1. Factor 0*l**2 + 2/21 - p*l + 4/21*l**3 - 2/21*l**4.
-2*(l - 1)**3*(l + 1)/21
Let w be (2 + -1)/(1/5). Find q such that -w*q**2 + 6*q**2 - q + 2*q = 0.
-1, 0
Let x be 12/7*(-14)/(-3). Factor a + 6*a + x*a**2 + 3 + a**3 - 3*a**2.
(a + 1)**2*(a + 3)
Let w = -49 + 59. Factor -w*j**2 - 2*j**3 + 0*j**3 - 117*j + 105*j.
-2*j*(j + 2)*(j + 3)
Let m = 137 + -107. Let v be (m/(-20))/((-3)/4). Factor 2*d + 0 + 2/3*d**v.
2*d*(d + 3)/3
Let k(l) be the second derivative of -24/85*l**5 + 16/51*l**3 - 5/357*l**7 - 8/51*l**4 + 0 + 0*l**2 - 28/255*l**6 + 12*l. Factor k(d).
-2*d*(d + 2)**3*(5*d - 2)/17
Factor -6/5*f**3 + 0*f**2 - 4/5*f**4 + 0 - 2/15*f**5 + 0*f.
-2*f**3*(f + 3)**2/15
Find j such that -3*j**4 + 60*j**3 + 4*j**4 + 269*j + 216*j**2 - 366*j - 2592 + 3*j**4 - 335*j = 0.
-6, 3
Let o = -23/3 - -25/3. Let f(d) be the second derivative of 0 + d**2 - 4*d + 1/6*d**4 - o*d**3. Factor f(j).
2*(j - 1)**2
Let k(m) be the first derivative of -m**4/14 + 32*m**3/21 - 11*m**2 + 28*m + 55. What is d in k(d) = 0?
2, 7
Let v(a) be the first derivative of 45*a**4/4 + 10*a**3/3 + 93. Suppose v(w) = 0. Calculate w.
-2/9, 0
Suppose s - 5 - 22 = -2*q, -5*q = -5*s - 90. Suppose q*n = 13*n + 4. Find x such that 0 - 5/3*x**n + 1/3*x**3 + 2/3*x + 5/3*x**4 - x**5 = 0.
-1, 0, 2/3, 1
Factor -1/8*u**2 - 3 - 5/4*u.
-(u + 4)*(u + 6)/8
Let y(f) = -6*f**2 - 21*f + 3. Let c(w) = -w**3 + w + 1. Let h(b) = 3*c(b) - y(b). Find q such that h(q) = 0.
-2, 0, 4
Let o(s) be the second derivative of 3*s**5/10 + s**4/4 + 11*s. Let y(d) = d**4 + 6*d**3 + 3*d**2. Let f(i) = -2*o(i) + 3*y(i). Factor f(u).
3*u**2*(u + 1)**2
Let i(m) = 6*m - 40. Let d be i(7). Factor -6*w**2 + 125 + 175*w - 631*w**3 + 636*w**3 + 61*w**d.
5*(w + 1)*(w + 5)**2
Suppose -214 = 9*p + 56. Let q = p + 61/2. Factor -q*b**2 - 1 - 3/2*b.
-(b + 1)*(b + 2)/2
Let n be 6*((-2)/15 + ((-973)/(-210) - 4)). Factor -24*k - 99/5*k**2 - 3/5*k**4 - 6*k**n - 48/5.
-3*(k + 1)**2*(k + 4)**2/5
Let g = -8655 + 8657. Factor 0 + 1/6*l**5 - l**4 + 2/3*l - 2*l**g + 13/6*l**3.
l*(l - 2)**2*(l - 1)**2/6
Let m be (-69 - -69)/((0 - -1) + -3). Let w(p) be the second derivative of 0 - p**4 + 4*p - 1/5*p**5 + m*p**3 + 8*p**2. Find h such that w(h) = 0.
-2, 1
Let j = -270/7 + 116/3. Let m(x) be the second derivative of 4*x + 1/70*x**5 + 0 + 4/21*x**3 + j*x**4 + 0*x**2. Suppose m(o) = 0. What is o?
-2, 0
Let g(k) be the second derivative of -5*k**4/48 + 155*k**3/12 - 4805*k**2/8 - k + 120. Factor g(p).
-5*(p - 31)**2/4
Let 32/5*k**2 + 0 + 0*k - 72/5*k**4 + 4*k**5 + 48/5*k**3 = 0. Calculate k.
-2/5, 0, 2
Let y = 27/62 + 167/186. Factor -1/3*k**3 + 0*k + y - k**2.
-(k - 1)*(k + 2)**2/3
Let y(q) be the first derivative of q**7/14 - q**6/5 - 3*q**5/20 + q**4/2 - 8*q - 4. Let b(i) be the first derivative of y(i). Suppose b(s) = 0. What is s?
-1, 0, 1, 2
Let g be (1*-4 - 0) + 10544/1977. Solve -5/3*o - g - 1/3*o**2 = 0 for o.
-4, -1
Let y(b) be the second derivative of b**4/48 - 23*b**3/2 + 4761*b**2/2 - 413*b. Determine v so that y(v) = 0.
138
Let c(u) be the first derivative of -u**7/840 + u**6/60 - u**5/10 + u**4/3 - 13*u**3/3 + 10. Let l(a) be the third derivative of c(a). Factor l(s).
-(s - 2)**3
Let y be (115/(-46))/((-2)/4). Factor -n - y*n**3 + 4*n**3 + 3*n + n**2.
-n*(n - 2)*(n + 1)
Let q(j) be the third derivative of j**5/60 + j**4/24 - j**3/3 - 436*j**2. Factor q(s).
(s - 1)*(s + 2)
Let s be (-4 + 6 - -3)*8/10. Factor 17*y + 7*y - 255*y**2 + s*y**3 + 275*y**2.
4*y*(y + 2)*(y + 3)
Let f(m) be the first derivative of 2*m**3/3 + 92*m**2 - 441. What is x in f(x) = 0?
-92, 0
Let f(y) = -3*y**4 - 34*y**3 - 55*y**2 - 20*y + 4. Let h(a) = 3*a**4 + 33*a**3 + 54*a**2 + 21*a - 3. Let i(k) = 3*f(k) + 4*h(k). Factor i(p).
3*p*(p + 1)**2*(p + 8)
Let c be (204/1122)/(8/22 + 0). Let q be 6/4 + 0 + -1. What is g in 1/2*g**2 + q*g + 0 - 1/2*g**4 - c*g**3 = 0?
-1, 0, 1
Let k be -1*(300/(-15))/10. Factor 0*r - 2/3*r**3 + 0 + 2/3*r**k.
-2*r**2*(r - 1)/3
Let k(q) be the first derivative of -1/51*q**6 + 0*q**2 - 13/34*q**4 + 16/85*q**5 + 4/17*q**3 + 0*q + 41. Factor k(n).
-2*n**2*(n - 6)*(n - 1)**2/17
Solve b - 1/4*b**3 - 1 + 1/4*b**2 = 0 for b.
-2, 1, 2
Suppose -c = -0*c - 2. Let 6*g**2 + 4*g**4 - 11*g**3 + 3*g**5 + 5*g**5 + g**c - 10*g**4 - 1 + 3*g = 0. What is g?
-1, -1/2, 1/4, 1
Let h(k) = 5*k**4 - 49*k**3 + 126*k**2 - 122*k + 34. Let s(u) = -u**4 + u**3 + 2. Let w(c) = h(c) + 3*s(c). Solve w(q) = 0.
1, 20
Suppose -8*o = 7*o - 1155. Let m be (-3)/(-9) + (o/3)/7. Determine x, given that 0 + 0*x - 2/7*x**3 - 6/7*x**5 + 0*x**2 - 8/7*x**m = 0.
-1, -1/3, 0
Suppose -32350 + 5*g + 32350 + g**2 = 0. Calculate g.
-5, 0
Let z(s) be the first derivative of s**8/4480 - s**7/1120 + s**6/960 + 25*s**3/3 + 3. Let t(w) be the third derivative of z(w). Factor t(q).
3*q**2*(q - 1)**2/8
Suppose 15*c**2 + 10*c**3 + 16 - 3 + 1 - 40*c + 1 = 0. Calculate c.
-3, 1/2, 1
Let o(p) = p**3 - 16*p**2 + 47*p - 36. Let t(i) = -4*i**3 + 65*i**2 - 187*i + 144. Let z(n) = -18*o(n) - 4*t(n). Find w, given that z(w) = 0.
1, 4, 9
Suppose 0 = 23*b - 24*b - 19. Let f be -1*b/(-38)*(-4)/10. Factor 0*p + 0*p**3 + 0 + f*p**4 - 1/5*p**2.
p**2*(p - 1)*(p + 1)/5
Let u(v) be the first derivative of v**5/110 + v**4/33 + v**3/33 - 45*v - 18. Let l(a) be the first derivative of u(a). Solve l(k) = 0.
-1, 0
Suppose 0 = w + 3 - 14. Find n, given that -5*n**2 + 22*n**3 - 5*n**3 - 11*n**3 + 10*n - w*n**3 = 0.
-2, 0, 1
Let j(f) be the first derivative of -3 - 4/3*f**3 + 1/4*f**4 + 5/2*f**2 - 2*f. Determine q so that j(q) = 0.
1, 2
Let n(a) be the third derivative of a**8/1680 - a**7/210 - 7*a**6/600 + 29*a**5/300 + a**4/4 - 16*a**2. Suppose n(c) = 0. What is c?
-2, -1, 0, 3, 5
Suppose 0 = 29*l - 34*l + 15. Determine v, given that 4*v - l - 12 + 11 - v**2 = 0.
2
Let x be -7 + 2 + (7 - -1) + -1. Factor 2/7*s**3 + 64/7*s - 20/7*s**x - 64/7.
2*(s - 4)**2*(s - 2)/7
Let o(x) be the third derivative of x**7/105 - x**5/15 + x**3/3 - 241*x**2. Solve o(r) = 0 for r.
-1, 1
Solve 36 - 27*s**2 - 3348*s**4 + 7*s - 11*s - 6*s**3 + 3349*s**4 = 0.
-2, 1, 9
Let k(s) be the first derivative of -s**6/120 + s**5/8 - s**4/2 - s**3/3 + 29. Let d(z) be the third derivative of k(z). Factor d(g).
-3*(g - 4)*(g - 1)
Let v = 9806/21 - 3236/7. Solve 2/3*d**4 - v*d**2 + 4/15*d**3 - 8/5 - 88/15*d = 0.
-2, -1, -2/5, 3
Let g(y) = 2*y + 24. Let q be g(-17). Let a(j) = -j - 10. Let t be a(q). Determine d, given that 0*d**2 + t*d + 0 - 2/7*d**4 + 2/7*d**5 + 0*d**3 = 0.
0, 1
Find d such that 6/5*d + 9/5*d**4 + 0 + 21/5*d**2 + 24/5*d**3 = 0.
-1, -2/3, 0
Let y(k) be the third derivative of -1/24*k**5 - 125/12*k**3 - 4*k**2 + 0*k - 25/24*k**4 + 0. Solve y(h) = 0.
-5
Let o(u) be the first derivative of u**6/360 - u**5/24 + u**4/6 + 2*u**3 + 19. Let j(y) be the third derivative of o(y). Find f such that j(f) = 0.
1, 4
Let w = 24 + -20. Suppose 24 = 4*j - w*q, 2*j + 4*q = -0*q - 6. Factor -7*d**2 - 5*d + 2*d**2 + 5*d**j + 5 + 0*d**2.
5*(d - 1)**2*(d + 1)
Suppose q - 6*q = -20. Factor 3*w**2 + 2 + 22*w**4 + 4*w**2 + 11*w**3 + 9*w + 8*w**2 - 19*w**q.
(w + 1)**3*(3*w + 2)
Let g be -9*(-10)/210*7. Let a(b) be the second derivative of 2/15*b**4 - b - 1/50*b**5 - 1/3*b**g + 2/5*b**2 + 0. Solve a(r) = 0 for r.
1, 2
Let v(q) be the second derivative of -q**6/75 - q**5/10 - q**4/15 + 8*q**3/15 - 10*q - 2. Factor v(b).
-2*b*(b - 1)*(b + 2)*(b + 4)/5
Let z = -46 - -50. Factor -5*j**z + 0*j**4 - 3*j**3 - j**4 - 5*j**2 + 8*j**2.
-3*j**2*(j + 1)*(2*j - 1)
Let l(k) be the third derivative of -k**6/360 + k**5/180 + k**4/72 - k**3/18 - k**2 + 14*k. Determine v, given that l(v) = 0.
-1, 1
Let -32/9 + 8/3*w + 16/9*w**2 - 2/9*w**4 - 2/3*w**3 = 0. Calculate w.
-4, -2, 1, 2
Suppose -14*i + 35*i = 105. Let p(u) be the first derivative of 26*u**2 - 149/4*u**4 - 112/5*u**i + 18*u**3 + 49/2*u**6 + 8*u - 3. Determine y so that p(y) = 0.
-2/3, -2/7, 1
Let f(b) = 2*b**2 - 7*b + 32. Let w(r) = r**2 + 9*r + 9. Let t be w(-9). Let k = t - 18. Let q(c) = c**2 - 4*c + 16. Let j(u) = k*q(u) + 4*f(u). Factor j(d).
-(d - 4)**2
Let x(l) = -l**4 - l**3 - 4*l**2 - 2*l. Let q(n) = -n**4 - 5*n**2 - 3*n. Let t = -47 + 45. Let d(b) = t*q(b) + 3*x(b). Find c such that d(c) = 0.
-2, -1, 0
Let a(m) be the third derivative of -m**7/1365 - 3*m**6/260 - 7*m**5/130 - 19*m**4/156 - 2*m**3/13 + 48*m**2. Let a(y)