(w + 13)
Let a(n) be the first derivative of n**5/4 + 25*n**4/6 + 80*n**3/3 + 80*n**2 + 25*n + 51. Let l(h) be the first derivative of a(h). Let l(i) = 0. What is i?
-4, -2
Let t be ((-21)/49)/((-79299)/(-2646) + -30). Determine u so that -2/7*u**3 - t*u + 0 - 4*u**2 = 0.
-7, 0
Let l(g) = -264*g + 7132. Let t be l(27). Suppose 3/2*u**3 + 0 - 25/6*u + 1/6*u**t + 5/2*u**2 = 0. Calculate u.
-5, 0, 1
Let i(s) = -18*s**3 + 74*s**2 - 6*s. Let v(a) = 98*a**2 - 15*a**3 + 16*a**3 - 97*a**2 + a. Let c(m) = -i(m) + 10*v(m). Factor c(d).
4*d*(d - 2)*(7*d - 2)
Let d(b) = -6*b**2 + 5800*b - 1956. Let c(w) = -w**2 + 1160*w - 391. Let s(z) = 21*c(z) - 4*d(z). Find t such that s(t) = 0.
-387, 1/3
Suppose -6*s + 23*s + 2*s**2 + 5 - s**2 + 10 - 9*s = 0. Calculate s.
-5, -3
Suppose -l + k = -4*l + 38943, -3*l + 38958 = -4*k. Determine x, given that -l*x + 13008*x + 36 - 8 - 2*x**2 = 0.
-1, 14
Let n(b) be the first derivative of 15/2*b**2 - 69 + 1/3*b**3 + 14*b. Determine o so that n(o) = 0.
-14, -1
Let k = 2601 - 2580. Let g(p) be the first derivative of -k + 0*p - 3/10*p**5 + 2/3*p**3 + 0*p**2 - 1/12*p**6 + 0*p**4. Suppose g(x) = 0. What is x?
-2, 0, 1
Let m be -1*16 - (696/(-435))/(12/135). What is i in -3*i**5 - 69/4*i + 15/4*i**4 - 33/4*i**m + 81/4*i**3 + 9/2 = 0?
-2, -1, 1/4, 1, 3
Let x(a) = -65*a**4 + 25*a**3 - 75*a**2 - 195*a - 60. Let z(b) = 2*b**4 + b**3 + 2*b + 2. Let s(p) = -x(p) - 30*z(p). Factor s(m).
5*m*(m - 9)*(m - 3)*(m + 1)
Let x = 68482/187 + -4018/11. Let -x + 44/17*t**2 - 46/17*t**3 + 8/17*t**5 - 10/17*t**4 + 56/17*t = 0. Calculate t.
-2, -1, 1/4, 2
Let r(y) = -y**2 + 2*y + 3. Suppose 16*i - 18 = 7*i. Let p(n) = n - 1. Let a(w) = i*r(w) + 6*p(w). Factor a(c).
-2*c*(c - 5)
Let z = 448057/3 - 149347. Factor -z + 1/3*x**2 - 2*x.
(x - 8)*(x + 2)/3
Let v be 4/(-10) + 5760/(-100) + 58. Suppose 5*h = 2*h + 5*l + 4, 3*h + 2*l - 11 = 0. Determine m so that 0*m**2 + 2/7*m**h + v - 2/7*m = 0.
-1, 0, 1
Let k(v) = -v**3 + 15*v**2 - 47*v - 24. Let u be k(8). Let p be 2/(u/(-104)) + 6. Let 2/3*n + n**4 - 4/3*n**3 + 0 - p*n**2 = 0. Calculate n.
-1, 0, 1/3, 2
Let a be (2 - -5) + (0 - 4). What is u in -3*u**3 + a*u**2 - 124*u + 245*u - 121*u = 0?
0, 1
Let r(k) = 2*k**3 - k**2 - 14*k. Let b be ((-6)/(-8))/((-33)/(-132)). Let y be r(b). Suppose -5/3*q**5 + 0 + 10/3*q**y + 0*q**2 - 5/3*q + 0*q**4 = 0. What is q?
-1, 0, 1
Suppose -4*z - 1527 = 3*c + 776, 3*c - 9 = 0. Let d = z - -582. Factor -1/3*o**3 + d + 4/3*o - o**2.
-(o - 2)*(o + 2)*(o + 3)/3
Let r(c) = c**4 + 43*c**3 + 198*c**2 + 380*c + 248. Let i(t) = t**4 + 46*t**3 + 198*t**2 + 380*t + 248. Let d(y) = 2*i(y) - 3*r(y). Factor d(l).
-(l + 2)**3*(l + 31)
Let m(n) be the second derivative of n**4/4 + 9*n**3 + 51*n**2/2 + 3247*n. Factor m(z).
3*(z + 1)*(z + 17)
Let q(r) = -8*r**2 + 61*r - 2*r**4 + 49*r**3 - 4*r**4 - 123*r**2. Let l(h) = -h**3 - h**2 - h. Let v(t) = -6*l(t) + 2*q(t). Factor v(z).
-4*z*(z - 4)**2*(3*z - 2)
Let k(b) be the second derivative of -1/4*b**4 + 0 + 0*b**2 + b**3 - 55*b. Determine a so that k(a) = 0.
0, 2
Let v(u) be the second derivative of -49*u**6/135 + 17*u**5/30 + 16*u**4/9 - 4*u**3/27 + 83*u. Find o such that v(o) = 0.
-1, 0, 2/49, 2
Let s(u) be the second derivative of u**7/168 - 13*u**6/120 - 183*u**5/80 + 2561*u**4/48 - 1183*u**3/12 + 2842*u. Determine j, given that s(j) = 0.
-14, 0, 1, 13
Let p(z) be the third derivative of 0 + 0*z**4 - 125*z**2 - z - 4/21*z**3 + 1/210*z**5. Suppose p(m) = 0. What is m?
-2, 2
Suppose -348 - 392 = -185*p. Let x(c) be the first derivative of 0*c**2 - 1/24*c**6 - 1/6*c**3 - 1/5*c**5 - 14 - 5/16*c**p + 0*c. Find m such that x(m) = 0.
-2, -1, 0
Let m(r) be the third derivative of r**5/210 + 34*r**4/21 + 4624*r**3/21 + 409*r**2. Factor m(w).
2*(w + 68)**2/7
Let d(a) be the first derivative of -a**4/21 + 76*a**3/21 - 74*a**2/7 + 144*a - 22. Let h(b) be the first derivative of d(b). Factor h(q).
-4*(q - 37)*(q - 1)/7
Determine c, given that 2368*c**4 + 119*c**2 - 416*c**5 + 19247*c - 96*c**5 + 2 - 2 - 19242*c + 936*c**3 = 0.
-1/8, 0, 5
Suppose 0 = -q - 79*q + 16 + 144. Let g(v) be the first derivative of -18 + 0*v**3 + 6*v - 3/4*v**4 + 9/2*v**q. Find p, given that g(p) = 0.
-1, 2
Suppose -3 = -11*x + 63. Let -7*y**4 + x*y**2 - 5*y**3 - 3*y**4 + 11*y**4 = 0. Calculate y.
0, 2, 3
Let u(y) be the third derivative of y**10/226800 - 19*y**5/60 + y**4/24 + 41*y**2. Let g(x) be the third derivative of u(x). What is n in g(n) = 0?
0
Let r(i) be the third derivative of 0 - 13/4*i**4 + 0*i + 130*i**2 - 1/20*i**5 + 0*i**3. Find x, given that r(x) = 0.
-26, 0
Let h(i) be the second derivative of i**5/50 - 2677*i**4/10 + 7166329*i**3/5 - 19184262733*i**2/5 + 2452*i. Find l such that h(l) = 0.
2677
Let v(g) be the second derivative of -g**6/60 - 33*g**5/80 - 59*g**4/48 + 25*g**3/4 - 7*g**2 + 1288*g. Suppose v(t) = 0. What is t?
-14, -4, 1/2, 1
Let l(n) = -50*n**3 - 280*n**2 + 1545*n - 1275. Let z(b) = 7*b**3 + 40*b**2 - 221*b + 182. Let d(r) = 2*l(r) + 15*z(r). Solve d(m) = 0.
-12, 1, 3
Find q, given that -3/5*q**3 + 0 - 651/5*q**2 + 0*q = 0.
-217, 0
Let q(k) be the third derivative of 3*k**8/280 - 26*k**7/175 - k**6/6 + 22*k**5/15 - 119*k**4/60 + 6*k**3/5 + 120*k**2 - 4. Determine x so that q(x) = 0.
-2, 1/3, 1, 9
Let k be ((-11099)/(-44))/(1180/(-16)) + 5. Let n = 13/59 + k. Factor -n + 8/5*x + 1/5*x**2.
(x - 1)*(x + 9)/5
Let k(t) = t**2 + 31*t + 193. Let a(p) = 3*p + 112. Let d be a(-45). Let w be k(d). Factor 12*i**3 - 3*i**2 + w*i**4 + 3/2*i**5 - 27/2*i - 6.
3*(i - 1)*(i + 1)**3*(i + 4)/2
Let p(u) be the third derivative of u**5/60 + 191*u**4/24 + 63*u**3 - 10304*u**2. Suppose p(s) = 0. Calculate s.
-189, -2
Let f(d) be the third derivative of -1/30*d**5 - 52/21*d**4 + d**2 - 50*d + 20/7*d**3 + 0. Factor f(o).
-2*(o + 30)*(7*o - 2)/7
Let p(l) be the third derivative of l**8/112 + l**7/70 - 3*l**6/8 + 23*l**5/20 - 5*l**4/4 + 4384*l**2. Factor p(u).
3*u*(u - 2)*(u - 1)**2*(u + 5)
Determine a, given that 0*a + 1/4*a**5 - 7/4*a**2 - 9/4*a**4 + 0 + 15/4*a**3 = 0.
0, 1, 7
Let q(t) be the third derivative of 1/315*t**7 - 1/10*t**5 + 0 - 127*t**2 - 1/45*t**6 + 1/1008*t**8 + 0*t**3 + 0*t - 1/8*t**4. Determine i, given that q(i) = 0.
-3, -1, 0, 3
What is d in d**5 - 22*d**4 + 69*d**3 - 83*d**3 + 86*d**3 = 0?
0, 4, 18
Let b be 3/(-4) + 1799161/28. Let 64255 - 432*x - b - 3*x**3 + 72*x**2 = 0. Calculate x.
0, 12
Let l = -153231 - -1379087/9. Determine c, given that 0 + l*c - 2/9*c**3 + 32/9*c**2 - 8/9*c**4 = 0.
-2, -1/4, 0, 2
Factor 723/2*g + 360*g**2 - 3/2*g**3 + 0.
-3*g*(g - 241)*(g + 1)/2
Let f = -64 + 37. Let m = f - -31. Find z such that z**2 + 4*z**2 + 8*z**3 - 25*z - 8*z**m + 3*z**4 + 17*z**3 = 0.
-1, 0, 1, 5
Let m(f) be the second derivative of f**5/130 + 31*f**4/78 - 176*f**3/39 + 144*f**2/13 - 2537*f. Suppose m(y) = 0. Calculate y.
-36, 1, 4
Suppose 9*v**4 + 52*v**5 + 3*v**3 - 12*v**3 - 22*v**5 - 3*v**2 - 26*v**5 - v**3 = 0. Calculate v.
-3, -1/4, 0, 1
Let s(v) be the third derivative of 85/4*v**5 - 4/3*v**6 + 1/42*v**7 + 0 - 640/3*v**3 + 20/3*v**4 + 0*v + 222*v**2. Suppose s(b) = 0. Calculate b.
-1, 1, 16
Let b(a) = -2*a + 84. Let y be b(40). Factor -30*p**3 - 7*p**y + 30*p + 6 + 10*p**4 + 40*p**2 + 2*p**4 - 51.
5*(p - 3)**2*(p - 1)*(p + 1)
Let v(n) be the first derivative of 2*n**3/21 + 19*n**2/7 - 132*n/7 - 629. Solve v(a) = 0.
-22, 3
Let d(r) be the first derivative of -1355*r**3 + 2030*r**2 + 5*r - 7710. What is s in d(s) = 0?
-1/813, 1
Let b(o) be the second derivative of o**7/336 - o**6/120 - 3*o**5/160 + o**4/12 - o**3/12 - 3727*o. Factor b(h).
h*(h - 2)*(h - 1)**2*(h + 2)/8
Let k(u) be the first derivative of 243 - 36*u + 2/9*u**3 + 53/3*u**2. Factor k(c).
2*(c - 1)*(c + 54)/3
Let z = -145 + 149. Determine k, given that 35*k**3 + 37*k**3 - 123*k**z + 120*k**4 - 208*k**2 - 224*k**2 = 0.
0, 12
Let s(k) be the third derivative of k**7/1050 + k**6/120 + k**5/150 - k**4/15 + 528*k**2. Factor s(v).
v*(v - 1)*(v + 2)*(v + 4)/5
Let o(z) be the third derivative of -z**7/105 - 17*z**6/10 - 493*z**5/30 - 65*z**4 - 388*z**3/3 - 602*z**2. Factor o(j).
-2*(j + 1)*(j + 2)**2*(j + 97)
Let i(d) be the first derivative of -4*d**3/9 + 142*d**2/3 - 272*d + 3344. Factor i(p).
-4*(p - 68)*(p - 3)/3
Suppose -3*o + 0*o + 2*m + 52 = 0, 5*m = 3*o - 58. Let h be (-30)/20*o/(