4/21 + 2*a**3/21 - 11*a. Factor t(f).
f*(f + 2)*(7*f + 2)/7
Let w = -15679 - -15682. Suppose -4/9*i**w + 8/9 + 4/9*i**4 + 4/9*i - 4/3*i**2 = 0. What is i?
-1, 1, 2
Suppose -m + 72 = -18. Solve 4*d**2 + m + 3*d - 26 + 29*d = 0.
-4
Let s(t) be the third derivative of -t**6/320 - 47*t**5/160 + 3*t**4/4 - 12*t**2 + 3*t. Determine r so that s(r) = 0.
-48, 0, 1
Let j be (-13)/(-4) + 39/(-15) + (-16)/40. Let 1/4*k**2 + j*k + 0 = 0. Calculate k.
-1, 0
Let s(y) = y**2 + 12*y - 16. Let g be s(-13). Let b be g*((-32)/54)/4. Factor 2/9*j - 2/9*j**2 + b.
-2*(j - 2)*(j + 1)/9
Let w(b) be the first derivative of 2/5*b**5 + 0*b**2 - 2*b**4 + 2 + 2*b**3 + 0*b. Factor w(r).
2*r**2*(r - 3)*(r - 1)
Let h be -2 + (-89)/(-11)*-104. Let i = h + 844. Factor -2/11 - i*z**2 + 6/11*z + 2/11*z**3.
2*(z - 1)**3/11
Let u(m) = -8*m + 2*m + 4*m**2 + 0*m + 8*m**2. Let y(n) = -n. Let v(b) = u(b) + 2*y(b). Factor v(o).
4*o*(3*o - 2)
Let b(o) = -2*o**2 + 44*o - 60. Let u(g) = g**2 - 21*g + 30. Let q(c) = -4*b(c) - 9*u(c). Factor q(n).
-(n - 10)*(n - 3)
Let v(m) = 8*m**2 - 63*m - 5. Suppose -19*l + 18*l = -8. Let t be v(l). Let -9/4*p**2 - 3*p + 7/4*p**t + 1 = 0. Calculate p.
-1, 2/7, 2
Let d(o) = 19*o**3 - 104*o**2 + 16*o + 54. Let f(j) = -28*j**3 + 156*j**2 - 24*j - 80. Let c(g) = 8*d(g) + 5*f(g). What is m in c(m) = 0?
-2/3, 1, 4
Suppose -130*t**2 + t + 127*t**2 - 10*t - 6 = 0. Calculate t.
-2, -1
Let q(v) = 80*v**3 + 60*v**2 + 200*v + 170. Let y(z) = 3*z**3 + z + 2. Let o(f) = -q(f) + 25*y(f). Factor o(i).
-5*(i + 1)*(i + 3)*(i + 8)
Let d(b) be the third derivative of b**7/3360 + b**6/720 + b**5/480 - 10*b**3/3 - 14*b**2. Let k(o) be the first derivative of d(o). Factor k(n).
n*(n + 1)**2/4
Let t(n) be the second derivative of 0*n**3 + 1/210*n**5 - 6*n + 0 - 1/441*n**7 + 1/315*n**6 - 1/126*n**4 + 0*n**2. What is l in t(l) = 0?
-1, 0, 1
Factor 312/7*l**2 - 16854/7 - 1113*l - 3/7*l**3.
-3*(l - 53)**2*(l + 2)/7
Let l(z) = z**2 + 2*z - 6. Let k be l(-7). Suppose 5*v + 20*v**4 + 10*v**3 + 5*v**5 + 20*v**2 - 6*v**3 - 3*v**3 + k*v**3 = 0. Calculate v.
-1, 0
Let o(k) be the second derivative of 15*k**4/4 - 5*k**3/6 - 20*k**2 - 3*k + 31. Factor o(q).
5*(q - 1)*(9*q + 8)
Let l(j) be the third derivative of -j**6/24 - 7*j**5/12 - 5*j**4/3 + 40*j**3/3 - 2*j**2 + 33. Factor l(z).
-5*(z - 1)*(z + 4)**2
Let y(m) be the third derivative of -m**8/504 + 2*m**7/945 + m**6/90 - 2*m**5/135 - m**4/36 + 2*m**3/27 + m**2 - 52*m. Solve y(x) = 0 for x.
-1, 2/3, 1
Let a(h) be the second derivative of -h**7/1260 - 7*h**6/2160 - h**5/360 - 7*h**4/6 - 7*h. Let m(q) be the third derivative of a(q). Solve m(f) = 0 for f.
-1, -1/6
Suppose -2*k + 36 = -3*k. Let x be ((-1)/(-1))/(k/(-12)). Factor 2/3*n**3 + 0 - x*n**2 - 1/3*n.
n*(n - 1)*(2*n + 1)/3
Suppose 12 - 80 = 4*o. Let s = o - -20. Solve -u + 3*u**5 - 4*u**s + 9*u - 2*u**3 - 5*u = 0.
-1, 0, 1
Let m = -1/121 + 245/363. Determine h so that 10/3*h**3 + 4/3 + 6*h**2 + m*h**4 + 14/3*h = 0.
-2, -1
Let f(w) be the third derivative of w**5/15 - w**3/6 - 5*w**2. Let n be f(-1). Let -6*o**2 + o**2 + 7*o**2 + o**n - 6*o**4 = 0. Calculate o.
-1/2, 0, 2/3
Let r = 17 - -10. Suppose -r*j - 16 = -31*j. Find b, given that -11/3*b + 3*b**2 + 4*b**5 + 19/3*b**3 - 31/3*b**j + 2/3 = 0.
-2/3, 1/4, 1
Let g(j) be the first derivative of 2*j**3/9 + j**2/3 - 4*j/3 - 43. Let g(o) = 0. Calculate o.
-2, 1
Let r be 4/10 - (-36)/60. Suppose -5 = -2*j + r. Let 16*d**2 + 9*d + 5*d**4 - 5*d**4 + 6*d**4 + 2 + 14*d**j + d**5 = 0. What is d?
-2, -1
Let h be (-3)/(-240)*322 + (-7 - -3). Let t(r) be the second derivative of -r + h*r**5 - 1/24*r**4 + 1/4*r**2 - 1/12*r**3 + 0. Determine k, given that t(k) = 0.
-1, 1
Let m = 54 + -57. Let t(r) = -6*r**4 + 15*r**3 - 9*r**2 - 9*r + 9. Let a(u) = 5*u**4 - 14*u**3 + 9*u**2 + 10*u - 10. Let y(o) = m*a(o) - 2*t(o). Factor y(i).
-3*(i - 2)**2*(i - 1)*(i + 1)
Let x(q) = -13*q + 1. Let v be x(-1). Let k(g) = -g**3 + 12*g**2 - 21*g + 12. Let u be k(10). Factor v*r - 4*r - u*r + 28*r**2.
4*r*(7*r + 2)
Let c = -49 + 51. Let p(l) = 3*l**2 + 4*l - 2. Let o be p(-2). Factor 2*h**3 - o*h**c - 2/3*h**4 + 2/3*h + 0.
-2*h*(h - 1)**3/3
Let p(k) = -4*k - 193. Let r be p(-49). Let w(h) be the second derivative of -6*h + 1/18*h**4 + 0*h**r + 0 - 1/3*h**2. Factor w(b).
2*(b - 1)*(b + 1)/3
Let d(k) = 3*k**2 - 2*k. Let t(w) = -w**4 - 6*w**3 + 8*w**2 + 26*w - 28. Let c(m) = -d(m) - t(m). Determine l, given that c(l) = 0.
-7, -2, 1, 2
Let b be 66/4356*(-1 + 2). Let v(f) be the second derivative of 2/11*f**2 + 10*f + 1/11*f**3 + b*f**4 + 0. Factor v(p).
2*(p + 1)*(p + 2)/11
Let b = 139 - 3337/24. Let q = b - -19/24. Factor 0*z + q*z**5 - 3/4*z**2 - 3/4*z**3 + 3/4*z**4 + 0.
3*z**2*(z - 1)*(z + 1)**2/4
Let h = -417 + 1258/3. Let o(x) be the first derivative of 2/3*x + 1/6*x**2 - h*x**3 + 7. Factor o(d).
-(3*d - 1)*(7*d + 2)/3
Let g(y) be the first derivative of -5*y**2 + y**2 + 7*y**2 + 5*y**3 - 14 - 1. Factor g(b).
3*b*(5*b + 2)
Suppose 0 = -4*n - 1 + 13. Suppose 5*s = -2*y + 22, -11 = -n*s - 4*y + 5. Solve 12*f + f**s - f**5 - 12*f = 0 for f.
0, 1
Suppose 0 = -2*j + 4*v, j - 3 = 2*j - 5*v. Factor 0 - 1/3*h**3 - 4/3*h - 4/3*h**j.
-h*(h + 2)**2/3
Let t(r) be the first derivative of -2 - 5*r**3 - 27/2*r**2 - 12*r. Factor t(n).
-3*(n + 1)*(5*n + 4)
Determine u, given that -5*u + 1/3*u**3 - 8/3 - 2*u**2 = 0.
-1, 8
Let a(c) be the first derivative of -25/4*c**2 - 5*c - 3 + 5/2*c**3. Factor a(v).
5*(v - 2)*(3*v + 1)/2
Let i be 1*(4 + (-9)/((-45)/(-20))). Let t(g) be the third derivative of 1/40*g**6 + 0*g**4 + 0*g - 1/20*g**5 + 0 - 2*g**2 + i*g**3. Factor t(x).
3*x**2*(x - 1)
Let y(i) be the second derivative of 0 + 1/10*i**5 - 4/15*i**3 + 1/75*i**6 + 4/5*i**2 - 1/105*i**7 - 1/6*i**4 + 5*i. What is x in y(x) = 0?
-2, -1, 1, 2
Let s(m) be the first derivative of -m**5/120 + m**4/24 - m**2/3 - 8*m + 10. Let l(c) be the first derivative of s(c). Find j such that l(j) = 0.
-1, 2
Find s such that 2/9*s**4 + 46/3*s**2 + 1352/9 + 44/9*s**3 - 1144/9*s = 0.
-13, 2
Determine s so that -32*s**2 + 4/3 + 92/3*s = 0.
-1/24, 1
Find y such that 9 - 12*y**2 + 3*y**4 - 781*y - 774*y - 6*y**3 + 1561*y = 0.
-1, 1, 3
Let u(z) be the first derivative of 2*z**3/5 + 144*z**2/5 + 282*z/5 + 87. Solve u(b) = 0.
-47, -1
Let q = -150/107 - -621/214. Factor -7/4*y + 0*y**2 + 1/4*y**3 - q.
(y - 3)*(y + 1)*(y + 2)/4
Let u(p) be the second derivative of p**7/126 + p**6/15 - 2*p**5/15 - p**4/6 + 7*p**3/18 + 67*p. Determine m so that u(m) = 0.
-7, -1, 0, 1
Suppose 0 = 4*f + 187 - 195. Solve -9/5 + 6/5*l - 1/5*l**f = 0 for l.
3
Let z = -716/3 + 239. Solve -z*s**2 + 0*s**3 + 1/3*s**4 + 0 + 0*s = 0.
-1, 0, 1
Suppose 18*s - 4*s = -12 + 54. Factor -13/3*u + 9*u**2 + 7/3*u**4 + 2/3 - 23/3*u**s.
(u - 1)**3*(7*u - 2)/3
Suppose -2*x - 2*u + 0*u = 2, -2*x + 13 = -3*u. Let o(r) be the second derivative of 0 - 1/9*r**x - 1/54*r**4 - 5*r + 2/27*r**3. Factor o(h).
-2*(h - 1)**2/9
Let 7/2*k + 1/2*k**5 - 3 - 4*k**3 + 3*k**2 + 0*k**4 = 0. What is k?
-3, -1, 1, 2
Let v(f) be the third derivative of f**5/120 + 2*f**4/3 + 31*f**3/12 + 313*f**2. Solve v(s) = 0.
-31, -1
Let j(v) = v**4 - 10*v**3 + 13*v**2 + 18*v + 2. Let p(u) = u**3 - u**2 + u - 1. Let g(n) = 2*j(n) + 4*p(n). Factor g(m).
2*m*(m - 5)*(m - 4)*(m + 1)
Suppose 5*b - 8*q = -4*q + 20, 5*q = -25. Suppose b = 5*s - 26 - 4. Factor -s*m**2 - 6*m - 2 + m + 3*m**2.
-(m + 1)*(3*m + 2)
Suppose 326 = -0*z - 4*z - 5*c, 2*z - 3*c = -152. Let g = z + 83. Find x, given that 0*x + 1/3*x**g + x**2 + 4/3*x**3 + 0 = 0.
-3, -1, 0
Suppose -8 = -3*u - 2. Factor -10*m + 5*m**2 + 4 - 17*m**2 + 3*m**u + 13*m**2.
2*(m - 2)*(2*m - 1)
Let k be (-24969)/(-43173) - (-3)/81. Solve 4/13*v**2 + 2/13*v**5 + 0 + 10/13*v**3 + 0*v + k*v**4 = 0 for v.
-2, -1, 0
Let t = -60 - -64. What is y in 185*y**3 - 14*y**3 - 7*y**5 + 51*y**4 - 54*y**2 + 22*y**5 - 147*y**t = 0?
0, 2/5, 3
Let g(f) be the first derivative of 28 + 4/27*f**3 - 10/9*f**2 + 8/3*f. Let g(d) = 0. Calculate d.
2, 3
Let d(t) = -t**2 + 6*t - 6. Let q be 6/(-12) - 18/(-4). Let p be d(q). Factor p*s**3 + 3*s**3 + 0*s**3 - s**3 + 6*s**4 + 2*s**5.
2*s**3*(s + 1)*(s + 2)
Determine y, given that -20/7*y**5 + 68/7*y**4 - 44/7*y**3 - 52/7*y**2 + 64/7*y - 16/7 = 0.
-1, 2/5, 1, 2
Let o = -938 - -952. Let i be 2/(2/2 - 0). Factor -50*d - 25*d - 35*d**i - 5