 + 3*k**2.
-3*k**2*(k + 1)**2*(5*k - 2)/2
Determine n, given that 69/2*n**2 - 1/2*n**4 - 21/2*n**3 + 12 - 71/2*n = 0.
-24, 1
Solve -4*o**5 - 122*o**3 + 43*o**2 - 141*o + 37*o**2 + 22*o**3 + 461*o - 40*o**4 - 256 = 0 for o.
-4, 1
What is w in 34/5 + 19/5*w + 1/5*w**2 = 0?
-17, -2
Let a be (-21)/21 - 6/(-2). Determine q, given that -7*q**2 + q - q**2 + 2*q**2 + 5*q**a = 0.
0, 1
Factor 132/5*g**2 + 4/5*g**3 + 1152/5*g + 1024/5.
4*(g + 1)*(g + 16)**2/5
Let t be -5 - (0 - -6 - 11). Let x(r) be the first derivative of 1/18*r**6 + 0*r - 1 + 2/15*r**5 + t*r**3 + 1/12*r**4 + 0*r**2. Factor x(g).
g**3*(g + 1)**2/3
Factor 12/5 + 1/5*m**4 - 17/5*m - 1/5*m**2 + m**3.
(m - 1)**2*(m + 3)*(m + 4)/5
Let j(a) be the third derivative of -18*a**2 + 0 - 135/2*a**3 - 1/12*a**5 + 15/4*a**4 + 0*a. Factor j(c).
-5*(c - 9)**2
Let s(m) be the second derivative of -7*m**6/180 - m**5/45 + 7*m**4/36 + 2*m**3/9 - 7*m**2/2 + m. Let a(z) be the first derivative of s(z). Factor a(c).
-2*(c - 1)*(c + 1)*(7*c + 2)/3
Let d(o) be the first derivative of -o**4/6 - 10*o**3 - 225*o**2 - 12*o + 37. Let r(n) be the first derivative of d(n). Factor r(m).
-2*(m + 15)**2
Let g(z) be the third derivative of 0 + 6*z**2 + 3/40*z**4 + 2/5*z**3 + 0*z - 1/100*z**5. Suppose g(u) = 0. Calculate u.
-1, 4
Let t = 82 + -50. Let i = t - 30. Find a such that -6/7 + 24/7*a**i - 9/7*a - 9/7*a**3 = 0.
-1/3, 1, 2
Factor -108*b + 108 + 39*b**2 - 6*b**3 + 1/3*b**4.
(b - 6)**2*(b - 3)**2/3
Suppose -2*k = -5*k + 15. Let v(j) be the second derivative of 0 + 1/9*j**3 + 1/10*j**k + 0*j**2 + 3*j + 1/6*j**4 + 1/45*j**6. Suppose v(y) = 0. What is y?
-1, 0
Let x = -22534/17 + 1326. Let b(f) = 5*f**3 + 66*f**2 + 13*f + 2. Let q be b(-13). Factor 2/17 - 10/17*p + x*p**q.
2*(p - 1)*(4*p - 1)/17
Let r = -9376079/840 - -11162. Let s(z) be the third derivative of 0*z**5 + 1/240*z**6 + 0 - 1/24*z**3 - 1/48*z**4 + 0*z - 6*z**2 + r*z**7. Factor s(w).
(w - 1)*(w + 1)**3/4
Factor 15*a**3 + 4*a**4 + 4*a - 26*a + 7*a - 21*a**2 - a**4 + 18.
3*(a - 1)**2*(a + 1)*(a + 6)
Let i(q) = 3*q**3 + 18*q**2 + 27*q - 5. Let c(m) = m**3 - 9*m**2 + 9*m - 7. Let z be c(8). Let g(o) = 1. Let w(h) = z*i(h) + 5*g(h). Solve w(j) = 0 for j.
-3, 0
Let o = 3270 - 3266. Let -36/5*a**2 - 2/5*a**o - 16/5 + 8*a + 14/5*a**3 = 0. What is a?
1, 2
Suppose 5 = -n + 16. Factor -4*h**2 - n + 67*h - 1 - 51*h + 0.
-4*(h - 3)*(h - 1)
Suppose 19*l + 1 = 39. Let q = -5/17 + 79/153. Factor q*j**l + 0 - 2/9*j.
2*j*(j - 1)/9
Let l(d) = 17*d - 25. Let x be l(5). Determine g, given that -g**2 + 147*g - 82*g + 6*g**2 + x = 0.
-12, -1
Suppose 4*i - 11 = -3*j, 0 = 5*i - 4*j - j - 5. Let m(h) be the second derivative of 3/10*h**i + 3/10*h**3 + 3/20*h**4 + 0 + 3/100*h**5 + 4*h. Factor m(b).
3*(b + 1)**3/5
Let i(m) be the second derivative of 0 - 1/6*m**4 + 2/7*m**3 + 0*m**2 - 4*m + 1/70*m**5. Factor i(c).
2*c*(c - 6)*(c - 1)/7
Let d(r) = 3*r**2 - 2*r - 4. Let l be d(2). Factor -3*q**3 - 11515 + 3*q**l + 11515 + 3*q - 3*q**2.
3*q*(q - 1)**2*(q + 1)
Factor -22/7*t - 36/7 - 2/7*t**2.
-2*(t + 2)*(t + 9)/7
Let o(y) = 3*y + 29. Let l be o(-9). What is f in -13*f**2 - 2*f**l + 39*f + 27*f - 24 = 0?
2/5, 4
Suppose -n = -2*z, 0*n + n = -z + 6. Suppose -4*g - 1 - 11 = n*r, -33 = -4*r + 5*g. Factor -3/7*t + 1/7*t**r + 0.
t*(t - 3)/7
Let b(l) be the first derivative of -2*l**3/3 - 10*l**2 - 50*l - 75. Factor b(f).
-2*(f + 5)**2
Factor 2/9*b**3 - 112/3*b**2 + 6272/3*b - 351232/9.
2*(b - 56)**3/9
Let t(k) be the first derivative of -k**6/120 + k**5/40 - 17*k**3/3 + 3. Let q(i) be the third derivative of t(i). Factor q(z).
-3*z*(z - 1)
Suppose -18 = -0*j - 3*j. Let x be (-4)/j*(-540)/160. Suppose -9/4*s**3 - 3/4*s - 3/4*s**4 - x*s**2 + 0 = 0. Calculate s.
-1, 0
Suppose 0*d + 40 = 5*d. Let c(x) = x**3 - 8*x**2 - x + 10. Let o be c(d). Let -72*a**2 + 2*a**4 - o*a**5 + 72*a**2 = 0. Calculate a.
0, 1
Let i = -1101 - -3305/3. Let j(a) be the first derivative of 0*a + i*a**3 + a**4 - 2/5*a**5 - 2*a**2 - 2. Find q such that j(q) = 0.
-1, 0, 1, 2
Let p = 3194/2661 - -118/887. Factor -28/3 + p*g**2 + 8*g.
4*(g - 1)*(g + 7)/3
Let m(d) = -d**4 - 2*d**3 - d**2 + d. Let f(y) = -24*y**3 + 70*y**2 - 106*y + 54. Let o(g) = f(g) - 2*m(g). Solve o(t) = 0.
1, 3
Let x(m) be the second derivative of 0*m**3 + 1/10*m**5 + 7*m - 1/2*m**4 + 0 + 0*m**2. Factor x(d).
2*d**2*(d - 3)
Let o(f) be the third derivative of 22*f**2 + 1/270*f**5 - 7/108*f**4 + 0 + 0*f + 0*f**3. Let o(k) = 0. Calculate k.
0, 7
Factor 45 - 5*u**3 + 108*u - 22 - 3*u**3 - 22*u**2 + 67.
-2*(u - 3)*(u + 5)*(4*u + 3)
Let p(g) be the first derivative of 5*g**4/12 - 50*g**3/3 + 250*g**2 + 13*g + 29. Let w(j) be the first derivative of p(j). Factor w(s).
5*(s - 10)**2
Let w(z) be the second derivative of 2/105*z**6 + 10/21*z**3 - 4/7*z**2 + 0 - 23*z - 1/7*z**4 - 1/35*z**5. Determine i so that w(i) = 0.
-2, 1
Let v = 33019/71 + -465. Let o = v + 272/213. Let o - 14/3*q**4 - 6*q + 6*q**3 + 10/3*q**2 = 0. What is q?
-1, 2/7, 1
Suppose 0 = 4*h + l - 5, -4*h + 2*l + 7 = -7. Suppose h = -3*p + 8. What is m in 0*m**p + 4/9*m**4 - 2/9*m**5 + 0 + 0*m + 0*m**3 = 0?
0, 2
Let k = 234 + -232. Suppose -3 = -k*b - 3*q, 0 - 2 = -2*b - 4*q. Find i such that 0*i**b + 2/17*i**2 + 0 + 0*i - 2/17*i**4 = 0.
-1, 0, 1
Let u(m) be the second derivative of -4*m**3 - 3/2*m**2 - 11*m - 4*m**4 + 0. Determine b, given that u(b) = 0.
-1/4
Suppose -9/4*q**3 - 11*q + 15/2*q**2 + 6 + 1/4*q**4 = 0. What is q?
2, 3
Solve -26/3*y + 2*y**2 + 8/3 = 0 for y.
1/3, 4
Let p(t) = t**3 - 4*t**2 + t + 2. Let j = 28 - 24. Let o be p(j). Factor -9*d**2 - 3*d - 2 + o*d + 8*d**2.
-(d - 2)*(d - 1)
Factor 9*m - 24*m**2 + 9*m + 108*m - 8*m**3 + 0*m - 108.
-2*(m + 6)*(2*m - 3)**2
Let d(l) = 8*l**2 - 13*l - 16. Suppose 28*v - 15 = 25*v. Let t(f) = -12*f**2 + 20*f + 24. Let a(z) = v*t(z) + 8*d(z). Let a(r) = 0. What is r?
-1, 2
Let v(m) = m**2 - 2*m. Let g(n) = 2*n**3 - 38*n**2 + 70*n - 40. Let o(r) = -2*g(r) + 12*v(r). Factor o(y).
-4*(y - 20)*(y - 1)**2
Find u such that 28/5*u**2 + 96/5*u - 2/5*u**4 + 54/5 - 16/5*u**3 = 0.
-9, -1, 3
Factor -4 + 38*t**2 - 3*t**2 - 42 + 2*t + 11*t**2 - 2*t**3.
-2*(t - 23)*(t - 1)*(t + 1)
Let d(n) be the second derivative of n**5/12 - 5*n**4 + 120*n**3 - 1440*n**2 + 13*n. Solve d(b) = 0.
12
Let g(h) = h**2 - 13*h + 12. Let m be g(12). Suppose -u - u = m. Solve 4/5*d + 2/5*d**2 + u = 0.
-2, 0
Determine a, given that 36/5*a**2 + 28/5*a - 28/5*a**3 + 4/5*a**4 - 8 = 0.
-1, 1, 2, 5
Let t(c) be the first derivative of c**3/7 + 18*c**2/7 + 33*c/7 - 10. What is z in t(z) = 0?
-11, -1
Suppose -4*d = 4*t + 4, 3*d + 13*t = 9*t - 6. Suppose -5/4*l - 1/4 + 9/4*l**3 - 3/4*l**d = 0. Calculate l.
-1/3, 1
Suppose -5*y + 3*h + 403 = -h, -5*y + 430 = 5*h. Let p = y - 83. Factor -2/13*z**4 - 2/13 + 0*z + p*z**3 + 4/13*z**2.
-2*(z - 1)**2*(z + 1)**2/13
Suppose -14*q - 12 = -20*q. Let w(t) be the third derivative of -3/40*t**5 - 1/80*t**6 + t**q - 1/4*t**3 + 0*t - 3/16*t**4 + 0. Factor w(y).
-3*(y + 1)**3/2
Let v(w) be the third derivative of -w**5/390 - w**4/78 + 124*w**2. What is l in v(l) = 0?
-2, 0
Let g(b) = -4*b**2 + 4*b**3 + 3*b + b**3 - 2*b**3 - 6. Let u(x) = -x**2 + x + 1. Let i(n) = -g(n) - 4*u(n). Factor i(c).
-(c - 1)**2*(3*c - 2)
Let p be (-1 - -5)*2*1/4. Factor 24*t**p - 14*t**2 - 15*t**3 - t**4 + 6*t**4.
5*t**2*(t - 2)*(t - 1)
Solve -21/2*l + 9/2 + 15/2*l**2 - 3/2*l**3 = 0.
1, 3
Let b(u) = -u**3 + 9*u**2 - 13*u - 2. Let h be b(7). Factor 6*y + 4*y + 10*y**2 + h*y**3 - 3*y - 2*y.
5*y*(y + 1)**2
Let b(z) = 2. Let x(v) = -3267*v**2 - 198*v - 9. Let n(t) = -3*b(t) - x(t). Factor n(q).
3*(33*q + 1)**2
Let j(f) be the third derivative of f**5/330 + f**4/132 - 2*f**3/33 + 2*f**2 - 6*f. Determine i, given that j(i) = 0.
-2, 1
What is v in -214*v**2 + 10*v**5 + 15*v - 37*v**3 - 15*v**4 + 209*v**2 - 8*v**3 = 0?
-1, 0, 1/2, 3
Let l(o) be the third derivative of 21*o**6/100 + 16*o**5/75 + o**4/15 + 157*o**2 + 2*o. Find m, given that l(m) = 0.
-2/7, -2/9, 0
Let f be (-40)/320*2/(3*-2). Let n(v) be the second derivative of -2*v + 0*v**2 + f*v**4 + 1/12*v**3 + 0. Factor n(z).
z*(z + 1)/2
Let m = -4/3487 + 185267/397518. Let w = m + -5/38. Factor a - 2/3*a**2 - w.
-(a - 1)*(2*a - 1)/3
Suppose 0 - 22/9*i**4 + 0*i + 8/9*i**2 + 2*i**5 - 32/9*i**3 = 0. Calculate i.
-1, 0, 2/9, 2
Let c = -62 - -90