 5*n**4 + 13*n**3 - 3*n**2 - 5*n - 4. Let l(a) = -11*a**4 - 28*a**3 + 7*a**2 + 10*a + 9. Let c(x) = 13*g(x) + 6*l(x). Factor c(b).
-(b - 1)**3*(b + 2)
Suppose -h + 2 = -5*b - 5*h, -4*b + 5*h = -23. Let l(r) = r**3 + 3*r**2 - 2. Let v be l(-2). Determine i, given that -b - 2*i - 2 - 6*i - 4*i**v = 0.
-1
Let t(x) be the second derivative of 8*x**2 - 64/3*x**3 - 6*x + 77/3*x**4 - 49/5*x**5 + 0. Suppose t(j) = 0. Calculate j.
2/7, 1
Let q be 6 + 3/(-6)*2. Let z be (0 - -1)/(q/10). Determine j, given that 3*j**z - 4*j**3 + 6*j**2 - 5*j**2 = 0.
0, 1
Let g(k) be the third derivative of -2/21*k**4 + 1/140*k**6 + 0 - 4/735*k**7 + 1/21*k**5 + 0*k - 4*k**2 + 0*k**3 - 1/1176*k**8. Let g(z) = 0. Calculate z.
-4, -2, 0, 1
Let z(b) be the first derivative of b**6/320 - b**5/60 + 7*b**4/192 - b**3/24 + 11*b**2 - 11. Let p(g) be the second derivative of z(g). Factor p(w).
(w - 1)**2*(3*w - 2)/8
Let r(m) = 2*m**2 - 16*m + 13. Let q be r(7). Let a be (-9)/(-48)*-4*1/q. Factor 0 + 3/4*n - 3/4*n**2 + 3/4*n**4 - a*n**3.
3*n*(n - 1)**2*(n + 1)/4
Suppose -2/5*a**4 - 86/5*a**3 - 714/5*a + 1764/5 - 962/5*a**2 = 0. What is a?
-21, -2, 1
Let g(v) be the third derivative of v**5/12 - 20*v**4/3 + 155*v**3/6 + 593*v**2. Factor g(u).
5*(u - 31)*(u - 1)
Find g, given that -240*g**2 + 8*g**3 + 16*g + 75*g**2 + 102*g**2 - 4*g**4 + 91*g**2 = 0.
-1, 0, 4
Let m(t) be the first derivative of -t**3/12 + 25*t**2 - 2500*t - 68. Factor m(d).
-(d - 100)**2/4
Suppose 133*b - 138*b = -10. Suppose 0 = 2*c - z - 2*z - 7, -2*c = -b*z - 6. Let 1/4 + 0*y - 1/4*y**c = 0. What is y?
-1, 1
Let d = -2/6145 - -55313/24580. Determine u so that 3/2*u - 1/4*u**2 - d = 0.
3
Let a(m) be the second derivative of -3*m**5/40 + 11*m**4/8 - 15*m**3/4 - 81*m**2/4 - 85*m. Factor a(y).
-3*(y - 9)*(y - 3)*(y + 1)/2
Suppose 1504*y - 1499*y = 20. Factor 0 + 0*b - 4/7*b**3 + 2/7*b**y + 2/7*b**2.
2*b**2*(b - 1)**2/7
Factor 2*w**2 - 6147 + 3071 + 3070 - 4*w.
2*(w - 3)*(w + 1)
Let h(o) be the second derivative of o**6/18 - 7*o**5/60 - o**4/12 + 7*o**3/18 - o**2/3 + 60*o. Factor h(x).
(x - 1)**2*(x + 1)*(5*x - 2)/3
Suppose k - o = -1, -3*k - 2*o = -o - 9. Suppose -18 = -2*y + k*s, -8 - 5 = -5*y - 3*s. Factor -4*c**2 - c**5 - 3*c**3 - 12*c**4 + 5*c**y + 3*c**3 + 12*c**3.
4*c**2*(c - 1)**3
Let b(u) be the second derivative of -u**6/120 + u**5/20 - u**4/16 - u**3/6 + u**2/2 + 2*u - 185. Solve b(c) = 0.
-1, 1, 2
Let w(c) = 8*c**2 + 3*c + 7. Let y(d) = 9*d**2 + 4*d + 7. Let z(u) = -7*w(u) + 6*y(u). Let t(f) = 4*f**2 - 5*f + 15. Let m(k) = 3*t(k) + 7*z(k). Factor m(b).
-2*(b - 2)*(b - 1)
Let k be 592/(-37) + 348/21. What is x in 0 + 2/7*x + 2/7*x**3 - k*x**2 = 0?
0, 1
Let f(x) = -x**2 - 2*x + 24. Let z be f(4). Let i(c) = -2*c - 6. Let l be i(-3). Factor z*n + l - 1/2*n**3 - 1/2*n**2 + 1/2*n**5 + 1/2*n**4.
n**2*(n - 1)*(n + 1)**2/2
Let i = 223 - 230. Let u be (-36)/273 - 2/i. Factor 2/13*z**3 - 10/13*z + u*z**2 + 6/13.
2*(z - 1)**2*(z + 3)/13
Let d(c) = 2*c**5 - c**4 + c**2 + c + 1. Let w(v) = -15*v**5 - 45*v**4 - 297*v**3 - 735*v**2 - 654*v - 6. Let y(g) = 6*d(g) + w(g). Factor y(f).
-3*f*(f + 3)**3*(f + 8)
Let x(r) be the second derivative of -17*r + 0 - 1/10*r**5 + 0*r**2 + 1/15*r**6 - 1/6*r**4 + 1/3*r**3. Factor x(i).
2*i*(i - 1)**2*(i + 1)
Suppose 0 = 4*i - s - 9, 164*i = 167*i - s - 7. Factor -4/7*f**i + 8*f - 28.
-4*(f - 7)**2/7
Let o(v) be the third derivative of -2*v**7/105 + v**6/30 + 4*v**5/15 - 2*v**4/3 - 568*v**2. Factor o(x).
-4*x*(x - 2)*(x - 1)*(x + 2)
Suppose 3/8*u - 3/8*u**3 - 3/2 + 3/2*u**2 = 0. Calculate u.
-1, 1, 4
Let f(w) = 8*w - 2. Let c be f(1). Let j(p) be the third derivative of -5*p**2 + 0*p + 1/30*p**5 - 1/6*p**4 - 1/360*p**c + 4/9*p**3 + 0. What is n in j(n) = 0?
2
Let c be 154/42 + 7/(-15). Solve -4/5*y**2 + 4 - c*y = 0 for y.
-5, 1
Let a(u) be the third derivative of 0 + 8/3*u**3 + 0*u + 5/6*u**4 + 39*u**2 + 1/15*u**5. Find i, given that a(i) = 0.
-4, -1
Let l(i) = i**3 + 8*i**2 + 4*i - 7. Let g be l(-7). Let m be ((-4)/3)/(1/(-3)). Factor -18*x**3 + 14*x**4 - 4*x**m - x - 2*x**5 + g*x**2 - 3*x.
-2*x*(x - 2)*(x - 1)**3
Suppose 0 = q + 4*q - 35. Suppose -3 = 2*g - q. Let 0 + 0*w**3 + g + 2*w**3 - 4*w**3 - 6*w + 6*w**2 = 0. What is w?
1
Let z(p) be the second derivative of -14/3*p**3 + 2/5*p**5 + 0 - 46*p - 7/6*p**4 - 3*p**2. Factor z(v).
2*(v - 3)*(v + 1)*(4*v + 1)
Let h(v) = 1. Let m(x) = -x**2 + 8*x - 17. Let d = 3 + 0. Let t(l) = d*m(l) + 3*h(l). Suppose t(i) = 0. What is i?
4
Let d = 46 - 43. Suppose -d*c = -2*c. Factor -2/9*w**3 + c*w - 2/9*w**2 + 0.
-2*w**2*(w + 1)/9
Let o(b) be the first derivative of 1/20*b**5 + 0*b - 1/12*b**3 - 7 - 1/16*b**4 + 1/8*b**2. Factor o(u).
u*(u - 1)**2*(u + 1)/4
Let l be (-2)/((-42)/8 - -4). Let s = 1471/5 + -293. Solve -s + l*n - 2/5*n**2 = 0.
1, 3
Let o(m) = -3*m**2 + 9*m. Let v(j) = -j. Let f(l) = -o(l) + 15*v(l). Solve f(c) = 0.
0, 8
Let i(y) be the first derivative of y**3/9 - 2*y**2 - 13*y/3 - 114. Factor i(q).
(q - 13)*(q + 1)/3
Factor 81/5*y + 3/5*y**2 + 78/5.
3*(y + 1)*(y + 26)/5
Let g(l) be the first derivative of -l**4/24 + l**3/4 - l**2/2 - 3*l + 13. Let i(z) be the first derivative of g(z). Factor i(u).
-(u - 2)*(u - 1)/2
Let v be (-15 - -18) + 250/(-12) + 0. Let i = v + 58/3. Factor 9/4*w + i + 3/4*w**2.
3*(w + 1)*(w + 2)/4
Let w = -10541/6 - -1757. Factor -1/6*k**3 + 0*k + 0 + 1/6*k**2 + w*k**5 - 1/6*k**4.
k**2*(k - 1)**2*(k + 1)/6
Let k(n) be the third derivative of -n**7/525 + n**6/60 + 13*n**5/150 + 7*n**4/60 - 2*n**2. Factor k(c).
-2*c*(c - 7)*(c + 1)**2/5
Let h(x) be the second derivative of -x**6/90 + x**4/36 + 3*x + 13. Solve h(p) = 0.
-1, 0, 1
Factor -36/11*z**2 - 210/11*z - 392/11 - 2/11*z**3.
-2*(z + 4)*(z + 7)**2/11
Let p(u) be the third derivative of 40*u**2 + 0*u**3 + 0 - 8/9*u**4 - 1/360*u**6 + 4/45*u**5 + 0*u. Factor p(z).
-z*(z - 8)**2/3
Let q be (2/52)/((-330)/(-1430)). Find u such that 1/6*u**3 - q*u - 1/3 + 1/3*u**2 = 0.
-2, -1, 1
Let p(f) = f - 3. Suppose 0 = 2*l - 4 - 14. Let k be p(l). Factor -7*v**2 + k*v**2 - 4 - 4*v + 8*v.
-(v - 2)**2
Suppose -227*s**3 + 4*s**5 + 106*s**3 + 109*s**3 + 8*s**2 = 0. Calculate s.
-2, 0, 1
Let j(g) be the third derivative of -g**9/30240 - g**8/40320 + g**7/20160 + g**5/20 + 21*g**2. Let p(n) be the third derivative of j(n). Factor p(v).
-v*(2*v + 1)*(4*v - 1)/4
Let k(u) be the second derivative of u**7/1260 - u**6/270 - 19*u**3/6 + 17*u. Let z(h) be the second derivative of k(h). Factor z(f).
2*f**2*(f - 2)/3
Let w(d) = 2*d**3 + 21*d**2 + 39*d + 20. Let r be (2 + -7)*14/10. Let h(m) = -3*m**3 - 31*m**2 - 58*m - 30. Let f(y) = r*w(y) - 5*h(y). Let f(q) = 0. What is q?
-5, -2, -1
Let u(o) be the second derivative of -3*o**5/25 - 13*o**4/10 + 43*o**3/5 - 54*o**2/5 - 259*o. Factor u(p).
-6*(p - 2)*(p + 9)*(2*p - 1)/5
Let f(r) = -17*r**4 - 47*r**3 - 30*r**2 + 47*r + 47. Let l(w) = -9*w**4 - 24*w**3 - 15*w**2 + 24*w + 24. Let x(a) = 4*f(a) - 7*l(a). Factor x(j).
-5*(j - 1)*(j + 1)*(j + 2)**2
Suppose 11*k = 7*k + 48. Suppose 0*o + 4*o + k = 0. Let n(w) = w**2 - w. Let q(x) = x**2 - 5*x + 4. Let d(m) = o*n(m) - q(m). Determine j, given that d(j) = 0.
1
Let t(a) be the second derivative of a**6/15 + 13*a**5 + 924*a**4 + 73568*a**3/3 - 170368*a**2 + 830*a. Solve t(p) = 0 for p.
-44, 2
Let a(i) be the first derivative of -2*i - 14 + 3/2*i**2 - 1/3*i**3. Factor a(d).
-(d - 2)*(d - 1)
Let k = -5 + 3. Let n(v) = 4*v**4 + 18*v**3 + 8*v**2 - 14*v - 14. Let j(x) = -x**3 - x + 1. Let p(a) = k*j(a) - n(a). Find w, given that p(w) = 0.
-3, -1, 1
Let 14/11*f + 36/11 - 2/11*f**2 = 0. Calculate f.
-2, 9
Factor -2/13*i**5 - 42/13*i**4 + 0 - 200/13*i**2 - 240/13*i**3 + 0*i.
-2*i**2*(i + 1)*(i + 10)**2/13
Let c(p) be the third derivative of -p**5/60 + 5*p**4/4 - 75*p**3/2 - p**2 + 33. What is i in c(i) = 0?
15
Let k = 0 - -10. Let y = k - 8. Solve w - 2*w**3 - y*w**3 - 2*w**4 - 6*w**2 - 3*w - 2*w**3 = 0 for w.
-1, 0
Factor k**4 - 4*k**4 + 8*k**3 + 4*k**3 - 4674*k**2 + 60*k + 4728*k**2 + 21.
-3*(k - 7)*(k + 1)**3
Let f be ((-3)/(-6))/((-1)/2)*-61. Let i = f - 59. Let -8/7*s - 60/7*s**4 + 22/7*s**3 - 50/7*s**5 + 0 + 24/7*s**i = 0. Calculate s.
-1, 0, 2/5
Let a(t) be the first derivative of -t**3/9 - 14*t**2/3 + 29*t/3 + 110. Factor a(k).
-(k - 1)*(k + 29)/3
Let z = -13 + 15. Let f(i) = 1 - i**3 + 2*i - 4*i**2 + 5