*b - 5. Let d(u) be the first derivative of s(u). Solve d(m) = 0.
-1, 1
Let z(v) = -v**5 - 29*v**4 - 72*v**3 - 58*v**2 - 14*v + 3. Let p(s) = -28*s**4 - 72*s**3 - 56*s**2 - 12*s + 4. Let y(t) = -3*p(t) + 4*z(t). Factor y(c).
-4*c*(c + 1)**3*(c + 5)
Let c(h) = 3*h**2 - h - 6. Let o(g) = -g**3 + 9*g**2 - g - 18. Let x(z) = -7*c(z) + 2*o(z). Let r be x(-2). Factor -2/3*s**2 + r + 2/3*s.
-2*s*(s - 1)/3
Suppose -4*y = -4 - 44. Find k, given that 6*k - 12*k**4 - y*k**2 + k + 3*k**5 - 4*k - 9*k**3 + 27*k**3 = 0.
0, 1
Let g(a) be the third derivative of a**7/630 - a**6/120 - 8*a**5/45 - 5*a**4/6 - 16*a**3/9 - 631*a**2. Solve g(p) = 0 for p.
-2, -1, 8
Factor 244/7*b - 36 - 4/7*b**3 + 12/7*b**2.
-4*(b - 9)*(b - 1)*(b + 7)/7
Let i = -84/109 + 806/763. Factor i*u**2 + 44/7*u + 242/7.
2*(u + 11)**2/7
Suppose -2 = -11*o + 10*o. Factor 0*d**4 - 4*d**4 + 3*d**2 + d**o.
-4*d**2*(d - 1)*(d + 1)
Suppose -5*d + 20 = 4*r, 385*d + 3*r - 12 = 382*d. Factor -8*u - 8/3*u**3 - 3 - 1/3*u**d - 22/3*u**2.
-(u + 1)**2*(u + 3)**2/3
Suppose y = 5*q - 117, -2*q + 3*y + 87 = 2*q. Suppose -q = 3*d - 9*d. Factor -3/5*r**d - 3/5*r + 6/5*r**2 - 3/5 - 3/5*r**5 + 6/5*r**3.
-3*(r - 1)**2*(r + 1)**3/5
Let i(g) be the first derivative of -3*g**4/28 - 270*g**3/7 - 36450*g**2/7 - 2187000*g/7 + 47. Factor i(j).
-3*(j + 90)**3/7
Suppose -4*l + 32 = -4*a + 8*a, 4*a + l = 23. Factor -2/5*x**2 - 1/5*x**a - 1/5*x + 2/5*x**3 + 1/5*x**4 + 1/5.
-(x - 1)**3*(x + 1)**2/5
Let k(m) be the third derivative of -m**7/1470 - m**6/420 + m**5/15 + 13*m**4/21 + 16*m**3/7 - m**2 - 89. Factor k(s).
-(s - 6)*(s + 2)**2*(s + 4)/7
Let y(q) = -4*q**4 + 5*q**2 - 1. Let s = -107 - -110. Let p(t) = 12*t**4 - 16*t**2 + 4. Let m(z) = s*p(z) + 8*y(z). Find n such that m(n) = 0.
-1, 1
Let o(d) be the third derivative of -3*d**2 + 0*d - 1/25*d**5 + 1/3*d**3 - 1/15*d**4 + 1/525*d**7 + 1/75*d**6 + 0. Factor o(p).
2*(p - 1)**2*(p + 1)*(p + 5)/5
Let d(h) be the second derivative of -5/6*h**3 + 0*h**2 + 13*h + 0 + 5/12*h**4. Solve d(z) = 0 for z.
0, 1
Let y(u) = 2*u**2 + u + 5. Let g be y(-2). Suppose 8*z + 11 - g = 0. Factor 0 - 1/2*m**3 + 1/2*m**5 + 1/2*m**4 + z*m - 1/2*m**2.
m**2*(m - 1)*(m + 1)**2/2
Let h = 80 + -78. Let t(p) be the first derivative of 0*p - 2/7*p**3 - 9 - 2/35*p**5 + 3/14*p**4 + 1/7*p**h. Factor t(q).
-2*q*(q - 1)**3/7
Let v(f) be the second derivative of -1/96*f**4 + 0*f**2 + 1/16*f**3 + 2*f + 0. Factor v(d).
-d*(d - 3)/8
Let v(p) = -119*p**2 - 361*p - 9. Let c be v(-3). Solve 92/7*s**2 + 100/7*s**5 + 76/7*s**c - 32/7*s - 16/7 - 220/7*s**4 = 0 for s.
-2/5, 1
Let q(i) be the second derivative of -2*i**7/105 + 2*i**6/15 - 2*i**5/5 + 2*i**4/3 - 2*i**3/3 + 2*i**2/5 - 61*i. Solve q(w) = 0.
1
Let u(p) be the first derivative of -3 + p**3 + 0*p + 0*p**2 - 3/4*p**4. Factor u(d).
-3*d**2*(d - 1)
Suppose 17*p - 29*p + 383*p**2 - 382*p**2 - 28 = 0. Calculate p.
-2, 14
Let l = 1343 + -1340. Let s(x) be the first derivative of 2/9*x**l + 0*x + 1/6*x**4 - 1/3*x**2 - 2/15*x**5 + 9. Factor s(t).
-2*t*(t - 1)**2*(t + 1)/3
Let l(r) be the second derivative of 14*r - 2/85*r**5 + 0*r**2 - 1/34*r**4 + 1/51*r**3 + 0. Factor l(z).
-2*z*(z + 1)*(4*z - 1)/17
Let m(j) be the third derivative of 0*j + 0 + 0*j**3 - 1/210*j**6 + 39*j**2 - 1/42*j**4 + 2/105*j**5. Solve m(p) = 0.
0, 1
Let k = 45/31 + -545/589. Let k*q**3 + 4/19*q**2 + 0 + 0*q = 0. Calculate q.
-2/5, 0
Factor -40/11 + 2/11*u**2 + 38/11*u.
2*(u - 1)*(u + 20)/11
Let c(u) = u + 1. Let r be c(1). Suppose 3*m + f - 4 = 0, -3 = r*m + f - 5. Factor -8*g**m + 2 - 6 - 4 - 20*g.
-4*(g + 2)*(2*g + 1)
Let w(s) = -2*s**2 + 6*s - 10. Let i(k) = k - 1. Let t(d) = -20*i(d) + 2*w(d). Factor t(x).
-4*x*(x + 2)
Let m(c) be the third derivative of c**8/1680 - 29*c**7/1050 + 79*c**6/150 - 392*c**5/75 + 416*c**4/15 - 1024*c**3/15 + 26*c**2 + c. Factor m(b).
(b - 8)**3*(b - 4)*(b - 1)/5
Let b be 4/(-30) - 6580/(-2100). Factor 2/9*y**b + 4/9 - 2/3*y + 0*y**2.
2*(y - 1)**2*(y + 2)/9
Let a(k) be the second derivative of k**6/360 - k**5/90 + k**4/54 - 49*k**3/6 + 7*k - 3. Let s(h) be the second derivative of a(h). Let s(g) = 0. What is g?
2/3
Let h(x) be the first derivative of -x**4/4 + 22*x**3 - 510*x**2 - 2312*x - 153. Factor h(u).
-(u - 34)**2*(u + 2)
Let z(p) = -54*p**2 - 595*p + 158. Let u(f) = -9*f**2 - 99*f + 26. Let x(b) = 39*u(b) - 6*z(b). Let x(n) = 0. What is n?
-11, 2/9
Factor 2/11*c**2 + 0*c + 0 + 2/11*c**3.
2*c**2*(c + 1)/11
Let s = 1 + -4. Let g(v) = 3*v**4 + 3*v**3 + 2*v - 2. Let i(x) = 4*x**4 + 4*x**3 + 3*x - 3. Let o(p) = s*g(p) + 2*i(p). Find r, given that o(r) = 0.
-1, 0
Suppose -2*b = -3 - 3. Let h(g) = -3*g**2 + 10*g - 1. Let f be h(3). Determine c, given that -4*c**f + b*c - c + 5*c + c = 0.
0, 2
Find z, given that -21216/7*z + 414/7*z**2 - 2/7*z**3 - 21632/7 = 0.
-1, 104
Let d(o) be the second derivative of o**5/10 - 17*o**4/6 - 38*o**3/3 + 938*o. Factor d(n).
2*n*(n - 19)*(n + 2)
Let o(j) be the second derivative of -j**6/15 - j**5/10 + j**4/2 + 5*j**3/3 + 2*j**2 - 36*j - 7. Suppose o(t) = 0. What is t?
-1, 2
Let u be 497/30 - (-120)/1200. Let 20/3*f**2 + u*f**3 + 8/9*f + 125/9*f**4 + 0 = 0. Calculate f.
-2/5, 0
Factor 120/7*x**2 + 0 + 2/7*x**4 + 144/7*x + 4*x**3.
2*x*(x + 2)*(x + 6)**2/7
Let w(v) be the second derivative of -v**7/2 - 19*v**6/10 + 123*v**5/20 + 11*v**4/4 - 17*v**3 + 12*v**2 + 32*v. Suppose w(h) = 0. What is h?
-4, -1, 2/7, 1
Let n(a) = -325*a**2 + 317*a + 12. Let y(q) = q + 1. Let t(i) = -n(i) + 2*y(i). Factor t(j).
5*(j - 1)*(65*j + 2)
Let c = 101 + 113. Factor 1104*n + 137*n**2 + 74*n**4 - 270*n**4 + 70 - c + 1288*n**3 - 2589*n**2.
-4*(n - 3)**2*(7*n - 2)**2
Let a = -27 + 36. Factor a*l**3 - 10*l**4 - 4*l**3 + 2*l**5 + 3*l**5.
5*l**3*(l - 1)**2
Let f(y) = -22*y**4 - 10*y**3 + 88*y**2 + 64*y - 18. Let a(c) = -23*c**4 - 7*c**3 + 88*c**2 + 62*c - 17. Let l(k) = -6*a(k) + 7*f(k). What is h in l(h) = 0?
-3, -1, 1/4, 2
Let z(y) be the first derivative of -4/7*y**3 + 15 + 1/14*y**4 - 16/7*y + 12/7*y**2. What is d in z(d) = 0?
2
Let v = -12494 - -12497. Factor 1/2*a - 1/2*a**v + 1/3 - 1/3*a**2.
-(a - 1)*(a + 1)*(3*a + 2)/6
Factor 804*p**2 + 810*p**3 - 1013*p**5 + 1016*p**5 + 189*p + 78*p + 276*p**4.
3*p*(p + 1)**3*(p + 89)
Suppose -16*p + 11*p + 8 = 4*b, 0 = 3*p + 4*b. Let c(u) be the first derivative of 0*u**3 - 1 + 1/26*u**p + 0*u + 0*u**2. Factor c(v).
2*v**3/13
Let j(c) be the second derivative of -c + 0*c**2 + 1/10*c**5 - 2/3*c**4 + 4/3*c**3 + 0. Factor j(z).
2*z*(z - 2)**2
Let d(f) be the second derivative of 0*f**4 - 5/6*f**3 + 0 + 0*f**2 + 1/4*f**5 + 14*f. Factor d(p).
5*p*(p - 1)*(p + 1)
Let o = -2459 - -2462. Suppose 56/9*r**2 + 94/9*r**4 + 8/3*r**5 + 0 + 118/9*r**o + 8/9*r = 0. What is r?
-2, -1, -2/3, -1/4, 0
Let k(u) = -3*u**3 - 61*u**2 + 32*u - 208. Let v be k(-21). Factor 7/3*r**4 + 26/3*r**3 - 8/3*r + 20/3*r**v + 0.
r*(r + 2)**2*(7*r - 2)/3
Let j(c) = -16*c**3 - 56*c**2 - 60*c. Let w(g) = g**3 + g**2 + 5*g. Let f(p) = -j(p) - 12*w(p). Factor f(v).
4*v**2*(v + 11)
Let r be ((-1)/(-11)*(-61 + 66))/(25/10). Factor -50/11 + 70/11*d - 2*d**2 + r*d**3.
2*(d - 5)**2*(d - 1)/11
Let p(z) be the first derivative of -z**2 + 8/5*z**3 + 1/5*z**4 + 1/100*z**5 + 3 + 0*z. Let a(w) be the second derivative of p(w). Factor a(l).
3*(l + 4)**2/5
Suppose -4 = -2*g - 0. Factor 0*d**2 + 0*d**g - 2*d**2 + 3*d**2.
d**2
Let q(m) be the third derivative of -m**7/70 + 2*m**6/5 - 71*m**5/20 + 7*m**4 + 72*m**3 + 201*m**2. Factor q(s).
-3*(s - 9)*(s - 4)**2*(s + 1)
Let p = 179414/5 - 35878. Factor p*d**4 - 3/5*d - 16/5*d**5 + 9/5 - 29/5*d**2 + 3*d**3.
-(d - 1)**3*(4*d + 3)**2/5
Let 38/3*p - 22/3*p**2 - 2*p**3 - 10/3 = 0. What is p?
-5, 1/3, 1
What is f in 13*f + 14389*f**2 + 64 - 101*f - 14401*f**2 = 0?
-8, 2/3
Let i(m) = 3*m**2 - 9*m - 23. Suppose 0*o + 45 = 5*o. Suppose 0 = -2*r - r + o. Let h(k) = k**2 - 5*k - 11. Let u(g) = r*i(g) - 7*h(g). Factor u(b).
2*(b + 2)**2
Suppose -3*i = 2*f + 6 + 5, -4*f - 4*i = 20. Let q be 0 - (-1)/(f/(-16)). Factor t - 2*t**3 + 3*t**2 - t**3 - 4*t**4 + t**q + 2*t.
-3*t*(t - 1)*(t + 1)**2
Let b(u) be the second derivative of -u + 0 + 1/70*u**5 - 1/14*u**4 + 1/7*u**3 - 1/7*u**2. Let b(f) = 0. Calculate f.
1
Let n(t) be the third derivative of 0*t**4 + 0*t + 0 + 32*t**2 + 1/150*t**5 - 4/15*t**3. Determine y, given that n(y) = 0.
-2, 2
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