d**4 + 184*d**3/9 + 434. Factor u(p).
-2*p**2*(p - 23)*(p - 2)**2/3
Let a(z) be the third derivative of -z**6/480 + 1337*z**5/80 - 1787569*z**4/32 + 2389979753*z**3/24 - 38*z**2 - 36*z. Determine u, given that a(u) = 0.
1337
Let n be 7 - 5*(20 - (-114)/(-6)). What is i in -15*i + 3/8*i**n + 150 = 0?
20
Suppose 15*l = d + 17*l - 26, -5*l = 3*d - 65. Factor -2/5*p**3 + d - 2/3*p**2 + 2/15*p**5 - 4/15*p + 2/15*p**4.
2*p*(p - 2)*(p + 1)**3/15
Let a = 589 + -445. Suppose 8*i = -28*i + a. Let 0*g**2 - 10/13*g - 4/13 + 10/13*g**3 + 4/13*g**i = 0. Calculate g.
-2, -1, -1/2, 1
Let c = 254045/2 - 127021. Factor c*z**2 + 54 - 18*z.
3*(z - 6)**2/2
Let c(a) be the second derivative of a**7/112 - 7*a**6/80 - 33*a**5/40 + 4*a**4 + 10*a**3 - 75*a**2 + a - 2219. Find x such that c(x) = 0.
-5, -2, 2, 10
Let w(b) = 10 + 21*b - 8*b**3 - 8765*b**2 + 8758*b**2 + 0 - b + 2. Let o(k) = -k**3 - k**2 + k. Let f(l) = -14*o(l) + 2*w(l). Factor f(j).
-2*(j - 4)*(j + 1)*(j + 3)
Suppose 3*x - 47 = -32. Factor 56*o - 11*o**3 + 2*o**x + 4*o**4 + 61*o**3 + 76*o**2 + 16 + 12*o**4.
2*(o + 1)**2*(o + 2)**3
Let o be 94/(-470) - (1 + 1863/10). Let r = o - -1133/6. Factor 2/9*t**3 + 10/9*t**2 + r*t + 0.
2*t*(t + 2)*(t + 3)/9
Let k(g) = -g**4 + g**3 - g**2 - g - 1. Let z(p) = 661*p**4 - 1313*p**3 + 645*p**2 + 9*p + 1. Let a(i) = k(i) + z(i). Factor a(t).
4*t*(t - 1)**2*(165*t + 2)
Let t(a) = -a**2 - a + 1. Let i(b) be the first derivative of 8/3*b**3 - 6 + 15/2*b**2 + 9*b. Let v(r) = -5*i(r) - 35*t(r). Find x, given that v(x) = 0.
-4
Let q(c) be the third derivative of 0*c + 0 - 67*c**2 + 1/15*c**5 + 25/6*c**3 - 5/6*c**4. Factor q(y).
(2*y - 5)**2
Let d be (-504)/10*100/(-40). Factor d*x + 18 - 232*x**2 + 89*x + 1084*x**2 + 1104*x**3 - 64*x**4.
-(x - 18)*(4*x + 1)**3
Factor -4*f**4 - 744*f**2 - 777438 + 380*f**3 + 777438.
-4*f**2*(f - 93)*(f - 2)
Suppose -36 + 418 + 22 = 202*c. Solve 640*p - 200*p**c - 2048/3 + 125/6*p**3 = 0.
16/5
Let w(r) be the second derivative of r**7/21 - 52*r**6/5 + 1493*r**5/10 - 2429*r**4/3 + 1952*r**3 - 2336*r**2 + 5997*r. Find u, given that w(u) = 0.
1, 4, 146
Let n = -823764 - -823764. What is d in n - 48/7*d + 3/7*d**2 = 0?
0, 16
Let p(y) be the third derivative of 0*y + 0 + 2/3*y**3 + 31/120*y**4 + 272*y**2 - 7/600*y**6 + 1/100*y**5 + 1/1050*y**7. Factor p(n).
(n - 5)*(n - 4)*(n + 1)**2/5
Let g be (-36)/(612/119)*(-4)/7. Find f such that 1/5*f**5 - 1 - f**g - 2/5*f**3 + 1/5*f + 2*f**2 = 0.
-1, 1, 5
Suppose -26*b**2 + 23302*b - 23346*b - 3*b**4 + 5*b**4 + 20*b**3 = 0. Calculate b.
-11, -1, 0, 2
Let n(v) be the third derivative of -v**5/20 + 69*v**4/28 + 20*v**3/7 + 2*v**2 - 292. Factor n(a).
-3*(a - 20)*(7*a + 2)/7
Suppose -4*x + 7149 = 2*r - 3*r, -3*x - 3*r + 5358 = 0. Determine i, given that -3402*i + 3498*i - x - 517 - i**2 = 0.
48
Let m(a) = -12*a**2 - 2972*a - 541692. Let x(o) = 26*o**2 + 5951*o + 1083383. Let w(y) = -9*m(y) - 4*x(y). Find k such that w(k) = 0.
-368
Let y be (8 - 105/(-23 - -38))*0. Factor y - 3/2*v**4 - 2*v**3 + 5/2*v**2 + v.
-v*(v - 1)*(v + 2)*(3*v + 1)/2
Let a(c) be the first derivative of -c**9/189 - c**8/420 + 2*c**7/105 + c**6/90 + 6*c**3 - 41. Let j(t) be the third derivative of a(t). What is b in j(b) = 0?
-1, -1/4, 0, 1
Let 39/2*u**2 - 6*u - 78 + 3/2*u**3 = 0. What is u?
-13, -2, 2
Let a(x) = -x**5 - 2*x**3 - x**2 + x. Let v(c) = 3*c**5 + 31*c**3 - 14*c**2 - 44*c. Let r(y) = 4*a(y) + v(y). Let r(l) = 0. What is l?
-5, -1, 0, 2, 4
Let q(t) be the first derivative of -t**4/2 - 838*t**3/3 - 835*t**2 - 834*t + 824. Determine b so that q(b) = 0.
-417, -1
Let z(o) be the second derivative of 1/3*o**7 - 2*o + 31/24*o**4 + 29 - 29/40*o**5 + 1/12*o**3 - 1/2*o**2 - 29/60*o**6. Let z(u) = 0. Calculate u.
-1, -1/4, 2/7, 1
Let d(n) be the third derivative of -n**8/1008 + 37*n**7/630 + 53*n**6/120 + 203*n**5/180 + 41*n**4/36 - 1918*n**2 - 2. Find a, given that d(a) = 0.
-2, -1, 0, 41
Let u(y) = -139*y - 1. Let l(i) = -2*i**2 - i + 4. Let w(h) = -4*l(h) + u(h). Determine q, given that w(q) = 0.
-1/8, 17
Let j(f) be the first derivative of 26 + 7/12*f**4 + 0*f**2 + 1/3*f**3 - 9/20*f**5 + 5*f. Let x(w) be the first derivative of j(w). Factor x(q).
-q*(q - 1)*(9*q + 2)
Let i(z) be the third derivative of 50/3*z**3 + 35/8*z**4 + 1/12*z**5 + 0*z + 125 + 2*z**2. Factor i(d).
5*(d + 1)*(d + 20)
Let c be 32992/156712*(3/(-3))/((-2)/19). Factor -32/3 - 8*s**c - 4/3*s**3 - 16*s.
-4*(s + 2)**3/3
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