 1)
Suppose 27*o - 641 = -533. Let i(q) be the first derivative of 4/25*q**5 + 0*q**3 + 1/15*q**6 + 0*q**2 + 0*q - 1 + 0*q**o. Factor i(a).
2*a**4*(a + 2)/5
Let k(h) be the first derivative of 5*h**4/12 + 1775*h**3/3 + 630125*h**2/2 + 223694375*h/3 - 2478. What is j in k(j) = 0?
-355
Suppose 50*p = -8*p + 1218. Let w(h) be the third derivative of 0 + 1/420*h**5 + 1/168*h**4 + p*h**2 + 0*h**3 + 0*h. Determine r so that w(r) = 0.
-1, 0
Let w(v) = -2*v**4 - 2*v**2 - 4*v. Let q(j) = 57*j**4 + 2362*j**3 - 1218*j**2 + 140*j. Let o(n) = q(n) - 3*w(n). Factor o(y).
y*(y + 38)*(7*y - 2)*(9*y - 2)
Determine b, given that -3308208*b + 0 - 495/4*b**4 - 20541*b**3 - 1163252*b**2 - 1/4*b**5 = 0.
-164, -3, 0
Let r(t) = 8*t**2 + 146*t + 341. Let o(a) = 72 + 99 + 74*a + 43*a**2 - 17*a**2 - 22*a**2. Let z(n) = -5*o(n) + 3*r(n). Find w, given that z(w) = 0.
-14, -3
Let u(n) be the third derivative of 121/40*n**5 - 11/40*n**6 + 0*n**3 + 0*n - 71*n**2 + 0 + 1/140*n**7 + 0*n**4. Solve u(j) = 0.
0, 11
Let i(s) = 2*s**2. Let u be i(1). Suppose -7*b + 3*b - 4 = 2*g, -g = -2*b - 14. What is k in -k**3 + 15*k**5 - 207*k**2 + g*k**3 + 212*k**u - 25*k**4 = 0?
-1/3, 0, 1
Factor 90/7*c**2 + 2/7*c**4 + 22/7*c**3 + 162/7*c + 108/7.
2*(c + 2)*(c + 3)**3/7
Let x(h) be the first derivative of -4*h + 59 + 4/3*h**2 + 4/9*h**3. Find u such that x(u) = 0.
-3, 1
Let t(b) be the second derivative of 17*b**6/3 + 1123*b**5/4 + 20625*b**4/4 + 228085*b**3/6 + 6655*b**2/2 - 4*b + 23. Factor t(a).
5*(a + 11)**3*(34*a + 1)
Let q(w) = -425*w**3 + 1575*w**2 - 9790*w + 14000. Let b(g) = 32*g**3 - 121*g**2 + 753*g - 1077. Let c(d) = -40*b(d) - 3*q(d). Factor c(n).
-5*(n - 12)*(n - 9)*(n - 2)
Let z = -611 + 613. Let i(n) be the first derivative of -n**z + 13 - 4*n + 2/3*n**3. Factor i(d).
2*(d - 2)*(d + 1)
Let c be (5 - 4)*(304/133 - 2). Let t(l) be the first derivative of c*l**2 + 2/21*l**6 - 2/7*l**4 + 0*l**5 + 0*l**3 + 0*l + 40. Factor t(s).
4*s*(s - 1)**2*(s + 1)**2/7
Find b such that -633*b + 12258*b**3 - 14*b**4 - 9*b**2 - 12045*b**3 + 17*b**4 + 426 = 0.
-71, -2, 1
Let r(t) = 8*t**3 - 187*t**2 + 36*t + 22. Let y(f) = 3*f**3 - 67*f**2 + 12*f + 8. Let z(n) = -4*r(n) + 11*y(n). Factor z(o).
o*(o - 1)*(o + 12)
Let u(q) be the second derivative of q**4/54 + 8*q**3/9 - 20*q**2 - 2*q - 2722. Factor u(w).
2*(w - 6)*(w + 30)/9
Let a be (403/2821)/(1/8). Let y(b) be the first derivative of 3 - 2/35*b**5 - a*b - 3/14*b**4 + 3/7*b**2 + 10/21*b**3. Let y(f) = 0. What is f?
-4, -1, 1
Let u = 236703/20 - 11835. Let z(v) be the second derivative of 0*v**3 - 23*v - 1/5*v**6 + 0*v**2 + 0 - 1/14*v**7 + 1/2*v**4 + u*v**5. Solve z(s) = 0 for s.
-2, -1, 0, 1
Let i be (1389/6482)/(5/70). Solve 5/2*d**4 - 15/2*d**2 + 8*d - d**i - 2 = 0 for d.
-2, 2/5, 1
Let m(d) = d**3 - d**2 + 53*d - 106. Suppose -4*o - 2 = 3*s, 0 = 2*s - 5*o - 29 + 15. Let f be m(s). Solve 3 + 189/2*l**3 + 27*l + 327/4*l**2 + 147/4*l**f = 0.
-1, -2/7
Let s(j) = -317*j - 634. Let p be s(-2). Let o(f) be the second derivative of -1/15*f**6 + 0 - 1/3*f**4 + p*f**2 + 0*f**3 - 3/10*f**5 + 18*f. Factor o(q).
-2*q**2*(q + 1)*(q + 2)
Let d(k) be the second derivative of 0 - 3/2*k**3 - 3*k**2 - 1/4*k**4 + 41*k. Suppose d(f) = 0. What is f?
-2, -1
Factor 3/5*n**3 - 3072/5 + 0*n**2 - 576/5*n.
3*(n - 16)*(n + 8)**2/5
Let w(p) be the first derivative of 6*p**3 - 1919*p**2 + 852*p + 2430. Factor w(t).
2*(t - 213)*(9*t - 2)
Let s be 2 - (12/78 - 84/39). Let z be s/(-5)*70/(-2). What is d in -8*d**3 + 2*d**4 - z + 67 - 21 - 4*d**2 + 24*d = 0?
-1, 3
Let c(p) be the second derivative of 3*p - 8/15*p**3 - 1/15*p**4 + 1/75*p**5 + 0 + 1/300*p**6 + 5/2*p**2. Let k(n) be the first derivative of c(n). Factor k(j).
2*(j - 2)*(j + 2)**2/5
Let z(s) = s - 7. Let f be z(14). Suppose r - 5*l + 21 = 0, -3*r + 3*l - f = -r. Factor -15*c**2 + 20 + 2*c - 25*c**3 + 22*c + c - 2*c**r - 3*c**4.
-5*(c - 1)*(c + 1)**2*(c + 4)
Let u(t) = -t**3 + 4*t**2 + 2*t - 2. Let o be u(5). Let x = -12 - o. Suppose v**3 + 9*v**2 + 2*v**4 + v - 6*v**2 - 5*v**4 - 2*v**x = 0. What is v?
-1, -1/2, 0, 1
Let h = 1759/2 + -877. Let p(u) be the second derivative of 19*u + 0 - 45/2*u**2 + h*u**3 + 1/4*u**5 + 25/12*u**4. Factor p(v).
5*(v - 1)*(v + 3)**2
Let s be (58 - 4)/(15/90). Let o = s + -320. Find u such that 68/7*u**2 - 48/7*u**3 + 16/7*u**o - 46/7*u - 2/7*u**5 + 12/7 = 0.
1, 2, 3
Let k(w) = -13*w**4 + 66*w**3 - 216*w**2 - 4*w - 16. Let d(y) = 15*y**4 - 65*y**3 + 220*y**2 + 5*y + 20. Let f(t) = 4*d(t) + 5*k(t). Factor f(x).
-5*x**2*(x - 10)*(x - 4)
Let x = -4791 + 43135/9. Factor 2/9*w**3 + x + 34/9*w + 20/9*w**2.
2*(w + 1)**2*(w + 8)/9
Let z(l) = -5*l**2 - 11*l + 13. Suppose -19 = -2*m - 3. Let j(g) = 6*g**2 - m + 3 + 12*g - 9. Let w(y) = -3*j(y) - 4*z(y). Let w(a) = 0. What is a?
-5, 1
Let o(x) = 5*x**3 - 13*x**2 + 7*x + 37. Let f(n) = -4*n**3 + 12*n**2 - 9*n - 34. Let r(q) = -4*f(q) - 3*o(q). Find t such that r(t) = 0.
-1, 5
Suppose 4*m - 273 - 31 = 0. Suppose 0 = -233*f + 230*f. Suppose 65*u**3 - 4*u**2 + 24*u**4 + m*u**2 + 3*u**5 + 27*u + f*u**3 + u**3 = 0. Calculate u.
-3, -1, 0
Let o(l) be the first derivative of l**8/840 - l**7/315 + 13*l**3/3 - 46. Let y(j) be the third derivative of o(j). Factor y(b).
2*b**3*(3*b - 4)/3
Let y(n) be the second derivative of 61*n + 7/12*n**4 - 7/30*n**6 + 0*n**2 + 1/10*n**5 - 1/3*n**3 + 0. Solve y(t) = 0 for t.
-1, 0, 2/7, 1
Suppose 0 = 7*b + 251 + 127. Let l be (-51)/(-18) + -3*(-6)/b. What is m in l*m - 5/4 - 5/4*m**2 = 0?
1
Let b = 42 + -34. Suppose b*i - 9931 - 877 = 0. Solve -3*q**2 - 1360*q - 3*q**3 + 27 + i*q + 4*q**3 = 0 for q.
-3, 3
Let l be (-1)/4 + 14/32*(-6880)/(-7224). Solve -l*o**2 + 5/2 + 1/3*o = 0 for o.
-3, 5
Let z(t) = -t + 9. Let l = -13 - -19. Let v be z(l). Factor 3*q**3 + 12*q**2 - q**3 - 22*q - 4*q**v + 12.
-2*(q - 3)*(q - 2)*(q - 1)
Let k = -435/26 - -35/2. Let i = -13620/13 + 1048. Factor 6/13*b**2 + i - 2/13*b**4 - 2/13*b**3 + k*b.
-2*(b - 2)*(b + 1)**3/13
Let 2/5*v**5 + 0 - 24/5*v + 1/5*v**3 - 11/5*v**4 + 10*v**2 = 0. Calculate v.
-2, 0, 1/2, 3, 4
Let c(v) be the third derivative of -v**7/525 + 7*v**6/150 - 16*v**5/75 - 7*v**4/30 + 11*v**3/5 + 847*v**2. What is f in c(f) = 0?
-1, 1, 3, 11
Suppose 580*k - 595*k - 5430 = 0. Let w = -721/2 - k. Suppose 0 - 3/4*y**3 - 9/4*y**2 - w*y = 0. What is y?
-2, -1, 0
Let d(i) = 3*i - 33. Let t be d(6). Let h be (-2152)/(-85) + t/(-510)*-4. Find u, given that 0*u + 134/5*u**2 + h*u**3 - 8/5 = 0.
-1, -2/7, 2/9
Let c(o) = -4*o**5 - 92*o**4 + 336*o**3 + 298*o**2 - 782*o - 648. Let s(u) = -2*u**4 - u**2 + u. Let k(q) = -c(q) - 2*s(q). Determine l so that k(l) = 0.
-27, -1, 2, 3
Let o(m) = 88*m**2 - m. Let g(h) = 705*h**2 - 61*h - 938. Let y(n) = -g(n) + 8*o(n). Find c, given that y(c) = 0.
-14, 67
Let o be (34*94/(-799))/(0 - 8/6). Let p(t) be the second derivative of -16/5*t**2 + 0 + 8/15*t**o - 1/30*t**4 + 38*t. Factor p(b).
-2*(b - 4)**2/5
Suppose -2*k = -2*j + 33 + 15, 48 = 2*j - 5*k. Let v(i) be the third derivative of 5/3*i**3 + 65/24*i**4 - j*i**2 + 1/2*i**5 + 0 + 0*i. Factor v(n).
5*(n + 2)*(6*n + 1)
Suppose -4*p + 0 = -84. Let c be (-10)/(-2) + 8/(13 - p). Factor 0 - 5*k - 25/4*k**3 - 20*k**2 + 125/4*k**c.
5*k*(k - 1)*(5*k + 2)**2/4
Let j be 2*2/(-12) - (-306)/27. Suppose 5*y + 1 = j. Find c such that -47*c**2 - 30*c**3 - 7*c - 10*c**2 - 3*c**y - 33*c - 5*c**4 = 0.
-2, 0
Let b(c) be the first derivative of -1/14*c**4 - 4/7*c**3 + 9/7*c**2 + 4*c - 227. Let b(j) = 0. What is j?
-7, -1, 2
Let o(a) be the first derivative of a**5/120 - 11*a**4/16 - 17*a**3/6 + 107*a**2/2 - 2*a - 124. Let c(i) be the second derivative of o(i). Factor c(w).
(w - 34)*(w + 1)/2
Let w = -389 - -409. Suppose -w*s = -7*s - 26. Solve 8/3 + 0*j - 2/3*j**s = 0 for j.
-2, 2
Let j(i) be the second derivative of i**6/120 - i**5/40 - i**4/2 + 3*i**3/4 + 135*i**2/8 + 251*i. Factor j(l).
(l - 5)*(l - 3)*(l + 3)**2/4
Let s = -845393/2 - -422697. Solve -1/2*i**3 - 1/2*i**4 + 0 + 1/2*i**2 + s*i = 0.
-1, 0, 1
Let p(k) = -40*k**2 - 1428*k - 8. Let j(x) = 71*x**2 + 2855*x + 14. Let i(g) = -4*j(g) - 7*p(g). Let i(y) = 0. What is y?
-356, 0
Factor 1/5*s**3 - 18 - 16/5*s**2 + 69/5*s.
(s - 10)*(s - 3)**2/5
Suppose 25174*q**2 - 17*q - 12 + 3*q - 25178*q**2 - 2*q = 0. Calculate q.
-3, -1
Determine g, given that 1/5*g**4 + 289/5 + 544/