 4
Let k = 20 + -15. Suppose -2*p + 5*l + 25 = p, -l - 27 = -5*p. Determine r, given that 4*r**2 - k*r + 8*r - 12 + p*r = 0.
-3, 1
Let j = -1043 + 1045. Let a(z) be the first derivative of -1/20*z**5 + 5 + 1/8*z**j + 0*z + 1/12*z**3 - 1/16*z**4. Factor a(w).
-w*(w - 1)*(w + 1)**2/4
Let i(g) = g**5 + g**3 + g + 1. Let u(m) = 3*m**5 - 2*m**4 - 4*m**3 + 4*m**2 + 15*m + 8. Let s(a) = 10*i(a) - 5*u(a). Determine x so that s(x) = 0.
-1, 2, 3
Let a be 2/5 - 8*6/10368. Let v = 1/216 + a. Suppose 0 + 2/5*i**4 + 2/5*i - v*i**3 - 2/5*i**2 = 0. Calculate i.
-1, 0, 1
Suppose -16 = 5*k + 4*a, -k + 73*a - 68*a + 20 = 0. Suppose 32/5 + k*q**4 - 4/5*q**5 - 8/5*q**2 + 28/5*q**3 - 48/5*q = 0. Calculate q.
-2, 1, 2
Factor 2*j**2 - 23*j**3 + 38*j**3 - 7*j**2 - 3*j**2 + j.
j*(3*j - 1)*(5*j - 1)
Find y such that -12 + 11/4*y - 1/8*y**2 = 0.
6, 16
Let a(c) be the third derivative of -c**6/720 - 7*c**5/90 + 5*c**4/12 - 2*c**2 - 33*c. Factor a(r).
-r*(r - 2)*(r + 30)/6
Let l = 55 - 53. Let f(c) = c**4 - c**3 - c**2 - c. Let g(s) = -3*s**4 + 3*s**3 + 6*s**2 - 2*s. Let y(p) = l*f(p) + g(p). What is r in y(r) = 0?
-2, 0, 1, 2
Let j(z) be the third derivative of 0 - z**4 - 24*z**3 + 2*z - 1/60*z**5 - 16*z**2. What is k in j(k) = 0?
-12
Let d(k) be the first derivative of -5*k**4/18 - 26*k**3/27 + 56*k**2/9 - 40*k/9 + 74. Solve d(x) = 0 for x.
-5, 2/5, 2
Let k(t) be the third derivative of -t**7/70 + t**6/20 - 15*t**2 - 10*t. Find o, given that k(o) = 0.
0, 2
Find h, given that 5/2*h**2 + 8*h + 1/4*h**3 + 8 = 0.
-4, -2
Let y(h) be the third derivative of -h**6/120 - 31*h**5/60 - 7*h**4/6 + 10*h**3 - 395*h**2. Factor y(l).
-(l - 1)*(l + 2)*(l + 30)
Let f(h) = -h. Let u(q) = 2*q**2 + 22*q - 34. Let c(b) = -10*f(b) + u(b). Factor c(w).
2*(w - 1)*(w + 17)
Let s(n) = -7*n**2 - 3*n - 1. Let y(o) = 6*o**2 + 2*o. Suppose -5*c + 90 = -c + 2*x, c - 27 = 4*x. Let p = 28 - c. Let f(b) = p*y(b) + 4*s(b). Solve f(k) = 0.
-1, 2
Suppose 4*p = 2*l + 3*l + 19, 2*p - 4*l - 8 = 0. Let q be (p/(-15))/((-21)/15). Determine u, given that -q*u + 6/7*u**3 - 4/7*u**4 + 0 + 0*u**2 = 0.
-1/2, 0, 1
Let k(d) = d**3. Let p(o) = 4*o**3 + 2*o. Suppose m + 17 = 23. Let t(i) = m*k(i) - p(i). Factor t(x).
2*x*(x - 1)*(x + 1)
Factor 16*u - 98/3*u**3 - 8/3 - 14*u**2.
-2*(u + 1)*(7*u - 2)**2/3
Let s be (-3754)/(-6) + 12/(-18). Determine g, given that -276*g**4 + 76 + 42*g - 1474*g**4 + 825*g**3 + 1090*g**2 + 44 - s*g**5 - 782*g = 0.
-3, -1, 2/5
Let q = -433 - -16453/38. Let w = q + 10/19. Find o, given that 1/2 + 0*o + w*o**4 + 0*o**3 - o**2 = 0.
-1, 1
Let y = 54 + -34. Let c = y - 18. Find z such that 19*z**c - 2*z**3 - 25*z**2 - z**3 = 0.
-2, 0
Suppose -2611*k - 1000 + 6*k**5 + 241*k**3 - 5*k**5 - 430*k**2 + 911*k - 28*k**4 = 0. Calculate k.
-1, 10
Let z(a) be the third derivative of a**8/33600 - a**6/1200 + 53*a**5/60 + 7*a**2. Let w(r) be the third derivative of z(r). Solve w(y) = 0 for y.
-1, 1
Let s(m) be the second derivative of -m**6/300 + 2*m**5/75 - m**4/15 + 25*m**2/2 - 22*m. Let f(t) be the first derivative of s(t). Factor f(u).
-2*u*(u - 2)**2/5
Let o(f) be the third derivative of -1/1176*f**8 + 0*f**3 + 0*f - 7*f**2 + 1/84*f**4 + 0*f**6 - 2/735*f**7 + 1/105*f**5 + 0. What is c in o(c) = 0?
-1, 0, 1
Suppose -2*s + 30 = 4*s. Solve -s*g - 2*g**2 - g**2 - 10 + 8*g**2 = 0 for g.
-1, 2
Let s = 1 + 9. Let w = -6 + s. Factor -3*u + 4*u**w - 10*u**3 + 5*u**2 - u**2 + 3*u.
2*u**2*(u - 2)*(2*u - 1)
Let o(n) be the first derivative of -n**3/3 - n - 39. Let c(g) = -2*g**4 - 4*g**3 + 17*g**2 + 11. Let t(v) = 2*c(v) + 22*o(v). Factor t(s).
-4*s**2*(s - 1)*(s + 3)
Suppose 24*x - 42 - 6 = 0. Factor 3/4 - 3/8*d**x + 3/8*d.
-3*(d - 2)*(d + 1)/8
Solve 0 + 76/9*c**2 - 4*c + 4/9*c**4 - 44/9*c**3 = 0.
0, 1, 9
Factor -21*f - 58*f**2 + 2*f**3 + 43*f**2 - 3*f**3 - 9*f - 33*f - 49.
-(f + 1)*(f + 7)**2
Let b(s) = 5*s + 33. Let c be b(-6). Factor -2*v**2 + 1 - 1227*v**c + 1229*v**3 - 1.
2*v**2*(v - 1)
Factor -7 + 2*r**2 - 38*r - 2 + 9.
2*r*(r - 19)
Suppose 0*j = -j + 2. Let b = -1152 - -2307/2. Factor 1/2 + g**3 - 3/2*g + 1/2*g**5 + g**j - b*g**4.
(g - 1)**4*(g + 1)/2
Let p(m) be the third derivative of m**8/112 + 2*m**7/35 - 13*m**6/20 - 3*m**5 + 225*m**4/8 - 758*m**2. Factor p(h).
3*h*(h - 3)**2*(h + 5)**2
Let t be 3256/(-3663) - 16/(-18). Factor -4/9*a**5 + 32/9*a**4 + t*a**2 + 0*a - 64/9*a**3 + 0.
-4*a**3*(a - 4)**2/9
What is i in 8*i + 1919 - 6*i**2 - 3*i**3 + i**4 - 1919 = 0?
-2, 0, 1, 4
Let w(p) = -p**2 - 6*p + 1. Let o be w(-17). Let c be o/(-54) - (-8)/(-18). Factor 2/7*a**2 + 0 + 0*a - 1/7*a**c.
-a**2*(a - 2)/7
Factor 0*f + 2/5*f**4 + 0*f**3 + 0 - 2/5*f**2.
2*f**2*(f - 1)*(f + 1)/5
Let a(q) be the first derivative of q**6/150 - 2*q**5/75 + q**4/30 - q**2/2 - 7. Let v(g) be the second derivative of a(g). Factor v(x).
4*x*(x - 1)**2/5
Solve 27/2 + 33/4*z + 3/4*z**2 = 0 for z.
-9, -2
Let b be -4*4/(-3)*2. Let i be 1120/175*(-5)/(-2). Factor i*a - b*a**2 - 6.
-2*(4*a - 3)**2/3
Let i(m) = -m**3 + 13*m**2 + 15*m + 13. Let n be i(14). Let a be 1/(-3)*-1*n. Let 4*z + 6*z**3 - a*z - z**3 = 0. What is z?
-1, 0, 1
Let r = -1836 + 1121. Let f be ((-44)/r)/((-6)/(-15)). Find k such that -4/13*k**3 + 0*k + 2/13*k**2 + f*k**4 + 0 = 0.
0, 1
Let h = 53 - 58. Let l(r) = -3*r**4 - r**3 - 3*r**2 + 6*r - 9. Let p(o) = o**4 - o**3 + o**2 + 1. Let j(q) = h*p(q) - l(q). Solve j(m) = 0 for m.
-1, 1, 2
Let r be 7/(-1) + 75/10. Let k be (-2)/(-6) - (-6)/(-18). Solve k*b + 0*b**3 + r*b**4 + 0*b**2 + 0 = 0.
0
Let b(u) be the first derivative of -4*u**3/21 - 276*u**2/7 - 19044*u/7 - 23. Determine n, given that b(n) = 0.
-69
Let c be 1 - (-3)/((-9)/(-21)). Let b be (-3 - c/(-4))*-2. Factor v**4 + 3*v**b - v + 81 - 81 - 3*v**3.
v*(v - 1)**3
Let x(v) be the first derivative of v**6/9 - 2*v**4/3 - 4*v**3/9 + v**2 + 4*v/3 - 168. Let x(p) = 0. What is p?
-1, 1, 2
Suppose -y + 64 - 14 = -3*m, 0 = -2*y + 4. Let l be (-12)/m - (-1)/(-4). Factor l*o**2 + 0*o - 5/4*o**3 - 7/4*o**4 + 0.
-o**2*(o + 1)*(7*o - 2)/4
Let j be ((-4)/6)/(8/(-12)) + 13. Let w be 12/j*56/36. Factor 0 + w*z - 2*z**2.
-2*z*(3*z - 2)/3
Suppose 5*a + 2*q - 5 = 9, 0 = -3*q - 9. Let z(i) be the first derivative of 2/65*i**5 + 0*i + 10/39*i**3 - 2/13*i**4 - 2/13*i**2 + a. Solve z(c) = 0 for c.
0, 1, 2
Suppose -4*l + i = 20 - 33, 4*l + 5*i = -17. Factor 0*d + 0*d**3 - 2/13 + 4/13*d**l - 2/13*d**4.
-2*(d - 1)**2*(d + 1)**2/13
Let g = -21515 - -21515. Factor 1/2*p + 2*p**3 - 5/2*p**2 + g.
p*(p - 1)*(4*p - 1)/2
Let w(q) = -6*q + 232. Let n be w(38). Let y(u) be the second derivative of 0 + 1/24*u**n - 1/20*u**5 + 0*u**3 + 0*u**2 - 7*u. Suppose y(i) = 0. What is i?
0, 1/2
Let z(w) be the third derivative of -w**6/60 - 2*w**5/5 - 11*w**4/12 + 3*w**2 + 1. What is c in z(c) = 0?
-11, -1, 0
Let f(m) be the third derivative of 5*m**8/336 + 2*m**7/21 + m**6/4 + m**5/3 + 5*m**4/24 - 2*m**2 + 61. Find l such that f(l) = 0.
-1, 0
Suppose -12*v = -166 + 46. Let p be (-7)/(-3) + (30/(-9))/v. Factor -2*l**3 + 2 + 2*l - 1/2*l**4 - 3/2*l**p.
-(l - 1)*(l + 1)*(l + 2)**2/2
Let 8256*r**2 + 7730*r**2 - 623*r + 11570*r**2 + 1951*r + 16 = 0. Calculate r.
-2/83
Let b(j) be the third derivative of j**8/504 - 2*j**7/45 + 5*j**6/36 - 2*j**5/15 - 44*j**2. Find k, given that b(k) = 0.
0, 1, 12
Let l(n) be the third derivative of 7/32*n**4 + 1/80*n**5 + 0*n + 49*n**2 + 3/4*n**3 + 0. Find t such that l(t) = 0.
-6, -1
Let m(w) be the third derivative of -w**7/2520 - w**6/2160 + w**5/180 + 13*w**4/24 - w**2. Let j(y) be the second derivative of m(y). Factor j(i).
-(i + 1)*(3*i - 2)/3
Let i(a) = -a**2 + 5*a. Let c = -10 + 5. Let z(l) = 4*l. Let x(g) = c*z(g) + 4*i(g). Determine b, given that x(b) = 0.
0
Let f = -2545 - -2550. Factor -2/13*m**2 - 2/13*m**3 + 2/13*m**f + 0*m + 0 + 2/13*m**4.
2*m**2*(m - 1)*(m + 1)**2/13
Let u(f) = -f**3 - 3*f**2 + 23*f + 68. Let i be u(-5). Factor -21/4*h**i + 69/4*h**2 - 15*h + 3.
-3*(h - 2)*(h - 1)*(7*h - 2)/4
Let c(d) = d + 26. Let k be c(-23). Let n = k + -1. Determine s so that -1/2 + 5/4*s - s**n + 1/4*s**3 = 0.
1, 2
Let i(p) be the second derivative of p**6/255 - 3*p**5/34 + 2*p**4/17 + 28*p**3/51 + 2*p - 113. Suppose i(n) = 0. What is n?
-1, 0, 2, 14
Let y(x) be the third derivative of -18*x**2 + 0 - 1/1995*x**7 - 1/190*x**6 + 0*x - 13/570*x**5 - 4/57*x**3 - 1/19*x**4. What is g in