*l**3 + 67*l**2 - 112*l - 5. Let y(o) = -4*o**3 + 33*o**2 - 56*o - 3. Let s(v) = 3*n(v) - 5*y(v). Factor s(p).
-4*p*(p - 7)*(p - 2)
Solve -j**4 - 7*j**3 + 20*j**2 + 108*j**2 - 4*j**3 + 136*j**2 + 234 - 1116*j + 630 = 0.
-24, 1, 6
Let g(h) be the first derivative of -9/35*h**5 + 27/28*h**4 - 1 + 0*h + 0*h**2 - 5/7*h**3 - 1/14*h**6. Factor g(m).
-3*m**2*(m - 1)**2*(m + 5)/7
Let c(d) = -5*d**4 + 4*d**3 + d**2 - 6*d + 2. Let l(o) = -o**2 - o**4 + o - o**3 - o + 0*o**2 + 1. Let h(u) = -c(u) + 2*l(u). Suppose h(j) = 0. Calculate j.
-1, 0, 1, 2
Let v be 4/34 + (4 - (-598)/(-170)). Let z(t) be the first derivative of -1/2*t**6 - v*t**5 - 2 + 3/2*t**4 + 0*t + 0*t**3 + 0*t**2. Factor z(d).
-3*d**3*(d - 1)*(d + 2)
Factor -7*w - 101 + 133 - w**2 - 7*w.
-(w - 2)*(w + 16)
Let a(c) be the first derivative of 55/8*c**4 - 5/3*c**3 - 8*c**5 + 0*c**2 - 16 + 0*c + 35/12*c**6. Factor a(s).
5*s**2*(s - 1)**2*(7*s - 2)/2
Let -275*v**3 + 5*v + 17 + 14 - 280*v**2 - 21 = 0. What is v?
-1, -1/5, 2/11
Let -10*n**5 - 44*n**2 - 6*n**4 + 356*n**2 + 11*n**5 - 16*n**5 + 96*n + 180*n**3 = 0. Calculate n.
-2, -2/5, 0, 4
Let p(l) be the second derivative of -1/2*l**4 + 1/2*l**2 + 7/20*l**5 - 1/20*l**6 - 2*l**3 + 0 + 2*l. Let c(v) be the first derivative of p(v). Factor c(z).
-3*(z - 2)**2*(2*z + 1)
Let f(u) be the first derivative of -8*u**4 + 0*u**2 - 4*u**3 - 8/3*u**6 + 9 + 0*u + 12*u**5. Determine v so that f(v) = 0.
-1/4, 0, 1, 3
Let z(t) be the third derivative of t**2 + 0 + 0*t**3 + 1/210*t**5 + 1/1176*t**8 + 0*t + 1/140*t**6 + 1/245*t**7 + 0*t**4. Let z(f) = 0. What is f?
-1, 0
Suppose 2*d - 36 = -28. Solve -14*t**4 - 4*t**5 + 4*t**4 - 10*t**d - 13*t**3 - 3*t**3 = 0 for t.
-4, -1, 0
Let b(u) be the third derivative of u**7/189 + u**6/270 - 13*u**5/270 + u**4/18 - 120*u**2. Suppose b(p) = 0. Calculate p.
-2, 0, 3/5, 1
Factor 1/3*y**3 - 48 + 8/3*y**2 - 4*y.
(y - 4)*(y + 6)**2/3
Let d = -254/15 + 58/3. Let f(c) be the first derivative of 12/25*c**5 + 6*c**2 - 1 + 33/5*c**3 + 3*c**4 + d*c. Factor f(o).
3*(o + 2)**2*(2*o + 1)**2/5
Let v(i) be the third derivative of -i**8/84 + 2*i**7/105 + 11*i**6/30 - 29*i**5/15 + 13*i**4/3 - 16*i**3/3 - 35*i**2. Factor v(y).
-4*(y - 2)*(y - 1)**3*(y + 4)
Let q be (-6 - (-4)/4)*(-36)/10. Factor -q*p**4 + 6*p**3 + 0 - 3*p**4 - 6*p + 21*p**2 + 0.
-3*p*(p - 1)*(p + 1)*(7*p - 2)
Let c(q) = -5*q + 27. Let h be c(5). Let w be (1 - 0)*0/h. Determine t so that -1/4*t**5 + 1/4*t**3 + 0*t**4 + w*t + 0*t**2 + 0 = 0.
-1, 0, 1
Let p(l) be the third derivative of l**6/45 + 13*l**5/9 + 76*l**4/9 + 40*l**3/3 - 4*l**2 + 4*l. Suppose p(f) = 0. Calculate f.
-30, -2, -1/2
Suppose 4*y = -3*y + 14. Suppose -y*g + g + 2 = 0. Factor 3*w**g + 75*w - 75*w.
3*w**2
Let z be (-4)/(-3)*(-3 - 49/(-16)). Let h(a) be the first derivative of 1/8*a**2 - 1/4*a**5 + 0*a - 3/16*a**4 - z*a**6 + 1/12*a**3 + 2. Factor h(p).
-p*(p + 1)**3*(2*p - 1)/4
Let i(v) be the first derivative of v**7/945 + 23*v**2/2 - 26. Let r(c) be the second derivative of i(c). Find a such that r(a) = 0.
0
Let t = -84/263 - -851/1841. Factor -t*r**2 + 2/7*r - 1/7.
-(r - 1)**2/7
Factor -51/4 - 13*f - 1/4*f**2.
-(f + 1)*(f + 51)/4
Solve 4*k**3 + 2/3*k**5 + 2/3*k + 0 - 8/3*k**4 - 8/3*k**2 = 0 for k.
0, 1
Let u(z) be the third derivative of z**9/22680 - z**7/3150 + z**5/900 - 11*z**3/6 + 9*z**2. Let w(j) be the first derivative of u(j). What is g in w(g) = 0?
-1, 0, 1
Let f(v) = 7*v**5 - 2*v**4 - 13*v**3 + 74*v**2 - 66*v + 30. Let n(r) = r**5 + r**3 + r**2 - r + 5. Let m(s) = -f(s) + 6*n(s). Factor m(d).
-d*(d - 3)*(d - 2)**2*(d + 5)
Let y = -67 - -37. Let r = y + 32. Find h such that -22*h**3 - 6*h + 11*h**2 + 16*h**r + 14*h - 60*h**4 - 3*h**2 + 50*h**5 = 0.
-2/5, 0, 1
Let j = 22 + -21. Let t = j + 12. Determine s so that -t - s**2 - s + 5 + 10 = 0.
-2, 1
Solve 27/7*h**2 + 90/7*h - 24/7 - 12/7*h**3 = 0 for h.
-2, 1/4, 4
Let b be (9/(-12))/(5/(-60)). Let q(r) be the first derivative of 1/3*r**3 - b + 0*r - 1/2*r**2. Determine x, given that q(x) = 0.
0, 1
Let w(k) be the first derivative of -k**5/30 + 2*k**4/9 - 5*k**3/9 + 2*k**2/3 + 13*k + 14. Let z(b) be the first derivative of w(b). Factor z(q).
-2*(q - 2)*(q - 1)**2/3
Find x such that -24/13 + 4/13*x**3 - 238/13*x**2 + 34/13*x**4 - 232/13*x = 0.
-2, -1, -2/17, 3
Let b(t) = -2*t**5 + 7*t**4 + 4*t**3 + 7*t**2 - 2*t - 7. Let m(d) = -d**5 + 3*d**4 + 2*d**3 + 3*d**2 - d - 3. Let i(n) = 6*b(n) - 14*m(n). Factor i(p).
2*p*(p - 1)**2*(p + 1)**2
Find f such that 16/11*f**3 - 18/11*f + 0 + 2/11*f**5 + 12/11*f**2 - 12/11*f**4 = 0.
-1, 0, 1, 3
Find b such that 2*b**3 - 2/5*b**4 - 4/5 + 14/5*b - 18/5*b**2 = 0.
1, 2
Let t(i) be the first derivative of -3*i**3/7 - 15*i**2/14 - 6*i/7 + 21. Solve t(x) = 0.
-1, -2/3
Let z(m) be the first derivative of -3*m**4/4 + 13*m**3/3 - 4*m**2 - 12*m + 28. Determine y so that z(y) = 0.
-2/3, 2, 3
Suppose 5*z + 4*m - 62 = 0, z - 5*m = -12 + 36. Let g = 72/5 - z. Let 2/5*u**3 - 1/5*u**5 - g - 1/5*u - 2/5*u**4 + 4/5*u**2 = 0. Calculate u.
-2, -1, 1
Let o(h) be the third derivative of 0*h + 0 + 1/20*h**6 - 17*h**2 + 0*h**4 + 3/20*h**5 + 0*h**3 - 1/70*h**7. Factor o(d).
-3*d**2*(d - 3)*(d + 1)
Let b(l) be the first derivative of -2/11*l**4 - 1/11*l**2 - 10/33*l**3 + 24 + 0*l. Factor b(c).
-2*c*(c + 1)*(4*c + 1)/11
Let -118/17*o**2 + 0 - 30/17*o + 8/17*o**3 = 0. What is o?
-1/4, 0, 15
Let v be 6/4*(110/15 - 7). Let -v + 3/4*g - 1/4*g**2 = 0. Calculate g.
1, 2
Let t(k) be the first derivative of k**3/15 + 127*k**2/10 + 126*k/5 - 681. Suppose t(g) = 0. Calculate g.
-126, -1
Suppose 2*h - 2 = -4*b + 14, 4*b - 14 = -h. Suppose -2*l - 3*i + 9 = 3*l, -4*l = 4*i - 4. Factor 4*p**l - 4*p**3 - 5*p**2 - 4*p**2 + 6*p + 3*p**b.
3*p*(p - 2)*(p - 1)
Let m(u) be the first derivative of -6/7*u - 2/7*u**2 + 4 - 2/63*u**3. Factor m(y).
-2*(y + 3)**2/21
Let w be 192/30 - 3/(-5). Factor -28*q**2 + 0*q**5 - 5*q**3 - w*q + 2*q**5 - 6 - 7*q**3 + 2*q**4 - 15*q.
2*(q - 3)*(q + 1)**4
Let m(p) = -p - 11. Let f be m(-16). Suppose -8 - 1 + q**2 + f = 0. What is q?
-2, 2
Let q(w) be the second derivative of -7*w**5/60 + 11*w**4/12 + 6*w**3 + 14*w**2/3 + 3*w + 45. What is d in q(d) = 0?
-2, -2/7, 7
Let o(s) = 125*s**3 + 836*s**2 - 361*s - 11. Let d(i) = 25*i**3 + 167*i**2 - 72*i - 2. Let l(q) = 11*d(q) - 2*o(q). Determine r so that l(r) = 0.
-7, 0, 2/5
Let r = 784/3 - 259. Suppose -4*k - 538 = -550. What is u in 4*u**2 - k*u**3 + 4/3*u - r*u**4 + 0 = 0?
-2, -2/7, 0, 1
Let y(g) be the second derivative of 5/27*g**3 - 1/54*g**4 + 32*g + 0 - 4/9*g**2. What is t in y(t) = 0?
1, 4
Let c = -4 + 6. Suppose c*y - 2 = 2. Factor -j**2 + 5*j**3 - 2*j**y - 2*j**3.
3*j**2*(j - 1)
Let i(u) be the first derivative of 4*u**5/25 + 3*u**4/5 - 44*u**3/15 - 6*u**2/5 + 8*u - 28. Solve i(w) = 0 for w.
-5, -1, 1, 2
Let p(w) be the first derivative of 2/39*w**3 - 52 + 18/13*w**2 + 162/13*w. Factor p(a).
2*(a + 9)**2/13
Suppose -3/4 + 3/8*l + 3/8*l**2 = 0. What is l?
-2, 1
Suppose 1/7*f**2 + 8/7*f + 15/7 = 0. Calculate f.
-5, -3
Let -16/7*f - 12/7 - 1/7*f**3 - f**2 = 0. Calculate f.
-3, -2
Let b = 8640 - 25915/3. Solve -20*s**2 + 0 + 60*s + b*s**3 = 0 for s.
0, 6
Let c = 2168/15 - 716/5. Find a such that 4*a**2 + 8/3 + 20/3*a - c*a**3 - 4/3*a**4 = 0.
-1, 2
Let x(o) = -2*o**2 + 6*o**2 + 0*o - 25*o + 8. Let d be x(6). Suppose 0*t**d + 2/9*t**4 + 0 + 0*t + 0*t**3 = 0. What is t?
0
Let a(h) = -2*h**4 - 8*h**3 - 8*h**2 + 4*h + 6. Let o(t) = t**4 + t**3. Let q(i) = a(i) + 4*o(i). Find b, given that q(b) = 0.
-1, 1, 3
Let i(z) = -6*z**3 + 54*z**2 + 17*z - 54. Let y(d) = -2*d**3 + 18*d**2 + 6*d - 18. Let a(c) = 4*i(c) - 11*y(c). Factor a(m).
-2*(m - 9)*(m - 1)*(m + 1)
Let f(m) be the third derivative of m**7/15120 - m**6/2160 - 3*m**4/2 + 33*m**2. Let n(w) be the second derivative of f(w). Suppose n(o) = 0. What is o?
0, 2
Let a(j) be the third derivative of -j**5/270 - 31*j**4/27 - 3844*j**3/27 + 173*j**2. Determine p so that a(p) = 0.
-62
Let h(b) be the second derivative of b**6/480 - b**5/80 + b**4/32 - b**3/24 - b**2/2 + 11*b. Let a(n) be the first derivative of h(n). Factor a(l).
(l - 1)**3/4
Suppose -2*x = w + 4, 3*x + 2*x + 5 = -5*w. Determine p so that 10*p**w + 400 - 11*p**2 + 5*p**2 + 80*p = 0.
-10
Let o = 580762/15 - 38732. Let k = o + 74/5. Factor 2/5*u + 4/15*u**2 - k.
2*(u + 2)*(2*u - 1