72)*-16 - (54/(-92))/1. Factor 0 + g*z**2 - 1/2*z.
z*(z - 1)/2
Let x(z) be the first derivative of 7*z**5/20 - 31*z**4/8 + 15*z**3 - 81*z**2/4 - 27*z/4 + 1737. Factor x(q).
(q - 3)**3*(7*q + 1)/4
Let m(v) be the third derivative of 64*v**2 + 7/4*v**4 + 0 - 38/3*v**3 + 2*v - 1/30*v**5. Factor m(u).
-2*(u - 19)*(u - 2)
Suppose 20*f - 73875 - 12665 = 0. Find l, given that f + 2*l**2 + 25*l + 109*l + 90*l + 91 - 36*l = 0.
-47
Let x(f) be the third derivative of -f**8/3024 - f**7/315 - f**6/540 + f**5/27 + f**4/8 + 5*f**3/27 - 3*f**2 - 191*f. Find d, given that x(d) = 0.
-5, -1, 2
Suppose a - 1586 = -w, 0*a - 4*a = -2*w + 3172. Find j, given that -1582*j - 3*j**2 + 4*j**2 + w*j = 0.
-4, 0
Let w(j) = -4*j**5 - 76*j**4 - j**3 + 2*j + 1. Let h(p) = 3*p**5 - p**4 + p**3 - 2*p - 1. Let g(k) = 2*h(k) + 2*w(k). Solve g(u) = 0 for u.
-77, 0
Let r(b) = -14210*b + 170524. Let i be r(12). Factor 12150/11*x**i + 0 - 1080/11*x**3 + 24/11*x**2 + 0*x.
6*x**2*(45*x - 2)**2/11
Let z(i) be the first derivative of -4/3*i**3 - 89 - 34*i**2 + i**4 - 60*i. Suppose z(q) = 0. What is q?
-3, -1, 5
Factor 1/7*v**4 + 6/7*v**3 + 6/7*v + 11/7*v**2 + 0.
v*(v + 1)*(v + 2)*(v + 3)/7
Suppose 6*h = 54 - 96, -4*f - 2*h + 70 = 0. Let a(o) be the second derivative of 1/30*o**3 + 1/5*o**2 + 0 - 1/60*o**4 - f*o. Factor a(y).
-(y - 2)*(y + 1)/5
Let h(f) be the second derivative of 3*f**5/40 - 5*f**4/8 - 113*f**3/4 + 351*f**2/4 - 268*f - 2. Factor h(n).
3*(n - 13)*(n - 1)*(n + 9)/2
Let a(m) be the first derivative of m**5/3 - 125*m**4/4 - 520*m**3/3 - 790*m**2/3 - 762. Factor a(x).
5*x*(x - 79)*(x + 2)**2/3
What is l in 33/7*l**3 - 6/7*l**5 + 0 - 27/7*l - 51/7*l**2 + 51/7*l**4 = 0?
-1, -1/2, 0, 1, 9
Let b be 796/462 + 962/10101. Determine z so that -b*z + 2 - 2/11*z**2 = 0.
-11, 1
Let u(v) = -2*v**2 - 5*v + 154. Let g be u(0). Let n = g - 152. Suppose -6/5 + 3/5*h + 9/5*h**n = 0. What is h?
-1, 2/3
Let q(z) be the first derivative of z**8/11760 + z**7/840 + z**6/168 + 3*z**5/280 - 2*z**3/3 + 21. Let s(p) be the third derivative of q(p). Factor s(t).
t*(t + 1)*(t + 3)**2/7
Let l(q) be the second derivative of q**7/21 + q**6/75 - 117*q**5/50 + 59*q**4/6 - 268*q**3/15 + 84*q**2/5 + 698*q. Suppose l(v) = 0. Calculate v.
-6, 1, 14/5
Let y(j) = -5*j**2 + 55*j - 30. Let f be y(19). Let v = f + 792. Factor 1/4*s**v - 2*s + 4.
(s - 4)**2/4
Let c(u) be the third derivative of -u**8/72 - 277*u**7/630 + 439*u**6/90 - 1723*u**5/180 + 29*u**4/36 + 100*u**3/9 - 6402*u**2. Find o, given that c(o) = 0.
-25, -2/7, 1/2, 1, 4
Suppose 0 = 27*m - 26*m - 4. Let c(s) = -3*s - 3. Let f be c(-5). Factor -8 - y**2 - m*y**2 + f*y + y**2.
-4*(y - 2)*(y - 1)
Let g be (988/3458)/((-3)/(-3)). Determine c so that -4/7*c + 0 - g*c**3 + 6/7*c**2 = 0.
0, 1, 2
Let q be -1*((-80)/6 - -16*(-16)/64). Let n(m) be the first derivative of -10*m**2 - q*m**3 + 5 + 4*m - 7*m**4. What is r in n(r) = 0?
-1, 1/7
Let o(y) = -9*y**4 + 24*y**3 + 65*y**2 + 76*y + 18. Let g(d) = 45*d**4 - 120*d**3 - 313*d**2 - 380*d - 89. Let w(x) = -2*g(x) - 11*o(x). Factor w(n).
(n - 5)*(n + 1)*(3*n + 2)**2
Let q = 53760678/40859 + 993/3143. Let r = -1315 + q. Factor 2/13*w**2 + 16/13*w + r.
2*(w + 1)*(w + 7)/13
Let -14/3*b**4 - 4/9*b**5 - 26*b - 18*b**3 - 286/9*b**2 - 8 = 0. Calculate b.
-4, -3, -3/2, -1
Suppose -66 = -113*g + 386. Determine a so that -7/6*a**g + 0*a + 0 - a**2 + 23/6*a**3 = 0.
0, 2/7, 3
Suppose 5*q - 10 = 0, 5*b + 0*q - 3*q - 4 = 0. Find f such that -270385*f - 202904 + 63815*f - 3*f**4 - 20808*f**b - 265078*f - 3806104 - 408*f**3 = 0.
-34
Suppose -7*l + 31*l = -48. Let u be 4 - (0 + -8*l/8). Find f such that -2/5 + 0*f + 4/5*f**u - 2/5*f**4 + 0*f**3 = 0.
-1, 1
Factor 2*l**3 + 204570 + 222*l - 204958 - 20*l + 97*l**2 + 99*l**2 - 12*l.
2*(l - 1)*(l + 2)*(l + 97)
Let d(w) = -w**3 + 112*w**2 - 67*w - 4882. Let k be d(111). Determine n, given that -16/3*n**k + 2/3*n**3 + 16/3 - 2/3*n = 0.
-1, 1, 8
Let m(n) be the first derivative of -5*n**6/3 + 242*n**5/5 - 27*n**4/5 - 616*n**3/3 - 1048*n**2/5 - 384*n/5 + 1204. Suppose m(k) = 0. What is k?
-1, -2/5, 2, 24
Let a(w) be the first derivative of w**4/5 - 56*w**3/15 + 62*w**2/5 + 504*w/5 + 1636. Suppose a(t) = 0. Calculate t.
-2, 7, 9
Suppose 3*g = 17*g - 112. Suppose -2*p + g = 2*p. Find d, given that -4*d - 27*d**3 + 45*d**p + 3 + 4*d - 21*d = 0.
1/3, 1
Let n(x) be the second derivative of x**4/12 - 562*x**3 + 1421298*x**2 + 3*x - 771. Factor n(y).
(y - 1686)**2
Let w(r) be the first derivative of 2/3*r**4 + 0*r**2 - 16/9*r**3 - 206 + 0*r + 1/18*r**6 + 7/15*r**5. Solve w(v) = 0 for v.
-4, 0, 1
Suppose 31*p + 712899 - 712992 = 0. Factor -2/19*c**p - 198/19*c - 2*c**2 - 162/19.
-2*(c + 1)*(c + 9)**2/19
Let z(w) = -3*w**2 + 54*w - 243. Let d be z(9). Solve -1 + d*g + 1/4*g**2 = 0.
-2, 2
Let c(p) = -4*p**3 + 1388*p**2 + 158692*p + 6083516. Let h(s) = 3*s**3 - 1387*s**2 - 158693*s - 6083514. Let w(r) = -7*c(r) - 8*h(r). Factor w(u).
4*(u + 115)**3
Let q(b) be the third derivative of -b**6/24 + 43*b**5/12 - 205*b**4/12 + 1499*b**2. Determine k, given that q(k) = 0.
0, 2, 41
Let k(l) be the third derivative of -l**7/70 - 7*l**6/10 + 47*l**5/10 + 7*l**4/2 - 93*l**3/2 + 18*l**2 - 36. Solve k(a) = 0.
-31, -1, 1, 3
Solve 368/9 - 40*r + 28/3*r**2 + 2/9*r**3 = 0 for r.
-46, 2
Let c(q) = -175*q**3 + 30*q**2 + 175*q + 255. Let h(s) = 11*s**3 - 2*s**2 - 11*s - 16. Let r(g) = 6*c(g) + 95*h(g). Solve r(m) = 0.
-2, -1, 1
Let d(z) = 6*z**3 - 30*z**2 + 48*z + 78. Let m be ((-1 - -3) + 3)/1. Let v(y) = 11*y**3 - 59*y**2 + 94*y + 154. Let n(t) = m*d(t) - 3*v(t). Factor n(c).
-3*(c - 6)*(c - 4)*(c + 1)
Let t = 41829/2 - 20914. Factor -2 - t*l**2 + 2*l.
-(l - 2)**2/2
Let h(p) be the third derivative of p**2 + 16 + 0*p + 1/40*p**6 - 3/20*p**5 - 1/8*p**4 + 3/2*p**3. Factor h(y).
3*(y - 3)*(y - 1)*(y + 1)
Factor -1800000 - 6500*a**2 + 132346*a - 573*a**4 + 280*a**4 - 432346*a + 500*a**3 + 288*a**4.
-5*(a - 60)**2*(a + 10)**2
Let t(b) be the second derivative of 10/3*b**4 - 145*b - 1/2*b**5 + 0 + 45/2*b**2 + 15*b**3 - 1/6*b**6. Factor t(c).
-5*(c - 3)*(c + 1)**2*(c + 3)
Let d = -61 + 16. Let i = -42 - d. Find m such that 5*m**2 + 2 + 6*m - i*m**2 - 2*m = 0.
-1
Let a be (6/34)/((-2664)/(-25160)). Factor 0 + 5/3*i**4 - a*i**2 + 5*i**3 - 5*i.
5*i*(i - 1)*(i + 1)*(i + 3)/3
Let g(u) = -u**2 - 14*u - 11. Let v be g(-13). Suppose 14 - 3*a**2 + 5 - v + a**3 - 24*a - 45 = 0. Calculate a.
-2, 7
Let c be (60/(-50))/((-4)/(-170)). Let n be 280 - (8/20 + c/15). Factor n + 57*t + 21*t + 3*t**2 + 224.
3*(t + 13)**2
Let p(n) = -100*n + 9403. Let b be p(94). Factor b*o**2 + 3/2 + 15/4*o + 3/4*o**3.
3*(o + 1)**2*(o + 2)/4
Let u = 376 - 374. Let w be (2*u/8)/((-4)/(-12)). Let -3/2*n - 3/2*n**2 + 3/2*n**3 + w*n**4 + 0 = 0. What is n?
-1, 0, 1
Let n(c) = c**3 + 17*c**2 - 30*c - 3. Let a be n(-19). Let w = a - -158. Find h such that 3/2*h**2 + 0 - 3/2*h**4 + h - 1/2*h**5 - 1/2*h**w = 0.
-2, -1, 0, 1
Let x(i) be the first derivative of -81 + 3/5*i**5 + 0*i - i**3 + 3/2*i**2 - 3/4*i**4. Solve x(s) = 0 for s.
-1, 0, 1
Solve 38/3*l**2 - 1/3*l**3 - 38/3 + 1/3*l = 0.
-1, 1, 38
Let j(x) = 325*x - 4872. Let u be j(15). Let 0 + 8/3*z**u - 2/3*z**5 + 4/3*z**4 - 2*z - 4/3*z**2 = 0. What is z?
-1, 0, 1, 3
Let p(c) be the third derivative of -c**7/42 - c**6/12 + 7*c**5/12 - 5*c**4/6 - 45*c**2 + 10*c. What is s in p(s) = 0?
-4, 0, 1
Suppose -26*y**4 + 19 + 77 + 12*y**3 + 4*y**5 + 136*y**3 - 36*y**2 - 13*y**4 - 152*y - 21*y**4 = 0. Calculate y.
-1, 1, 2, 12
Let a be (-2)/(-7) - 1/(-7)*12. Factor 80*w - 69*w**2 + 30 - 16*w**a - 25.
-5*(w - 1)*(17*w + 1)
Let t be ((-5)/3)/(30/(-36)). Factor 20*p**2 - 25*p**3 + 3*p + 9*p**2 + 2*p - 9*p**t.
-5*p*(p - 1)*(5*p + 1)
Let m(h) be the first derivative of -h**5/12 + 5*h**4/6 - 10*h**3/3 + 7*h**2/2 - 2*h - 74. Let n(b) be the second derivative of m(b). Factor n(x).
-5*(x - 2)**2
Let u(q) be the third derivative of -q**6/900 + 4*q**5/75 - q**4/4 + 9*q**3/2 - 2*q**2 + 5*q. Let d(h) be the first derivative of u(h). Factor d(x).
-2*(x - 15)*(x - 1)/5
Solve -76*s**2 + 3*s**3 + 128*s**2 - 73*s**2 = 0.
0, 7
Let d be (6/27)/(-1) + 1376200/(-630). Let g = -2178 - d. What is k in 8*k - g*k**4 + 4/3 + 16/3*k**2 - 8*k**3 = 0?
-1, -1/5, 1
Let v(a) be the first derivative of 25 + 0*a**3 + 0*a**5 + 2/3*a**6 + 0*a + 2*a**2 - 2*a**4.