17*f**2 - 33*f + 21. Let m(r) = -6*r**3 + 50*r**2 - 98*r + 62. Let z(v) = -3*m(v) + 8*t(v). Factor z(j).
2*(j - 3)**2*(j - 1)
Let j(q) be the second derivative of 3*q + 0*q**4 - 1/9*q**3 + 1/30*q**5 + 0 + 0*q**2. What is p in j(p) = 0?
-1, 0, 1
Let q(w) = 5*w**3 + 3*w**2 - 5*w - 3. Let z(r) = 2*r**3 + r**2 - 2*r - 1. Let k(d) = -3*q(d) + 8*z(d). Factor k(s).
(s - 1)**2*(s + 1)
Let k = -31 - -31. Suppose 3*w - 9 + k = 0. Factor 0 + 2/3*l**w + 0*l**2 - 2/3*l.
2*l*(l - 1)*(l + 1)/3
Suppose 0 = -4*v + b + 39, -2 = 5*v - 4*b - 59. Let z be 28/6 - (-5 + v). Factor -2/3*s + 0*s**2 + z*s**3 + 0.
2*s*(s - 1)*(s + 1)/3
Let w = 4 + -2. Let o(l) be the first derivative of -l**w + 0*l - 2/3*l**3 - 2. Suppose o(q) = 0. What is q?
-1, 0
Let z(p) be the first derivative of -4*p**5/5 + 7*p**4 - 20*p**3 + 18*p**2 + 39. Factor z(k).
-4*k*(k - 3)**2*(k - 1)
Suppose -20*t - 1/3*t**4 - 4*t**3 - 25/3 - 46/3*t**2 = 0. Calculate t.
-5, -1
Let w = -4 + 3. Let q(b) = 3*b**2 - 4*b + 5. Let y(x) = 1 - 3*x**2 - 4*x + 3*x + 4*x**2. Let p(l) = w*q(l) + 4*y(l). Factor p(m).
(m - 1)*(m + 1)
Let f(x) be the second derivative of 5*x**7/42 + 11*x**6/15 + 23*x**5/20 + x**4/2 + 29*x. Solve f(d) = 0.
-3, -1, -2/5, 0
Let x(j) = -j**3 + 4*j**2 + 6*j - 3. Let i be x(5). Determine y, given that y**2 - 2 + i + y = 0.
-1, 0
Let f be (-75)/(-30)*(-1)/(5/(-4)). Factor -1/2*n + 1/4 + 1/4*n**f.
(n - 1)**2/4
Let l(j) = -3*j - 3*j - j - j**2 - 2. Let t be l(-6). Factor 3*h**4 - 2*h**2 + 3*h**2 - 4*h**t.
-h**2*(h - 1)*(h + 1)
Suppose -5 = 5*l - 35. Let m be (-9)/l*(-8)/6. Factor 6*k**3 + 8*k**m - 3*k - 4 + 0*k + k.
2*(k + 1)**2*(3*k - 2)
Let n = 87 + -85. Factor 0 + 1/2*r**5 - 1/2*r**3 + 1/2*r**n + 0*r - 1/2*r**4.
r**2*(r - 1)**2*(r + 1)/2
Let q(l) = -l**4 - 3*l**2 + 3*l + 3. Let b(x) = -2*x**4 - 4*x**2 + 4*x + 4. Suppose 0 = -4*z, z - 8 = 2*t - z. Let d(r) = t*q(r) + 3*b(r). Factor d(m).
-2*m**4
Let y(l) be the second derivative of -l**6/165 - l**5/110 - 12*l. What is m in y(m) = 0?
-1, 0
Let u(a) be the third derivative of a**5/510 - 4*a**3/51 + 6*a**2. Suppose u(r) = 0. Calculate r.
-2, 2
Factor 2/3*j**3 - 4/15*j**2 - 2/3*j + 4/15.
2*(j - 1)*(j + 1)*(5*j - 2)/15
Let w be (-2 + -1 + 1)*1. Let t(s) = -3*s - 2. Let l be t(w). Let 1/3*j**l - 1/3*j**2 + 1/3*j - 1/3*j**3 + 0 = 0. Calculate j.
-1, 0, 1
Factor -22*c**2 - 20 + 268*c - 30 - 13*c**2 - 83*c.
-5*(c - 5)*(7*c - 2)
Let q(y) be the second derivative of -3*y - 2/231*y**7 + 1/165*y**6 + 1/110*y**5 + 0*y**3 + 0*y**4 + 0 + 0*y**2. Let q(p) = 0. What is p?
-1/2, 0, 1
Let a(h) = -h + 15. Let l be a(13). Suppose 4*i - 7*b = -l*b + 22, -4*i = 3*b - 6. Factor -4/3*k**i - 4/3 + 1/3*k**4 + k**2 + 4/3*k.
(k - 2)**2*(k - 1)*(k + 1)/3
Suppose 3*p + 22 = 2*y, 6*y + p - 21 = y. Let b be 0 + 6/(-3) + y. Determine d, given that 27/4*d**b + 9/4*d + 1/4 + 27/4*d**2 = 0.
-1/3
Let p(u) be the third derivative of 1/30*u**5 - 1/3*u**3 + 0*u + 0 + 4*u**2 + 0*u**4. Factor p(d).
2*(d - 1)*(d + 1)
Let a(s) be the third derivative of -s**7/1365 + s**6/195 - s**5/65 + s**4/39 - s**3/39 + 6*s**2. Factor a(x).
-2*(x - 1)**4/13
Factor 0 + 9/2*b**2 + b.
b*(9*b + 2)/2
Let t = 61/48 - -1/16. Let y(w) be the second derivative of -4/9*w**3 + 2/15*w**5 + t*w**2 - 2*w - 1/45*w**6 - 1/6*w**4 + 0. Find o such that y(o) = 0.
-1, 1, 2
Suppose -h = -2*m, -m = 4*m - 2*h - 2. Let r = m + 1. Solve x**2 - 3*x**2 + r*x - x = 0 for x.
0, 1
Let g be -3*((-55)/15 + 1). Let b be (2/4)/(2/g). Factor 0*u + 0 + 4/9*u**3 - 2/3*u**4 + 2/9*u**b.
-2*u**2*(u - 1)*(3*u + 1)/9
Let y = 531 + -2647/5. Let z = 12338/5145 + 2/1029. Factor 2/5*a**4 - y*a + 2/5 + z*a**2 - 8/5*a**3.
2*(a - 1)**4/5
Let d = 599828 - 642415468/1071. Let z = d + -2/153. Let 0*g**3 + 2/7*g - 4/7*g**4 - z*g**5 + 0 + 4/7*g**2 = 0. Calculate g.
-1, 0, 1
Let j(d) be the second derivative of -d**9/1080 + d**8/1680 - d**4/12 + d. Let t(a) be the third derivative of j(a). Factor t(f).
-2*f**3*(7*f - 2)
Suppose -4*r + 3 - 3 = 0. Let b(g) be the third derivative of 0*g + r*g**3 + 0 + 1/90*g**5 - 1/36*g**4 + 2*g**2. Let b(i) = 0. What is i?
0, 1
Suppose 8 - 3 = 3*u + 2*l, 5*u - 9 = -3*l. Suppose -6*r + r = -2*q - 4, 6 = 4*r - u*q. Factor r + 9/4*n**2 - 3/4*n**3 - 3/2*n.
-3*n*(n - 2)*(n - 1)/4
Let w(k) be the second derivative of -k**7/105 - k**6/84 + k**5/105 - 5*k**2/2 + 4*k. Let s(r) be the first derivative of w(r). Factor s(j).
-2*j**2*(j + 1)*(7*j - 2)/7
Let a = 53 - 47. Suppose -3*r = a*r. Factor 1/3*k**2 + k**4 + 0 - 4/3*k**3 + r*k.
k**2*(k - 1)*(3*k - 1)/3
Let a(o) = o**2 + o - 5. Let r be a(-3). Let n(q) be the first derivative of q**3 - 3/2*q**4 + 3*q**2 - r + 0*q - 3/5*q**5. Factor n(s).
-3*s*(s - 1)*(s + 1)*(s + 2)
Let 57*x**5 - 8*x - 32*x**4 + 5*x**4 + 6*x**3 - 62*x**5 - 36*x**2 - 56*x**3 = 0. Calculate x.
-2, -1, -2/5, 0
Let f(q) = 4*q**2 - 12*q - 6. Let u be f(6). Factor 20*z**3 - 4*z**2 + u*z**5 - 62*z**5 - 4*z**2 - 16*z**4.
4*z**2*(z - 2)*(z - 1)**2
Let w(o) be the first derivative of -2*o**3/27 + 2*o**2/3 - 16*o/9 - 37. Factor w(z).
-2*(z - 4)*(z - 2)/9
Let y(d) = d**4 - 5*d**3 - 21*d**2 - 19*d - 4. Let h(r) = -r**4 + 10*r**3 + 41*r**2 + 39*r + 9. Let n(u) = 4*h(u) + 9*y(u). Factor n(q).
5*q*(q - 3)*(q + 1)**2
Let q(b) be the second derivative of 0*b**3 + 0 - 1/48*b**4 + 1/40*b**5 - 3*b + 0*b**2 - 1/120*b**6. Factor q(m).
-m**2*(m - 1)**2/4
Suppose -5*t = -5*v - 25, -17*t - 5*v = -15*t + 25. Let -4/9*h + t - 2/9*h**3 + 2/3*h**2 = 0. Calculate h.
0, 1, 2
Factor 3*w**4 - 2*w**3 + w**2 - 3*w**4 + w**4.
w**2*(w - 1)**2
Let w(t) be the first derivative of -2*t**5/5 + 8*t**4/3 - 176*t**3/27 + 64*t**2/9 - 32*t/9 - 2. Factor w(h).
-2*(h - 2)**2*(3*h - 2)**2/9
Let u(t) be the third derivative of -t**6/180 - t**5/30 - t**4/18 - 8*t**2. Factor u(g).
-2*g*(g + 1)*(g + 2)/3
Find d such that 14/3*d + 10/3*d**2 + 2 + 2/3*d**3 = 0.
-3, -1
Let o(v) be the second derivative of -2*v**6/15 + v**4 + 4*v**3/3 + 20*v. Factor o(t).
-4*t*(t - 2)*(t + 1)**2
Let o(w) = -7*w + 3*w - 3*w + 5*w**3. Let p(f) = -4*f**3 + 6*f. Suppose u = 4*u + 21. Let r(a) = u*p(a) - 6*o(a). Factor r(g).
-2*g**3
Let f(u) be the second derivative of -4/3*u**4 - 2/3*u**3 - 5*u + 0*u**2 + 0 - 6/5*u**5 - 2/21*u**7 - 8/15*u**6. Factor f(k).
-4*k*(k + 1)**4
Let o(b) be the first derivative of -3*b**5/40 + 7*b**4/24 - 5*b**3/12 + b**2/4 + 2*b - 4. Let z(d) be the first derivative of o(d). Factor z(h).
-(h - 1)**2*(3*h - 1)/2
Factor 0*n**2 + 3*n**2 + 15*n + 3 - 9*n.
3*(n + 1)**2
Let v = 24 - 21. Factor 3/2*o**4 + 0*o**2 + 0 - 1/2*o**v + 0*o.
o**3*(3*o - 1)/2
Factor 12/5 + 8/5*z**2 + 22/5*z - 2/5*z**3.
-2*(z - 6)*(z + 1)**2/5
Suppose -4*s - 3*z = -z + 2, 2*s + 3*z + 3 = 0. Let k(g) be the third derivative of 0 + 1/24*g**4 - 2*g**2 - 1/60*g**5 + s*g**3 + 0*g. Factor k(h).
-h*(h - 1)
Suppose -3*i + 2*i = 4*i. Factor -1/4*h**4 + 0 + 0*h**2 + i*h + 1/2*h**3.
-h**3*(h - 2)/4
Suppose -3 - 9 = -3*p. Let a(h) be the first derivative of 4/3*h**3 - 1/2*h**p - 4*h + h**2 - 4. Find k such that a(k) = 0.
-1, 1, 2
Let u(j) be the third derivative of -j**7/105 + j**6/40 - j**4/24 + 9*j**2. Determine t, given that u(t) = 0.
-1/2, 0, 1
Let i(z) be the first derivative of -z**3/3 - z**2 - z - 7. Let i(c) = 0. Calculate c.
-1
Suppose -22*z + 5*z = 0. Factor 3/5*a - 6/5*a**3 - 3/5*a**2 + z.
-3*a*(a + 1)*(2*a - 1)/5
Let o(q) be the third derivative of -2*q**2 + 1/5*q**5 - 1/8*q**4 + 0*q + 0*q**3 - 1/112*q**8 + 0 - 3/20*q**6 + 2/35*q**7. Suppose o(c) = 0. Calculate c.
0, 1
Let u = 414 + -412. Determine m, given that 0 - 1/4*m**u + 0*m - 1/4*m**5 + 1/4*m**4 + 1/4*m**3 = 0.
-1, 0, 1
Let g = 14 + -17. Let c be ((-4)/(-4))/(g/(-1)). Solve 1/3*a + 1/3 - 1/3*a**3 - c*a**2 = 0.
-1, 1
Let q(x) be the second derivative of x**7/42 - x**6/10 + x**5/10 + x**4/6 - x**3/2 + x**2/2 + 13*x. Factor q(b).
(b - 1)**4*(b + 1)
Let d = -274 - -276. Factor 4/9 - 4/9*r**3 + 2/9*r**5 - 14/9*r + 16/9*r**d - 4/9*r**4.
2*(r - 1)**4*(r + 2)/9
Suppose -5*u + 30 - 20 = 0. Factor 0*l + 1/5*l**3 + 0 + 0*l**u + 6/5*l**4 + 9/5*l**5.
l**3*(3*l + 1)**2/5
Let k(p) = p + 7. Let s be k(-7). Let x be 4/2 + s/2. Factor -6*n + n**x + 3*n**3 + 6*n.
n**2*(3*n + 1)
Let k(u) be the third derivative of -u**6/210 + u**5/105 + u**4/21 - 11*u**2. Factor k(s).
-4*s*(s - 2)*(s + 1)/7
Let -4*v**2 + 0*v**2 + 0*v**2 + v**2 = 0. Calculate v.
0
Let s(w) = 