47 - -2047. Determine t so that -1/4*t**3 + 0*t**2 + 0 + k*t + 3/4*t**4 + t**5 = 0.
-1, 0, 1/4
Let i(r) be the second derivative of 3*r**7/119 - 11*r**6/255 + r**5/85 - 225*r. Factor i(v).
2*v**3*(v - 1)*(9*v - 2)/17
Let p(t) be the third derivative of 1/90*t**6 + 1/9*t**3 + 0*t + 0 - 1/105*t**7 + 1/45*t**5 - 1/12*t**4 + 1/504*t**8 - 27*t**2. Suppose p(k) = 0. What is k?
-1, 1
Let v = -98 - -56. Let a be (-14)/v*(2 - -1). Factor -h**2 - 5*h + 0*h + 3*h - a.
-(h + 1)**2
Let r = 1/23 - -197/230. Let a(u) be the first derivative of r*u**4 - 4 + 7/5*u**2 + 2*u**3 + 2/5*u. Factor a(p).
2*(p + 1)*(3*p + 1)**2/5
Let y(n) be the second derivative of n**5/100 - n**4/12 + 2*n**3/15 + 455*n. Factor y(a).
a*(a - 4)*(a - 1)/5
Let k(f) be the third derivative of -f**7/210 - f**6/60 + 11*f**5/60 + f**4/2 - 6*f**3 + 251*f**2. Determine x so that k(x) = 0.
-3, 2
Let l(r) be the first derivative of r**6/3 - 12*r**5/5 + 9*r**4/2 + 61. Factor l(t).
2*t**3*(t - 3)**2
Let z = -276399784/698621 - 8/63511. Let t = z + 396. Factor -6/11*n**4 - t*n**2 + 0*n + 0 - 14/11*n**3.
-2*n**2*(n + 2)*(3*n + 1)/11
Suppose -8/11*p**4 + 0 - 458/11*p**2 - 12*p + 278/11*p**3 = 0. Calculate p.
-1/4, 0, 2, 33
Let h(u) = -34*u**2 - 54*u - 34. Let k(q) = -7*q**2 - 11*q - 7. Let c be 1/(-3)*-6 + 1. Let g(t) = c*h(t) - 14*k(t). Find l such that g(l) = 0.
-1
Let j(v) be the first derivative of 7*v**6/60 - 13*v**5/15 - 2*v**4/3 - 18*v**2 - 1. Let s(x) be the second derivative of j(x). Factor s(o).
2*o*(o - 4)*(7*o + 2)
Let s(h) be the third derivative of 13*h**2 + 0*h + 0*h**7 + 1/84*h**8 + 0*h**3 - 1/15*h**6 + 0 + 0*h**5 + 1/6*h**4. Determine y, given that s(y) = 0.
-1, 0, 1
Let j be (1*-1)/(-3 - 1). Suppose 4*p - 1072*t + 1071*t = -6, -2*t + 12 = -p. Find w such that -j*w**5 + p*w**2 - w**3 + 0 + 0*w + w**4 = 0.
0, 2
Suppose 64 - 2720/3*l - 750*l**5 + 12448/3*l**2 - 23600/3*l**3 + 5700*l**4 = 0. What is l?
2/15, 2/5, 2/3, 6
Factor -454/3*r - 448/3*r**2 - 38 + 8/3*r**3.
2*(r - 57)*(2*r + 1)**2/3
Let s(c) be the first derivative of -12*c - 2 - c**4 - 20/3*c**3 - 14*c**2. Factor s(t).
-4*(t + 1)**2*(t + 3)
Let l(c) be the third derivative of 0*c - 10*c**2 + 0 + 1/12*c**5 - 5/24*c**4 + 0*c**3. Determine o so that l(o) = 0.
0, 1
Let t(y) be the first derivative of -y**4/18 - 34*y**3/27 + 224. Factor t(k).
-2*k**2*(k + 17)/9
Let h(p) be the first derivative of p**4/12 + 5*p**3 + 88*p**2 + 484*p/3 + 56. What is z in h(z) = 0?
-22, -1
Let p = 20 + -19. Factor p - 3*l**2 - 4*l + 5*l**2 + 1.
2*(l - 1)**2
Let m(f) be the third derivative of f**7/280 - f**6/160 - 3*f**5/40 - 745*f**2. Solve m(t) = 0.
-2, 0, 3
Let x = -20 + 22. Factor 6*q**2 + 13*q - 3*q + 9*q**x.
5*q*(3*q + 2)
Let q(c) be the first derivative of -2*c**5/15 + 5*c**4/6 - 14*c**3/9 + c**2 + 453. Factor q(r).
-2*r*(r - 3)*(r - 1)**2/3
Suppose 3*m - 5*n + 6 - 5 = 0, 0 = -3*m - 4*n + 17. Factor -140*k**2 - 845*k**m - 20 - 368*k**2 + 39*k**2 - 280*k - 636*k**2.
-5*(k + 1)*(13*k + 2)**2
Suppose 11*c + 99*c = 7*c. Find m, given that -3/5*m**3 + 6/5*m + c + 3/5*m**2 = 0.
-1, 0, 2
Let c = -61 - -59. Let o be 1 + (-2 - -2*(-1)/c). Let 3*k**4 - 3/4*k**3 + 0*k + o + 0*k**2 = 0. What is k?
0, 1/4
Determine z, given that -139*z**5 + 158*z**3 + 184*z**5 + 21*z - 2 - 128*z**4 - 84*z**2 - 10*z**4 = 0.
1/3, 2/5, 1
Let b = -38 + 40. Let 16 + 25*j**2 - 4*j**5 + 32*j - 28*j**3 - 20*j**4 - 7*j**b - 14*j**2 = 0. Calculate j.
-2, -1, 1
Let j be (6/(-15))/(2576/4690). Let w = 1/46 - j. Factor w*l - 3/2*l**2 + 0 + 3/4*l**3.
3*l*(l - 1)**2/4
Let t be 8/14*8708/72 - 1. Let d = t + -68. Determine g so that 1/3*g**3 - 1/3*g + 1/9*g**4 - 2/9 + d*g**2 = 0.
-2, -1, 1
Let a(o) be the third derivative of -3*o**2 + 0*o + 0 - 1/20*o**4 + 0*o**3 + 1/150*o**5. Solve a(r) = 0.
0, 3
Let d(u) be the third derivative of -4*u**8/63 - 176*u**7/315 + 47*u**6/90 - 2*u**5/15 + 71*u**2. Let d(i) = 0. What is i?
-6, 0, 1/4
Solve 2*t**2 - 22/3*t**3 - 37/3*t**4 - 5*t**5 + 5/3*t - 1/3 = 0.
-1, 1/5, 1/3
Let z(w) be the third derivative of -w**7/1155 + 2*w**6/165 - w**5/15 + 2*w**4/11 - 3*w**3/11 - 2*w**2 + 29. Factor z(s).
-2*(s - 3)**2*(s - 1)**2/11
Let c(w) be the second derivative of 1/15*w**3 + 0 - 1/10*w**4 + 14*w - 1/50*w**5 + 3/5*w**2. Factor c(v).
-2*(v - 1)*(v + 1)*(v + 3)/5
Let m = 8 - 5. Let r be (2/(-10))/(19/(3040/(-48))). Suppose -2/3 - 2/3*i - 2/3*i**5 - r*i**4 + 4/3*i**m + 4/3*i**2 = 0. What is i?
-1, 1
Factor -504*b - 2*b**2 + 59*b - 533*b - 40000 + 178*b - 2*b**2.
-4*(b + 100)**2
Let h(a) = 7*a**2 + 5*a. Let l(r) = 5*r**2 + r - 1. Let s(f) = 6*h(f) - 4*l(f). Factor s(u).
2*(u + 1)*(11*u + 2)
Let u(j) = -j**2 - 31*j + 144. Let x be u(-35). Suppose 0*r**3 + 0*r - 1/3*r**x + 0 + 1/3*r**2 = 0. Calculate r.
-1, 0, 1
Let s(p) = -p + 20. Let w be s(-7). Factor -124*a**2 - 108 - 135*a + 88*a**2 + w*a - 4*a**3.
-4*(a + 3)**3
Let p(f) be the first derivative of f**6/6 - 7*f**5/5 + 7*f**4/2 - 2*f**3/3 - 15*f**2/2 + 9*f + 153. Factor p(o).
(o - 3)**2*(o - 1)**2*(o + 1)
Let g(v) = -3*v - 28. Let x be g(-12). Suppose x*z = 5*z + 6. Let -2/5*o**4 - 2/5*o + 6/5*o**z - 4/5 + 2/5*o**3 = 0. What is o?
-1, 1, 2
Let r = 176 - 199. Let n(m) = m + 25. Let b be n(r). Solve 0*x - 2/15*x**b + 2/15 = 0 for x.
-1, 1
Let h = 13895 + -13893. Factor 2/5*g**h + 0*g - 2/5.
2*(g - 1)*(g + 1)/5
Let r be (4/(-60)*-5)/((-2)/(-54)). Suppose -4*j = -r*j + 10. Determine m so that 10/9*m - 10/9*m**3 - 8/9*m**4 + 2/9 + 2/3*m**j = 0.
-1, -1/4, 1
Factor 233*v**4 + 3*v**3 + 0*v**3 - 6*v**3 - 236*v**4.
-3*v**3*(v + 1)
Find v, given that -245*v + 25 + 203*v - 57 - 85 - v**2 = 0.
-39, -3
Let v = 1 + -87. Let q = 260/3 + v. Factor q*n**3 + 4/3*n**2 - 2/3*n - 4/3.
2*(n - 1)*(n + 1)*(n + 2)/3
Let b = -12 + 35. Factor b*q**3 + 2 - 22*q**3 - q + 0*q - 2*q**2.
(q - 2)*(q - 1)*(q + 1)
Let t be (-70)/(-42) + (6/(-3) - -3). Factor t*p**2 + 16/3*p**3 + 0 + 0*p + 2/3*p**5 + 10/3*p**4.
2*p**2*(p + 1)*(p + 2)**2/3
Factor 16/17 + 6/17*q**2 - 20/17*q.
2*(q - 2)*(3*q - 4)/17
Let a(t) be the third derivative of t**7/630 - t**6/60 + 2*t**5/45 + t**4/12 - t**3/2 - 2*t**2 + 53*t. Find r such that a(r) = 0.
-1, 1, 3
Let v(i) be the second derivative of -4*i + 1/240*i**5 + 1/96*i**4 + 3/2*i**2 + 0*i**3 + 0. Let z(o) be the first derivative of v(o). Factor z(c).
c*(c + 1)/4
Determine n so that -14*n**4 + 18*n**4 + 2*n**5 - 6*n**5 + 2*n**5 = 0.
0, 2
Let s(z) be the second derivative of 1/3*z**2 + 0 + 0*z**4 + 1/60*z**5 - 1/6*z**3 + 11*z. Factor s(b).
(b - 1)**2*(b + 2)/3
Let w(v) be the first derivative of -1/24*v**3 - 3 + 0*v + 5/16*v**2. Factor w(r).
-r*(r - 5)/8
Factor 5*l**4 + 5*l**3 - 51 + 51 - 2*l**2 + 15*l - 23*l**2.
5*l*(l - 1)**2*(l + 3)
Let k(f) = 9*f**3 + 54*f**2 + 81*f + 54. Let t(p) = -p**3 - p**2 + p - 2. Let y(r) = -k(r) - 6*t(r). Find z such that y(z) = 0.
-14, -1
Suppose 11*m = 17 + 5. Factor 2 - 8*h**m + 11*h**2 + 4*h**4 - 8 + 9*h**3 - 9*h - h**4.
3*(h - 1)*(h + 1)**2*(h + 2)
Let u(m) be the second derivative of 2*m + 0 - 1/75*m**6 - 2/15*m**4 - 2/25*m**5 + 0*m**3 + 0*m**2. Determine b so that u(b) = 0.
-2, 0
Let y(b) be the second derivative of -4*b**5/5 + 19*b**4/3 - 56*b**3/3 + 24*b**2 + 8*b - 28. Factor y(d).
-4*(d - 2)**2*(4*d - 3)
Suppose 3 - 49 = -41*q + 18*q. Factor -2/3*t**q + 0 + 2*t.
-2*t*(t - 3)/3
Let o(t) be the third derivative of t**8/2688 + 19*t**7/1680 - t**6/30 + 19*t**5/60 + 17*t**2. Let q(c) be the third derivative of o(c). What is u in q(u) = 0?
-8, 2/5
Suppose 0 = -3*i - 3, -m - 5*i + 2 = 4. Factor 9*b + 2*b**4 + 6*b**m - 11*b + 6*b**2 - 12*b**3.
2*b*(b - 1)**3
Let t be (-2)/31 + (-46535)/(-175925). What is y in y + 0 + t*y**2 = 0?
-5, 0
Let s be (12/(-210))/(2/(-14)). Factor -4/5 - 6/5*l + 2/5*l**4 + 6/5*l**3 + s*l**2.
2*(l - 1)*(l + 1)**2*(l + 2)/5
Let d(q) = -q**3 - 25*q**2 - 23*q + 28. Let o(p) = -p - 14. Let v be o(10). Let j be d(v). What is f in 0 - 54*f**j - 8/3*f - 30*f**3 + 64/3*f**2 = 0?
-1, 0, 2/9
Suppose -15*x - 16 = -23*x. Factor 4*r + 61*r**2 + 41*r + 5*r**3 - 31*r**x.
5*r*(r + 3)**2
Let b(d) = d**2 - 3*d - 2. Let g be b(4). Let w be 3/g*26/1. Determine y so that -21*y**4 + 78*y**2 + 42*y**5 - 3*y - w*y**3 - 6 - 30*y**4 - 21*y**2 = 0.
-1, -2/7, 1/2, 1
Let h(u) be the first derivative of -u**4/4 + u**3 + 9*u**2/2 + 5*u + 63. Solve h(b) = 0 for b.
-1, 5
Let w = 5 + -9. Let v be 4/5 - (