r).
(r - 1)**2*(r + 1)*(r + 2)/3
Let k(o) = 8*o**5 - o**3 + 7*o**2 - 14*o. Let j(m) = 7*m**5 + m**4 - 2*m**3 + 6*m**2 - 12*m. Let r(a) = 7*j(a) - 6*k(a). Factor r(w).
w**3*(w - 1)*(w + 8)
Let b(f) be the first derivative of -5/32*f**4 + 3/80*f**5 + 0*f**2 + 1 + 4*f**3 + 0*f - 1/480*f**6. Let q(m) be the third derivative of b(m). Factor q(x).
-3*(x - 5)*(x - 1)/4
Suppose 9 - 1/2*r**3 - 9/2*r - 4*r**2 = 0. Calculate r.
-6, -3, 1
Let o(d) be the third derivative of -d**6/60 - 91*d**5/30 + 70*d**4/3 - 188*d**3/3 + 141*d**2 - 3*d - 1. What is t in o(t) = 0?
-94, 1, 2
Let f be 2/(11 + -41 + 35). Find y, given that -2/5*y**2 + 4/5*y - f = 0.
1
Solve 24*d**3 - d**4 + 3*d**4 + 4*d**4 - 8*d**4 + 74*d**2 - 6*d**3 - 72 - 18*d = 0.
-3, -1, 1, 12
Suppose 16*j = 18*j - 56. Solve 50*w + 4*w**2 - 32 - 30*w - j*w = 0.
-2, 4
Let r(q) be the first derivative of -5*q**4/4 + 95*q**3/3 - 30*q**2 - 540*q - 206. Solve r(p) = 0 for p.
-2, 3, 18
Suppose -362/9 - 4/3*z**2 - 730/9*z = 0. What is z?
-181/3, -1/2
Let a(h) be the second derivative of 35/24*h**4 + 2*h + 0*h**3 + 1/12*h**5 + 0 - 17/2*h**2. Let b(v) be the first derivative of a(v). Solve b(k) = 0 for k.
-7, 0
Let -29970*i - 982*i**2 - 8*i**4 + 170*i**3 + 1800 - 29493*i + 60103*i = 0. Calculate i.
-1, 9/4, 10
Suppose 39*u - u - 9462 = 0. Let a = -249 + u. What is v in 11/4*v**2 - 1/2*v + 7/4*v**4 + a - 4*v**3 = 0?
0, 2/7, 1
Let o(m) be the second derivative of -m**4/18 - 2*m**3/9 + 8*m**2 + 4*m + 149. Factor o(c).
-2*(c - 4)*(c + 6)/3
Let g(a) = a**2 + 34*a + 29. Let o(m) = -m**2 + m - 4. Let f(d) = 8*d**2 + 30*d + 52. Let r(c) = f(c) + 6*o(c). Let i(h) = -3*g(h) + 2*r(h). Factor i(l).
(l - 31)*(l + 1)
Let k(v) be the second derivative of -v**4/4 - 455*v**3/2 - 681*v**2 + 6201*v. What is l in k(l) = 0?
-454, -1
Let h(g) be the first derivative of 20/3*g**3 - 5*g**5 - 15/2*g**4 - 13 + 20*g**2 - 5/6*g**6 + 0*g. Factor h(b).
-5*b*(b - 1)*(b + 2)**3
Let o(p) be the third derivative of -1/112*p**8 + 21/40*p**6 - 47/20*p**5 - 15*p**4 + 72*p**3 + 0 + 58*p**2 + 0*p + 3/70*p**7. Determine j, given that o(j) = 0.
-3, 1, 4
Let p = -142767/8 - -714251/40. Factor p*u - 14/5*u**2 - 48/5.
-2*(u - 2)*(7*u - 12)/5
Let u(i) be the first derivative of -80/3*i**3 + 221 + 5/4*i**4 - 490*i + 385/2*i**2. Factor u(l).
5*(l - 7)**2*(l - 2)
Let o(m) = m**4 + 9*m**3 + 15*m**2 - 22*m - 3. Let g(i) = -4 - 2 + i - 1 + 4 + 2. Let r(p) = -3*g(p) + o(p). Let r(v) = 0. Calculate v.
-5, 0, 1
Suppose 17*f - 1764 + 836 = -877. Solve -4/7*j**f + 4/7*j + 4/7*j**2 - 4/7 = 0 for j.
-1, 1
Let k(t) = 5*t**3 - 82*t**2 + 629*t - 968. Let u(q) = -3*q**3 + 84*q**2 - 627*q + 969. Let r(l) = -3*k(l) - 4*u(l). Factor r(d).
-3*(d - 3)**2*(d + 36)
Let q(f) be the second derivative of f**5/100 - 83*f**4/30 + 163*f**3/30 + 33*f**2 + 2460*f. Factor q(j).
(j - 165)*(j - 2)*(j + 1)/5
Let l(g) be the third derivative of -289*g**7/1260 - 187*g**6/120 - 20*g**5/9 + 187*g**4/24 + 121*g**3/4 - 2805*g**2. Solve l(z) = 0.
-33/17, -1, 1
Suppose 7*p = 69*p + 18*p. Factor -1/2*v**2 + 1/2*v**4 + 2*v + p - 2*v**3.
v*(v - 4)*(v - 1)*(v + 1)/2
Let i(h) be the first derivative of h**4/8 - 23*h**3/6 + 30*h**2 + 72*h - 1956. Solve i(u) = 0.
-1, 12
Let x(o) = o**3 - 9*o**2 + 26*o + 36. Let f(d) = 3*d**3 - 12*d**2 + 27*d + 36. Let t(c) = -2*f(c) + 3*x(c). Determine r, given that t(r) = 0.
-2, 3
Let o = -610 - -613. Let h be (5 - o) + -3 - (-4)/1. Factor -93/10*c - 9/5 - 9/10*c**h - 28/5*c**2.
-(c + 3)**2*(9*c + 2)/10
Let m(r) be the second derivative of 7/25*r**5 + 0*r**2 - 2/75*r**6 + 6/5*r**3 - 277*r + 17/15*r**4 - 2. Determine i, given that m(i) = 0.
-1, 0, 9
Suppose 4*b + 0*b + 168 = -5*v, 0 = -v + 2*b - 42. Let j = -20 - v. Factor -16*i + j*i - 4*i**3 - 6*i**4.
-2*i**3*(3*i + 2)
Let p(d) be the second derivative of -d**5/60 - 47*d**4/36 - 22*d**3/9 + 46*d**2/3 + 8418*d. Factor p(a).
-(a - 1)*(a + 2)*(a + 46)/3
Determine v, given that -82/7*v**3 - 86/21*v**4 - 80/21*v + 0 - 2/21*v**5 - 242/21*v**2 = 0.
-40, -1, 0
Let u be 4 + (-4 + 5)*-1. Let k = 1919 - 3837/2. Suppose 1/6*n**u + k*n**2 - 1/6*n - 1/2 = 0. What is n?
-3, -1, 1
Let k(f) be the first derivative of f**6/60 + 37*f**5/50 + 33*f**4/40 - 109*f**3/30 - 17*f**2/10 + 36*f/5 - 1950. Determine z, given that k(z) = 0.
-36, -2, -1, 1
Let n(k) be the third derivative of -k**6/120 + 11*k**5/30 - 14*k**4/3 - 376*k**2 - 4. Suppose n(m) = 0. What is m?
0, 8, 14
Suppose -180*f - 72 = -192*f. Suppose -4*r = 3*m - 3, 3*r - 3*m = -f*m + 3. Find y such that r*y + 0*y**2 - 4/3*y**5 + y**3 + 0 - 11/3*y**4 = 0.
-3, 0, 1/4
Factor 1/4*h**4 - 8*h**3 + 225/4 - 120*h + 143/2*h**2.
(h - 15)**2*(h - 1)**2/4
Let b(c) be the third derivative of 0*c**3 - 7/8*c**4 - 1/120*c**6 + 0*c - 1/6*c**5 - 9 - 14*c**2. Factor b(k).
-k*(k + 3)*(k + 7)
Let s(l) = l**2 + 6*l + 2. Let i be s(-7). Let h = 2288 - 2286. Let i*b - 14*b - 5*b**3 + 10*b**h + 80*b**3 = 0. What is b?
-1/3, 0, 1/5
Let g(o) = -254*o**4 + 528*o**3 - 574*o**2 + 230*o - 980. Let u(j) = -11*j**4 + 23*j**3 - 25*j**2 + 10*j - 42. Let k(s) = 6*g(s) - 140*u(s). Factor k(f).
4*f*(f - 1)**2*(4*f - 5)
Let h be (-2268)/(-6426) - (-606)/306. Determine j, given that -1/3*j**5 - 4/3 + 0*j - j**4 + 1/3*j**3 + h*j**2 = 0.
-2, -1, 1
Let s(r) be the third derivative of r**8/1512 - r**7/135 + 11*r**6/540 + 19*r**5/270 - 5*r**4/9 + 4*r**3/3 + 513*r**2. Let s(f) = 0. Calculate f.
-2, 1, 2, 3
Let q(k) = 22*k**2 + 24*k + 12. Let w(i) = 12*i**2 + 12*i + 4. Let j(p) = 2*q(p) - 5*w(p). Suppose j(b) = 0. What is b?
-1, 1/4
Let g(x) be the third derivative of x**8/112 - x**7/14 + x**6/20 + 2*x**5/5 - 5712*x**2. Factor g(n).
3*n**2*(n - 4)*(n - 2)*(n + 1)
Let k(m) be the first derivative of -80*m**6 + 95 - 27/2*m**2 + 312/5*m**5 - 33/2*m**3 + 0*m + 489/8*m**4. Determine v so that k(v) = 0.
-3/8, 0, 2/5, 1
Let p(h) = -h**2 + 2*h + 9. Let i be p(3). Let z be -8*(-3)/i + 0. Factor -z*w - 4*w**5 + 4*w + 2*w**5.
-2*w**5
Let s(d) be the third derivative of d**7/1890 - d**6/45 + 197*d**5/540 - 35*d**4/12 + 12*d**3 - 119*d**2 + 5. Factor s(c).
(c - 9)**2*(c - 4)*(c - 2)/9
Solve -8/3*i**2 + 4/3*i - 34/3*i**4 - 3*i**5 - 37/3*i**3 + 0 = 0.
-2, -1, 0, 2/9
Let y(l) be the first derivative of -l**5/2 + 335*l**4/12 + 90*l**3 + 195*l**2/2 + 235*l/6 + 850. What is i in y(i) = 0?
-1, -1/3, 47
Suppose 52 = -638*w + 651*w. Suppose 4*x = w*r - 36, -13*r + 5*x + 50 = -7*r. Factor 16/5 + 11/5*m**4 + 43/5*m**3 + 1/5*m**r + 73/5*m**2 + 56/5*m.
(m + 1)**3*(m + 4)**2/5
Suppose 0 = 16*u - 13*u. Suppose u = -3*h + 7 + 2. Determine z, given that -5*z**2 + z + 2 + 7*z**2 + h*z + 0 = 0.
-1
Let d(y) be the second derivative of 3*y**5 + 548*y**4/3 + 578*y**3/3 + 72*y**2 + 1376*y. Factor d(s).
4*(s + 36)*(3*s + 1)*(5*s + 1)
Factor 0 + 2/5*s**4 + 14/5*s**2 - 16/5*s**3 + 0*s.
2*s**2*(s - 7)*(s - 1)/5
Let r = 441 - 469. Let t be (108/(-21))/(-6)*r/(-6). What is w in -8/3*w + 0 - 4/3*w**3 - t*w**2 = 0?
-2, -1, 0
Let q(y) be the first derivative of -2*y**5/5 - 5*y**4 - 64*y**3/3 - 38*y**2 - 30*y + 819. Factor q(d).
-2*(d + 1)**2*(d + 3)*(d + 5)
Let c = 305523 - 305521. Let l(g) = -g**3 - 5*g**2 + 3. Let w be l(-5). Factor -21/2*p - 9/2 - 15/2*p**c - 3/2*p**w.
-3*(p + 1)**2*(p + 3)/2
Let v(m) = 17*m - 89. Let p(i) = -34*i + 182. Let w(r) = -3*p(r) - 5*v(r). Let h be w(6). Suppose -5/2*b - 7/2*b**2 + h = 0. What is b?
-1, 2/7
Let f(v) be the third derivative of -v**7/70 - 13*v**6/40 - 39*v**5/20 + 13*v**4/8 + 20*v**3 + 2*v**2 - 200*v. Find g such that f(g) = 0.
-8, -5, -1, 1
Let y = 77065/12 - 6422. Let q(k) be the second derivative of 1/3*k**3 + 19*k + y*k**4 + 0 - 3/2*k**2. Suppose q(d) = 0. Calculate d.
-3, 1
Let v(f) be the first derivative of -183*f**3/2 + f**2/2 - 175. Find g, given that v(g) = 0.
0, 2/549
Let k(w) = -4*w**4 + 7*w**3 - 14*w**2 + 17*w - 6. Let j = 67 - 64. Let v(t) = t**4 - t**2. Let f(c) = j*v(c) + k(c). Let f(y) = 0. What is y?
1, 2, 3
Let n = -60 + 62. Let 5*x**2 - 24*x**4 + 16*x + 4*x**5 - 26*x**2 + 52*x**3 - 36*x**n + 9*x**2 = 0. What is x?
0, 1, 2
Let o = -10930/11 + 142310/143. Factor 0 - o*r - 2/13*r**2.
-2*r*(r + 10)/13
Determine o so that 24*o**2 - 4/9*o**5 + 0 + 40/9*o**4 - 12*o - 16*o**3 = 0.
0, 1, 3
Let r(s) = -98*s**2 + 1380*s - 1359. Let w(l) = 18*l**2 - 276*l + 272. Let x(y) = -2*r(y) - 11*w(y). What is i in x(i) = 0?
1, 13