a**3.
-3*a*(a + 1)*(5*a - 1)
Let i(u) be the first derivative of 4*u**5/25 - u**4 + 8*u**3/5 - 390. Factor i(k).
4*k**2*(k - 3)*(k - 2)/5
Factor 69/8*y**2 + 21/8*y**3 - 3 - 33/4*y.
3*(y - 1)*(y + 4)*(7*y + 2)/8
Find i, given that 4/7*i**5 - 4/7*i**3 - 4/7*i**4 + 0 + 4/7*i**2 + 0*i = 0.
-1, 0, 1
Let c(u) be the first derivative of 100*u**3/27 + u**2/3 - 183. Factor c(n).
2*n*(50*n + 3)/9
Suppose 3*w - 4*u - 77 + 45 = 0, 8*w - 17 = -3*u. Factor -1/4*a**w - 1/2*a**3 + 1/2*a + 1/4*a**2 + 0.
-a*(a - 1)*(a + 1)*(a + 2)/4
Suppose d = 5*d + 4*d. Suppose -v + o + 6 = d, 2*v = o - 0 + 8. Factor -7/2*x**v - 1 - 9/2*x.
-(x + 1)*(7*x + 2)/2
Let o(u) be the second derivative of 4*u + 0 + 5/24*u**4 - 7/12*u**3 + 1/2*u**2. Find n, given that o(n) = 0.
2/5, 1
Let b be ((-96)/18 - -8)*(-63)/(-56). Factor -1/3*s**4 - 1/3*s**2 + s - s**b + 2/3.
-(s - 1)*(s + 1)**2*(s + 2)/3
Let v(z) = z**3 + 76*z**2 - 71*z + 464. Let m be v(-77). Factor -4/7*q**4 + 0 - 8/7*q - 20/7*q**m - 16/7*q**3.
-4*q*(q + 1)**2*(q + 2)/7
Let m(r) be the second derivative of -r**5/160 + 7*r**4/96 - r**3/4 + 4*r - 12. Factor m(a).
-a*(a - 4)*(a - 3)/8
Let c(k) = -2*k**2 - 32*k - 51. Let w be c(-14). Let s(f) be the third derivative of 0*f + 7*f**2 + 0 - 1/4*f**3 + 1/80*f**w - 1/32*f**4. Factor s(q).
3*(q - 2)*(q + 1)/4
Let q = 82 - 79. Let g be 2/(-36)*(-1 - 7). Factor 10/9*n**2 + g*n + 8/9*n**q + 2/9*n**4 + 0.
2*n*(n + 1)**2*(n + 2)/9
Let i(h) be the first derivative of -h**6/24 + h**5/10 + h**4/8 - 2*h**3/3 + 7*h**2/8 - h/2 + 20. Factor i(q).
-(q - 1)**4*(q + 2)/4
Let g be (-10 + (-20 - -33))/((-126)/(-4)). Factor -4/21*f**2 - g*f**3 + 4/21 + 2/21*f.
-2*(f - 1)*(f + 1)*(f + 2)/21
Let k be (-28)/(-16) + 1 - (-21)/(-28). Let m = -13/5 - -3. Factor -2/5*j**3 + 2/5*j**4 + 0 - m*j**k + 2/5*j**5 + 0*j.
2*j**2*(j - 1)*(j + 1)**2/5
Let z(p) be the second derivative of p**9/7560 - p**8/1120 + p**7/630 + 19*p**4/12 - 18*p. Let m(u) be the third derivative of z(u). Factor m(i).
2*i**2*(i - 2)*(i - 1)
Let m be ((-8)/6)/(20/(-720)). Solve -3*i**3 - 56*i - 4*i - m + 0 - 24*i**2 = 0.
-4, -2
Factor -18/7*j**2 - 2/7*j**4 - 2*j - 4/7 - 10/7*j**3.
-2*(j + 1)**3*(j + 2)/7
Let k(u) be the second derivative of u**7/42 - u**6/30 - 3*u**5/20 + 5*u**4/12 - u**3/3 + 180*u. Let k(l) = 0. What is l?
-2, 0, 1
Let f = 16313/7 - 2329. Suppose -2/7 + f*q**2 - 6/7*q**3 + 6/7*q - 8/7*q**4 = 0. Calculate q.
-1, 1/4, 1
Factor 2450/3*l**3 + 1540*l**2 + 16/3 - 184*l.
2*(l + 2)*(35*l - 2)**2/3
What is c in 0 - 3/7*c**2 + 4/7*c**3 + 0*c + c**4 = 0?
-1, 0, 3/7
Let i(m) be the second derivative of m**7/6300 - m**6/1800 - m**5/150 - 11*m**4/6 - 32*m. Let f(j) be the third derivative of i(j). Find n such that f(n) = 0.
-1, 2
Let b = 53 + -51. Suppose 12 = -4*k - 3*s, b*s + s = -5*k - 12. Solve 4/5*c + k + 2/5*c**2 = 0 for c.
-2, 0
Factor 2*x**2 - 8*x**5 - 3*x**5 + 10*x**5 - 2*x**4 + x**3.
-x**2*(x - 1)*(x + 1)*(x + 2)
Let m be (120/528)/(20/16). Factor -4/11 + 2/11*q**2 + m*q.
2*(q - 1)*(q + 2)/11
Let q be ((-112)/79485)/(18/(-2805)). Let d = q - -2/757. Factor -d*x + 2/9*x**2 + 0.
2*x*(x - 1)/9
Let y = -93 + 287/3. Let z = -77/3 + 31. Factor -y + 38/3*b**2 + z*b + 14/3*b**3.
2*(b + 1)*(b + 2)*(7*b - 2)/3
Let p(f) be the third derivative of f**9/60480 - f**8/20160 - f**7/2520 - 2*f**5/5 + 34*f**2. Let r(k) be the third derivative of p(k). Factor r(g).
g*(g - 2)*(g + 1)
Let n be (4 - (-3984)/(-1140)) + (32/(-76))/4. Solve 12/5 - 14/5*d + n*d**2 = 0 for d.
1, 6
Let u(m) = m**2 + m - 1. Let g be u(2). Factor -2*d**4 + 18*d**4 + 10 + 4*d**g + 22 + 4*d**3 - 40*d**2 - 16*d.
4*(d - 1)**2*(d + 2)**3
Let c(g) be the second derivative of -g**6/180 + g**5/15 - g**4/3 + 13*g**3/6 - 9*g. Let s(x) be the second derivative of c(x). Let s(d) = 0. What is d?
2
Factor 486*z**5 + 243*z**5 - 20243*z**3 - 16*z**2 + 20043*z**3 - 513*z**4.
z**2*(z - 1)*(27*z + 4)**2
Let s(k) be the first derivative of -1/24*k**4 - 6*k + 0*k**2 - 1/24*k**3 + 8 - 1/80*k**5. Let x(u) be the first derivative of s(u). Factor x(c).
-c*(c + 1)**2/4
Let d be 1/3 + (-24)/(-9). Factor 21*x**4 + 5*x**5 - 2*x**3 + 14*x**4 + 32*x**d.
5*x**3*(x + 1)*(x + 6)
Let a(x) be the third derivative of 5*x**6/24 + 97*x**5/12 - 155*x**4/12 - 100*x**3/3 + 4*x**2 + x. Factor a(l).
5*(l - 1)*(l + 20)*(5*l + 2)
Let i(v) be the second derivative of v**8/1344 + v**7/420 - v**5/120 - v**4/96 - 3*v**2 + 6*v. Let o(p) be the first derivative of i(p). Factor o(q).
q*(q - 1)*(q + 1)**3/4
Let m(g) = -2*g**3 - 80*g**2 + 222*g - 180. Let h(t) = t**3 + 32*t**2 - 89*t + 72. Suppose 47 = -2*a + 37. Let r(x) = a*m(x) - 12*h(x). Factor r(y).
-2*(y - 3)**2*(y - 2)
Let y(n) be the third derivative of 1/42*n**4 + 1/2*n**3 + 1/140*n**5 + 1/1260*n**6 + 0 + 0*n - 4*n**2. Let c(i) be the first derivative of y(i). Factor c(w).
2*(w + 1)*(w + 2)/7
Let h(z) be the second derivative of 9*z - 1/5*z**5 + 0*z**3 + 0*z**4 + 2/5*z**6 + 0*z**2 - 4/21*z**7 + 0. Factor h(q).
-4*q**3*(q - 1)*(2*q - 1)
Suppose 36 = 4*x - 0*x. Suppose -4*j + x*j - 20 = 0. Find c such that 2*c**2 - 6*c**3 + 9*c - 11*c**j - 2 - 3*c**2 + 14*c**2 - 3*c**3 = 0.
-1, 2/11, 1
Let i(h) be the first derivative of 2*h**5/25 + 86*h**4/5 + 14792*h**3/15 - 282. Determine d so that i(d) = 0.
-86, 0
Let g(c) = 6*c - 34. Let s be g(7). Let z be 0 - s*5/(-10). Factor 2/3*b**z + 0*b**2 - 4/3*b**3 - 2/3 + 4/3*b.
2*(b - 1)**3*(b + 1)/3
Let p be (2/4)/((-1)/2). Let w be (-24)/108 - 68/18 - -2. Let j(c) = -c**2 - 4. Let u(g) = g**2. Let q(o) = p*j(o) + w*u(o). Determine l so that q(l) = 0.
-2, 2
Let y be 25 - 36 - 75/(-5). Let d(u) be the second derivative of 3*u**2 + 0 + 1/6*u**y - u - 4/3*u**3. Find a, given that d(a) = 0.
1, 3
Let -49*s + 7/2*s**4 + 0 + 243/2*s**2 + 174*s**3 = 0. What is s?
-49, -1, 0, 2/7
Let g(x) be the first derivative of x**6/480 + x**5/120 + 8*x**2 + 10. Let b(l) be the second derivative of g(l). Solve b(c) = 0 for c.
-2, 0
Let a(i) = 2*i + 39. Let c be a(-17). Let u(v) = -2*v**3 - v**2 + 1. Let n be u(-1). Factor -f**5 + 2*f**3 - 3*f**4 + f**3 - 3*f**n - 2*f**c + 6*f**2.
-3*f**2*(f - 1)*(f + 1)**2
Let p(w) be the second derivative of 5/3*w**3 + 0*w**2 + 0 - 35/12*w**4 - 19*w. Determine t, given that p(t) = 0.
0, 2/7
Let o(y) be the second derivative of y**4 - 1/10*y**6 - 9/2*y**2 + y**3 - 3/10*y**5 - 17*y + 0. Solve o(x) = 0 for x.
-3, -1, 1
Let z = -99 + 93. Let c be (z/4)/((-2)/4) + -1. Find j, given that -2/13*j**c - 2/13*j + 0 = 0.
-1, 0
Let t(j) = -4*j + 3. Let q be t(-5). Suppose 0 = -4*m - 5*b + q, b - 7 = -5*m + 2*b. Factor 18*w - 20*w**m + 6 + 6 - 16.
-2*(2*w - 1)*(5*w - 2)
Suppose -567/4*b**4 - 257/2*b**2 - 2 + 981/4*b**3 + 27*b = 0. What is b?
2/9, 2/7, 1
Let a(v) = -8*v**2 + 3*v + 5. Let d(u) = 20*u**2 - 8*u - 12. Let w be (-1)/(((-12)/20)/(-3)). Let l(r) = w*d(r) - 12*a(r). Let l(s) = 0. What is s?
0, 1
Let i(d) be the third derivative of 1/1365*d**7 + 2/195*d**5 + 0*d + 0*d**4 - 1/195*d**6 - 20*d**2 + 0*d**3 + 0. Factor i(f).
2*f**2*(f - 2)**2/13
Let h be 1/(-4) - (-27)/12. Let m be 6790/9800 + 2/35. Determine p so that 0 + 0*p + m*p**h = 0.
0
Let j(t) = -t + 3. Let m be j(1). Suppose 6*f**3 + 5*f - 5*f + 6 - 2 + 10*f**4 - 14*f**m - 6*f = 0. Calculate f.
-1, 2/5, 1
Let x(d) be the second derivative of -8/15*d**2 - 39*d - 1/90*d**4 + 0 - 1/5*d**3. Solve x(r) = 0 for r.
-8, -1
Let y(b) be the second derivative of b**4/24 + 7*b**3/12 + 5*b**2/2 + b - 6. Solve y(w) = 0 for w.
-5, -2
Factor -5*i**2 + 6*i - 3122786 + i**3 + 3122786.
i*(i - 3)*(i - 2)
Factor 0*n**2 + 2*n**4 + 0*n - 12/7*n**5 + 0 - 2/7*n**3.
-2*n**3*(n - 1)*(6*n - 1)/7
Let m(g) be the third derivative of -g**7/3780 - g**6/1620 + g**5/108 - g**4/36 - 13*g**3/6 - 12*g**2. Let z(y) be the first derivative of m(y). Factor z(c).
-2*(c - 1)**2*(c + 3)/9
Let d be 89/4 - 9/36 - 3. Factor 3*s + 35 - 18 - d + 4*s**3 - 7*s + 2*s**4.
2*(s - 1)*(s + 1)**3
Let z(v) be the first derivative of v**4/4 - 2*v**3 - 2*v**2 + 24*v - 20. Factor z(a).
(a - 6)*(a - 2)*(a + 2)
Let z(f) be the first derivative of -f**3/4 - 7*f**2/2 + 5*f + 48. Factor z(i).
-(i + 10)*(3*i - 2)/4
Let o(a) be the first derivative of a**5/15 + a**4/6 - a**3/3 - 48. Solve o(i) = 0.
-3, 0, 1
Let t be 6/2*32/24. Let q = -4 + 6. Factor -4 + t*d + d**2 + 16*d**3 - 15*d**q - 6*d**4 + 4.
-2*d*(d - 1)**2*(3*d - 2)
Suppose -2*p - 6