l(k) be the third derivative of -1/672*k**8 + 0 - 1/30*k**5 - 1/30*k**6 + 22*k**2 + 0*k**4 - 1/84*k**7 + 0*k**3 + 0*k. Factor l(n).
-n**2*(n + 1)*(n + 2)**2/2
Suppose 3*i - 29*i - 113 = -269. Solve 2/7*t**4 + 0 - i*t**3 - 98*t + 42*t**2 = 0 for t.
0, 7
Suppose -12*i - 324 = -3*i. Let k be (6/10)/(i/(-12)). Factor 1/5*r**3 - 1/5*r**2 - k*r + 0 + 1/5*r**4.
r*(r - 1)*(r + 1)**2/5
Let q(m) be the first derivative of -m**6/21 + 2*m**5/35 + 2*m**4/7 - 8*m**3/21 + 25. Suppose q(r) = 0. Calculate r.
-2, 0, 1, 2
Determine q, given that -5*q**4 - 5*q**3 - 1687 + 10*q**2 + 1687 = 0.
-2, 0, 1
Let i(n) be the first derivative of 1/10*n**4 + 19 - 1/5*n**2 + 2/5*n**3 - 2/25*n**5 - 4/5*n. Solve i(y) = 0 for y.
-1, 1, 2
Let h = 1055 - 1055. Let r(u) be the third derivative of 0*u - 1/54*u**4 + 1/9*u**3 + h - 4*u**2 - 1/270*u**5. Factor r(n).
-2*(n - 1)*(n + 3)/9
Let l(x) be the third derivative of -x**5/15 - 13*x**4/6 + 3*x**2 - 16. Factor l(a).
-4*a*(a + 13)
Let m(x) be the second derivative of x**5/150 + x**4/20 - 2*x**3/3 + 21*x**2 + 9*x. Let k(d) be the first derivative of m(d). Factor k(w).
2*(w - 2)*(w + 5)/5
What is y in 4/9*y + 20/9 - 4/9*y**3 - 20/9*y**2 = 0?
-5, -1, 1
Let q = 20263/4 - 5065. Factor 2*s**2 + q - 11/4*s.
(s - 1)*(8*s - 3)/4
Let -56/17*j**5 + 8/17*j**2 - 110/17*j**4 + 0 + 8/17*j**3 + 0*j = 0. Calculate j.
-2, -1/4, 0, 2/7
Let p(b) be the third derivative of b**8/80640 + 3*b**5/20 + 8*b**2. Let g(f) be the third derivative of p(f). Factor g(x).
x**2/4
Let a(z) be the third derivative of 2*z**7/735 + z**6/21 - z**5/105 - 5*z**4/21 - 42*z**2. Solve a(x) = 0.
-10, -1, 0, 1
Factor -8*m**2 - 29 + 20*m + 11*m**2 + 7*m**2 - 48*m + 20*m**2 + 28*m**3 - m**4.
-(m - 29)*(m - 1)*(m + 1)**2
Let q = -4527/3164 - -1/452. Let y = -2/21 - q. Factor -7/3*s**4 - 20/3*s**2 + y*s + 0 + 23/3*s**3.
-s*(s - 2)*(s - 1)*(7*s - 2)/3
Determine k, given that -20*k - 16 + 20*k**3 + 25*k**2 - 36*k**4 + 13*k**2 - 10*k**2 + 24*k**2 = 0.
-1, -4/9, 1
Suppose 4*u + 5*x = 13, 4*u + 6*x - 2*x - 16 = 0. Let t be (-21)/u*4/(-18). Factor -t*y**2 + 4/3 - 2/3*y.
-2*(y - 1)*(y + 2)/3
Suppose -3*b + 27 + 9 = 0. Let k(z) = z**2 - 12*z + 6. Let x be k(b). Factor -2*c - 5 + 2*c**2 + 12*c + x*c + 37.
2*(c + 4)**2
Let r(n) = 119*n - 830. Let f be r(7). Factor 1/2*a + 2*a**f + 0 + 5/2*a**2.
a*(a + 1)*(4*a + 1)/2
Let j(q) be the third derivative of q**5/30 - 7*q**4/4 + 20*q**3/3 + 427*q**2. Factor j(u).
2*(u - 20)*(u - 1)
What is b in -1/2*b + 3/8 + 1/2*b**3 - 1/8*b**4 - 1/4*b**2 = 0?
-1, 1, 3
Let a be (1/6*2)/(20/180). Let f(u) be the first derivative of 0*u + 2*u**2 + 6*u**4 - 16/3*u**a - 10 + 2/3*u**6 - 16/5*u**5. Factor f(q).
4*q*(q - 1)**4
Factor 3870*l**2 - 7*l - 3869*l**2 + 37*l + 29.
(l + 1)*(l + 29)
Solve -26*y - 4*y**2 + 2*y**2 + 4*y**2 - 9 + 28 + 5 = 0.
1, 12
Let c be (66/(-24) - 2)/((-2)/8). Suppose 3*v - c + 13 = 0. Suppose -4/15 + 2/5*r - 2/15*r**v = 0. What is r?
1, 2
Let b(y) = 3*y**2 + 10*y + 7. Let n(f) = 12*f**2 + 39*f + 27. Suppose -3*h - 6 = -4*d, -3 = 5*h - 3*d + 7. Let q(j) = h*n(j) + 9*b(j). Factor q(r).
3*(r + 1)*(r + 3)
Let h(w) = w**3 + 5*w**2 - 2*w - 6. Let k be h(-5). Suppose -2*n = -13*n + 242. Find z such that k*z - z**3 - z + n - 20 = 0.
-1, 2
Let b(n) be the first derivative of -n**4/26 + 2*n**3/39 + 17*n**2/13 + 30*n/13 - 463. Determine j, given that b(j) = 0.
-3, -1, 5
Suppose r = 14 - 12. Find i, given that -4*i**2 + 3 - 3*i - r*i**2 + 3 + 150*i**3 - 147*i**3 = 0.
-1, 1, 2
Let b = -2/60395 + 483166/181185. Suppose -4/3 + b*y + y**2 - 3*y**3 = 0. Calculate y.
-1, 2/3
Suppose 64 = 2*d + 2*y, 3*y + 19 = 5*d - 173. Let k = 38 - d. Determine u so that -1/2*u + 1/4*u**k + 1/4 = 0.
1
Let a(i) be the first derivative of -36 + 1/28*i**4 - 1/2*i**2 - 4/7*i - 2/21*i**3. Let a(t) = 0. What is t?
-1, 4
Factor 15/2 + 11/4*t + 1/4*t**2.
(t + 5)*(t + 6)/4
Let t be ((-158)/(-5))/(24/(-192)). Let i = -252 - t. Find k such that i*k**4 + 8/5*k + 0*k**2 - 4/5 - 8/5*k**3 = 0.
-1, 1
Suppose 0 = u - 3, -3*g - 5*u = -2*u - 9. Factor 0 + 0*a**2 + 2/3*a**4 + g*a + 4/3*a**3.
2*a**3*(a + 2)/3
Find d, given that 35*d**2 - 5*d + 36*d**2 - 70*d**2 + 3 + 3 = 0.
2, 3
Factor 19*q**2 + 2 - 20*q**2 - 2 - 3*q.
-q*(q + 3)
Let o(q) be the second derivative of 5*q**7/42 + q**6/3 - q**5/4 - 5*q**4/6 - 25*q. Factor o(c).
5*c**2*(c - 1)*(c + 1)*(c + 2)
Let b(q) be the third derivative of -q**7/1260 + q**5/15 + 11*q**4/24 - 11*q**2. Let a(s) be the second derivative of b(s). Determine t so that a(t) = 0.
-2, 2
Let k be 1/(-9)*-3 - (-128)/(-384). Find m such that -12/7*m**2 + 4/7*m**3 + 0 + k*m = 0.
0, 3
Suppose 4*w + 3*a = -21, -w + a + 4*a = -12. Let o be 0/(-15) + (1 - w). Solve o*d**2 - 3*d**2 + 2 + 6*d**2 + 9*d = 0 for d.
-1, -2/7
Let k be (-9 + -10)*(-4)/(-18). Let f = k - -199/45. Factor 2/5*b**2 + 0*b + f*b**3 + 0.
b**2*(b + 2)/5
Let v be (-13 - (-2 - 5)) + 9. Determine c so that 0*c**2 - 4/5*c**v + 0 - 6/5*c**4 + 0*c - 2/5*c**5 = 0.
-2, -1, 0
Let v(z) be the first derivative of -7/6*z**2 - z - 2/9*z**3 + 13. Factor v(h).
-(h + 3)*(2*h + 1)/3
Let q = 35932/21 + -5132/3. Let -q + 2/21*m**2 + 0*m = 0. What is m?
-2, 2
Let i(s) be the third derivative of -10*s**2 + 0 + 0*s**6 + 0*s**4 + 0*s - 1/315*s**7 + 1/45*s**5 - 1/9*s**3. Factor i(k).
-2*(k - 1)**2*(k + 1)**2/3
Let v(c) = 27*c - 25. Let g be v(1). Let w(n) be the first derivative of 6/5*n - 2 - 2/15*n**3 + 2/5*n**g. Factor w(u).
-2*(u - 3)*(u + 1)/5
Let j = 18265 - 18263. Suppose -10/7*z**j - 6/7*z + 2/7 + 6/7*z**3 + 8/7*z**4 = 0. Calculate z.
-1, 1/4, 1
Let i(c) be the first derivative of -12*c**2 - 6*c**3 + 8*c + 2 + 7/2*c**4. Find b, given that i(b) = 0.
-1, 2/7, 2
Factor 9*y**2 + 3*y**2 - 7 + 58 - 188*y + 189 - 64.
4*(y - 1)*(3*y - 44)
Let w = -2/24377 + 24391/170639. Determine t, given that 0 + w*t**3 - 2/7*t + 1/7*t**2 = 0.
-2, 0, 1
Suppose 7 = -5*m + 7*b, 5*m - 91*b = -93*b + 2. Let m*u**2 + 0 + 3/8*u - 3/8*u**3 = 0. Calculate u.
-1, 0, 1
Let h(r) be the third derivative of 0*r + 0 - 3/10*r**5 - 2*r**2 + 0*r**3 + 5/8*r**4 + 1/40*r**6. Factor h(n).
3*n*(n - 5)*(n - 1)
Suppose -218 + 96*y**2 + 588*y + 192*y**2 + 97 + 252 - 4*y**3 + 165 = 0. Calculate y.
-1, 74
Let s(c) be the first derivative of -c**6/18 + 2*c**5/15 + c**4/3 - 2*c**3/9 - c**2/2 + 5. Let s(k) = 0. Calculate k.
-1, 0, 1, 3
Let m(w) be the first derivative of -11*w**4/42 + 2*w**3/21 - 12*w + 14. Let n(f) be the first derivative of m(f). Factor n(l).
-2*l*(11*l - 2)/7
Suppose -69*l**4 - 64*l**4 - l**5 + 2*l**2 + 131*l**4 + l**3 = 0. What is l?
-2, -1, 0, 1
Let h be 2/3*4506/3755. Factor -8/5 + 2/5*a**2 - 1/5*a**3 + h*a.
-(a - 2)**2*(a + 2)/5
Let q(v) be the second derivative of v**5/45 - 8*v**4/9 - 110*v**3/27 + 52*v**2/3 - 306*v. Factor q(k).
4*(k - 26)*(k - 1)*(k + 3)/9
Let j(k) be the first derivative of -1/3*k**2 + 2*k + 1/6*k**4 - 2 - 2/3*k**3. Find u, given that j(u) = 0.
-1, 1, 3
Let x(i) be the third derivative of 3*i**5/80 + 7*i**4/8 + 9*i**3/8 - 3*i**2 + 1. Factor x(h).
3*(h + 9)*(3*h + 1)/4
Suppose 5*m - 4*j = 38, 3*m + 2*j - 76 = -62. Let i(u) be the second derivative of -m*u**2 - 1/3*u**4 + 8*u + 0 - 8/3*u**3. Determine p, given that i(p) = 0.
-3, -1
Suppose 5*o - 4 = 3*o. Suppose -k - 3 = -2*k. Factor u**k + 32*u**o + u**3 - 30*u**2.
2*u**2*(u + 1)
Let g be (115 - 118) + 1 + 4. Factor 0 + 4/7*q**g + 8/7*q - 4/7*q**3.
-4*q*(q - 2)*(q + 1)/7
Let v = 7 - 4. Let y(c) = 3*c - 4. Let a be y(v). Factor -5 + 0 - 2*n**4 + 2*n**2 + 2*n**3 + a - 2*n**5.
-2*n**2*(n - 1)*(n + 1)**2
Let z = 6 + -20. Let g be (-8)/(-28) + 32/z + 2. Suppose g*s + 2/3*s**4 + 0 + 2*s**3 + 4/3*s**2 = 0. What is s?
-2, -1, 0
Let y = 164 + -109. Let t = y + -55. Find j such that 9/7*j**2 + t - 3/7*j**3 - 6/7*j = 0.
0, 1, 2
Let p be (3 + (96/(-50) - 1))*(3 + 2). Factor 0 + p*m**2 + 0*m.
2*m**2/5
Factor -50*i**4 + i**3 + 2*i**5 - 35*i**4 + 95*i**4 + 0*i**5 + 11*i**3.
2*i**3*(i + 2)*(i + 3)
Let p = -49541/645 + 1/129. Let v = p - -77. Find h, given that -2/5*h**2 - 1/5*h**3 - v*h + 0 = 0.
-1, 0
Let n(t) = 2*t**4 + 8*t**3 + 76*t**2 + 97*t + 55. Let i(g) = 2*g**4 + 10*g**3 + 76*g**2 + 98*g + 54. Let j(h) = 7*i(h) - 6*n(h). Factor j(q).
2*(q + 1)*(q + 2)**2*(q + 6)
Let x(r) be the third derivative of -25*r**8/336 - 43*r**7/42 - 17*r**6/24 + 59*r**5/12 + 55*r**4/12 - 40*r**3/3 + 2*r**2 - 58*r. Fi