/4
Suppose 11*p + 2490 - 2490 = 0. Let n(w) be the second derivative of 8*w - 6*w**2 - 1/4*w**4 - 5/2*w**3 + p. Factor n(f).
-3*(f + 1)*(f + 4)
Let u(b) = -3*b**3 - 24*b**2 - 9*b - 9. Let s(y) = y**3 + 13*y**2 + 4*y + 4. Let c(n) = 9*s(n) + 4*u(n). Factor c(z).
-3*z**2*(z - 7)
Solve 26/7*l**2 + 12/7*l - 12/7*l**4 - 11/7*l**3 - 8/7 + 5/7*l**5 = 0 for l.
-1, 2/5, 2
Let o = 43983 + -43979. Determine w so that -1/2*w**o + 17/2*w + 15/2*w**2 + 3/2*w**3 + 3 = 0.
-1, 6
Let o(h) = -3*h**2 + 12*h - 12. Let g = -6 + 3. Suppose 9*p - 17*p = 64. Let w(i) = i**2 - 4*i + 4. Let v(b) = g*o(b) + p*w(b). Determine j so that v(j) = 0.
2
Let d = -1328 + 1331. What is r in -12/5*r**2 + 8/5*r - 2/5*r**4 - 2*r**d + 16/5 = 0?
-2, 1
Suppose 9*u - 10*u = -3. Suppose -4*n - 3*a = -3*n - 12, u*n - 4*a = -16. Suppose n + 0*r + 2/5*r**3 + 2/5*r**4 + 0*r**2 = 0. What is r?
-1, 0
Solve 4/11 + 46/11*d**2 - 50/11*d = 0 for d.
2/23, 1
Suppose 2*c - 5*k = 23, 0*c + 17 = 2*c + k. Suppose 0*g - 3*g = -c. Factor t**3 - 6*t**4 - 2*t**g + 5*t**4.
-t**3*(t + 1)
Factor -4/7*a**5 + 0 - 52/7*a**4 + 0*a - 300/7*a**2 - 220/7*a**3.
-4*a**2*(a + 3)*(a + 5)**2/7
Let f be 30032/336 - 2/3. Let c = 89 - f. Suppose -4/7 - c*h**2 + 6/7*h = 0. Calculate h.
1, 2
Let 4/13*u**3 + 42/13*u**2 - 44/13*u - 80/13 - 2/13*u**4 = 0. What is u?
-4, -1, 2, 5
Let i(c) be the third derivative of c**8/1008 - c**7/315 + c**6/360 - 85*c**2 + 2. Suppose i(a) = 0. What is a?
0, 1
Let o(s) = s - 8. Let t be o(10). Factor -2*i**t + 44*i + 4*i**3 - 40*i - 6*i**2.
4*i*(i - 1)**2
Let d(s) be the first derivative of s**7/56 + s**6/120 - 20*s + 1. Let c(y) be the first derivative of d(y). Factor c(l).
l**4*(3*l + 1)/4
Suppose 0 = -15*l + 20*l - 145. Solve 10*x - 29 + l + 2*x**2 - x**2 = 0 for x.
-10, 0
Let p(f) be the first derivative of -3*f**4/20 - 60*f**3 - 9000*f**2 - 600000*f - 739. Suppose p(r) = 0. What is r?
-100
Factor -131*l**3 + 119*l**3 - 4*l**4 + 18*l - 2*l.
-4*l*(l - 1)*(l + 2)**2
Suppose -5 + 28*y**2 - 16*y**2 - 17*y**2 + 85 = 0. Calculate y.
-4, 4
Let q = 46 + -47. Let v(n) = n**2 + 1. Let y(r) = -5*r**3 + 10*r**2 + 25. Let d(h) = q*y(h) + 25*v(h). Let d(f) = 0. Calculate f.
-3, 0
Let k(z) be the second derivative of 3*z**5/100 + z**4/5 + 3*z**3/10 - 39*z. Solve k(h) = 0 for h.
-3, -1, 0
Let s(o) be the third derivative of -o**6/480 + 11*o**5/240 + 7*o**4/12 + 5*o**3/2 + 2*o**2 - 55*o. Factor s(m).
-(m - 15)*(m + 2)**2/4
Let b(g) be the third derivative of g**8/1512 - 11*g**7/945 + g**6/15 - 8*g**5/135 - 16*g**4/27 + 3*g**2 + 5. Determine f, given that b(f) = 0.
-1, 0, 4
Let f(c) = -c**2 + 17*c + 2. Let a be f(17). Factor -10*n**2 + 4*n**5 - 4*n**5 - 12*n**4 + 4*n**5 + 26*n**a.
4*n**2*(n - 2)**2*(n + 1)
Let h(o) = -24*o - 6. Let w be h(1). Let g be (w/14 - -1)/(0 + -2). Solve 0 - g*f - 2/7*f**2 = 0 for f.
-2, 0
Suppose 6*x - 9 = 3*x. Suppose -5 = 5*k, -2*k = 5*j + 3*k - 5. Factor -y**5 - 3*y**j + y**x + y**2 + 151*y**4 - 149*y**4.
-y**2*(y - 2)*(y - 1)*(y + 1)
Let v(d) be the first derivative of 0*d + 7/18*d**3 - 1/30*d**5 - 1/3*d**2 - 1/12*d**4 - 21. Let v(u) = 0. Calculate u.
-4, 0, 1
Let v = 96/29 - 105/58. Factor 0*m**3 - 3/2 - v*m**4 + 0*m + 3*m**2.
-3*(m - 1)**2*(m + 1)**2/2
Let n(s) = -4*s**4 - 320*s**3 - 612*s**2 - 296*s. Let f(p) = -p**4 - 64*p**3 - 122*p**2 - 59*p. Let r(k) = -16*f(k) + 3*n(k). Factor r(c).
4*c*(c + 1)**2*(c + 14)
Let -32339*v + 32651*v - 324 - 4*v**3 + v**3 + 16*v**2 - 85*v**2 = 0. What is v?
-27, 2
Let h = -500 + 504. Let z(c) be the third derivative of 0*c + 1/18*c**3 + 1/72*c**h + c**2 + 0 - 1/360*c**6 - 1/180*c**5. Factor z(n).
-(n - 1)*(n + 1)**2/3
Suppose -2*u**2 + 0*u**2 + 24*u - 22 + 0*u**2 = 0. Calculate u.
1, 11
Suppose -201 = 3*x + 2*v - 225, -4*v = -3*x - 30. Factor -1/3*i**2 + x*i - 5/3.
-(i - 5)*(i - 1)/3
Let v(t) = -3*t**4 - 156*t**3 - 2880*t**2 - 21490*t - 49145. Let k(h) = -h**4 - 52*h**3 - 960*h**2 - 7164*h - 16382. Let c(q) = 7*k(q) - 2*v(q). Factor c(m).
-(m + 4)*(m + 16)**3
Let a = -47 + 52. Factor k**3 - k**4 - 1397*k**2 - 3*k**5 + 2*k**a + 1398*k**2.
-k**2*(k - 1)*(k + 1)**2
Let k(g) = g**3 - 9*g**2 + 10*g - 14. Suppose -y = -2*p + 12, 5*p + 2*y - 5*y - 28 = 0. Let u be k(p). Factor -6*s - 3*s**2 + 10*s**u - 4*s**2.
3*s*(s - 2)
Find k, given that -70 + 3*k**3 - 70 + 140 + 6*k**2 = 0.
-2, 0
Let c(b) be the second derivative of -b**9/3024 - b**8/1344 - 11*b**4/3 - 46*b. Let w(t) be the third derivative of c(t). Factor w(z).
-5*z**3*(z + 1)
Let a(n) be the second derivative of 5/6*n**4 + 0*n**2 + 1/4*n**5 - 1/6*n**6 - 3*n + 0 + 0*n**3. Factor a(b).
-5*b**2*(b - 2)*(b + 1)
Let b = 24313/276 + 80/69. Suppose 147/4*k**5 - 9*k**2 - 60*k**3 + 0*k - b*k**4 + 0 = 0. Calculate k.
-2/7, 0, 3
Let v(j) be the third derivative of 1/60*j**5 + 0 - 19*j**2 + 0*j - 1/6*j**4 - 5/6*j**3. Factor v(b).
(b - 5)*(b + 1)
Let r(d) = d. Let b(c) = -14*c**3 - 12*c**2 + 2*c**4 - 13*c + 3*c + 16*c**3. Let v(i) = -2*b(i) - 20*r(i). Factor v(l).
-4*l**2*(l - 2)*(l + 3)
Let b(l) be the third derivative of -l**5/180 + 43*l**4/24 + 184*l**2 + 1. What is n in b(n) = 0?
0, 129
Let f(c) be the first derivative of -c**7/4620 + c**6/990 + c**5/220 + 13*c**3/3 + c - 50. Let u(s) be the third derivative of f(s). Factor u(j).
-2*j*(j - 3)*(j + 1)/11
Let j = 144 - 138. Suppose d - j = 2*o - d, -2*d = 5*o - 6. Factor 0*b**3 + 4/13*b**2 + 2/13*b + o - 2/13*b**5 - 4/13*b**4.
-2*b*(b - 1)*(b + 1)**3/13
Suppose 4*c = 3*n - 7, 10 + 11 = 5*n - 2*c. Suppose -6*q = -n*q - 2*q. Factor -1/3*w**4 - w**3 + q - 1/3*w - w**2.
-w*(w + 1)**3/3
Let l(x) be the first derivative of 2*x**6/3 - 4*x**5 + 6*x**4 + 8*x**3/3 - 14*x**2 + 12*x - 93. Factor l(d).
4*(d - 3)*(d - 1)**3*(d + 1)
Suppose 0*u - 17*u = 306. Let q be (8/u)/(-15 - -13). Factor -q*t**4 + 0*t**3 + 0*t + 4/9*t**2 - 2/9.
-2*(t - 1)**2*(t + 1)**2/9
Let q(l) be the second derivative of -l**7/21 - 19*l**6/105 - 3*l**5/14 - l**4/42 + 2*l**3/21 - 14*l + 9. Determine i, given that q(i) = 0.
-1, 0, 2/7
Let d(y) be the third derivative of 0*y + 1/336*y**8 + 0*y**3 + 0*y**5 + 4/315*y**7 + 18*y**2 + 0 - 1/72*y**4 + 1/60*y**6. Factor d(m).
m*(m + 1)**3*(3*m - 1)/3
Let k(a) be the third derivative of a**6/420 - 23*a**5/70 + 55*a**4/4 + 175*a**3/3 - 3*a**2 - 68*a. Determine t, given that k(t) = 0.
-1, 35
Let f(s) be the second derivative of -s**4/24 + 13*s**3/12 + 12*s**2 + s - 2. Factor f(n).
-(n - 16)*(n + 3)/2
Let w be (4/(-10))/((-30)/25). Suppose -273*h = -330*h + 114. Factor 1/3*k + w*k**h - 2/3.
(k - 1)*(k + 2)/3
Let l(t) = -t + 56 + t**2 - 120 + 64. Let n(h) = 2*h**2 - 3*h + 4. Let w(b) = 3*l(b) - n(b). Factor w(p).
(p - 2)*(p + 2)
Let h be 1/(-1) + 15/(-5). Let k(m) = -3*m**2 + 2*m + 1. Let s(f) = -f + 1. Let x(n) = h*s(n) + k(n). Solve x(o) = 0.
1
Let o(i) = 7*i - 95. Let z be o(25). Let w be (-5)/(z/(-52)) - 2/8. Let -16/7*l**2 - 20/7*l - 8/7 - 4/7*l**w = 0. Calculate l.
-2, -1
Let b(v) = v + 5. Let m be b(-2). Let o be ((-10)/5)/(((-3)/2)/m). Determine w so that 2/7 - 10/7*w**o + 8/7*w**2 + 9/7*w**3 - 9/7*w = 0.
-1, 2/5, 1/2, 1
Factor 7/4*j**3 + 1/4*j**4 - 3*j**2 - 44*j - 80.
(j - 5)*(j + 4)**3/4
Let x(t) = -t**3 - t. Let g(o) = 7*o**3 - 4*o**2 + 4*o + 3*o**2 + 0*o + 4*o. Let b(m) = -3*g(m) - 24*x(m). Factor b(h).
3*h**2*(h + 1)
Let s(v) be the second derivative of -v**6/135 - v**5/10 - 4*v**4/9 - 20*v**3/27 - 341*v. Factor s(k).
-2*k*(k + 2)**2*(k + 5)/9
Let b(k) be the second derivative of -34*k**6/15 - 154*k**5/5 - 156*k**4 - 324*k**3 - 54*k**2 - 47*k. Factor b(l).
-4*(l + 3)**3*(17*l + 1)
Suppose -f = -2*f. Solve -12*w**2 - 3*w**5 + 3*w**4 + 3*w**3 + f*w**3 + 9*w**2 = 0 for w.
-1, 0, 1
Suppose 34 = 2*r - 2*a, -2*r - 5*a - 70 = -6*r. Suppose -r*z + 28 = -32. Let -19/4*q**2 - 1 - 25/8*q**3 - 7/2*q - 1/8*q**5 - q**z = 0. Calculate q.
-2, -1
Let s = 921 + -917. Let m(t) = 7*t + 1. Let d be m(2). Factor 6 - d*p + s + 5*p**2 + 0*p**2.
5*(p - 2)*(p - 1)
Suppose -c - 125 = -6*c. Let b = -1233 + 1240. Factor -12*r + c*r**3 - 5*r**2 - 17*r + 2 + b + 8*r.
(r + 1)*(5*r - 3)**2
Let k(g) be the first derivative of -4*g**5/35 - g**4/7 + 2*g**3/21 - 12*g + 2. Let w(i) be the first derivative of k(i). Factor w(h).
-4*h*(h + 1)*(4*h - 1)/7
Suppose -36 + 10 = -v + 3*a, v + 4*a - 12 = 0. Let p(y) = -y**3 + 3*y + 1. Let w be p(-2). What is b in v*b**2 - w - 16*b + 4 - 5 = 