.
-1/22
Let r(b) be the first derivative of -43*b**4 - 112*b**3 - 78*b**2 + 8*b + 201. What is c in r(c) = 0?
-1, 2/43
Let w(d) be the third derivative of -d**8/336 + d**7/21 - 4*d**6/15 + 19*d**5/30 - 5*d**4/8 + 2*d**2 + 2498*d. Find z, given that w(z) = 0.
0, 1, 3, 5
What is p in 326*p**3 + 16*p**4 - 1289 + 6216*p + 896 - 1191 - 2444*p**2 - 30*p**4 = 0?
2/7, 6, 11
Let s be (27/(-63))/(399/(-266)). Suppose -a - 8 = -5*a. Determine p, given that -s + 5/7*p**3 - 13/7*p**a - 2/7*p**5 + 9/7*p + 3/7*p**4 = 0.
-2, 1/2, 1
Let a(o) = 8*o**4 + 3090*o**3 + 298770*o**2 + 74492*o + 6. Let b(n) = -8*n**4 - 3090*n**3 - 298769*n**2 - 74493*n - 5. Let y(s) = 5*a(s) + 6*b(s). Factor y(x).
-2*x*(x + 193)**2*(4*x + 1)
Let v = -425359/40 - -10634. Let k(a) be the third derivative of 0*a**3 + a**2 + v*a**4 + 0 - 1/300*a**5 + 0*a. Factor k(f).
-f*(f - 3)/5
Let z(g) = 7*g**2 - 211*g + 32. Let b be z(30). Let q be (-904)/(-20) + b/(-5). What is l in -16/5 - 124/5*l + 64/5*l**3 - q*l**2 = 0?
-1/4, 4
Suppose 3*j = x - 2, -j - 41 = -3*x + j. Let z = -14 + x. Factor -6*w**3 + 15 + 20*w**3 - 15*w**2 - 9*w**z - 5*w.
5*(w - 3)*(w - 1)*(w + 1)
Let r(j) be the second derivative of j**5/20 - 3*j**4/2 - j**3/6 + 9*j**2 - 2*j - 3717. Determine g so that r(g) = 0.
-1, 1, 18
Let c = 41 - 39. Suppose -5*w + 16 = c*h - 4*h, -2*h + 24 = 5*w. Find x, given that -33*x - 32*x + 3*x**w + 65*x = 0.
0
Let p(w) be the second derivative of -w**4/28 + 6*w**3 - 480*w**2/7 + 93*w. Determine d, given that p(d) = 0.
4, 80
Let m(y) be the third derivative of -27*y**6/40 + y**5/150 - 731*y**2. Determine k, given that m(k) = 0.
0, 2/405
Let a(p) be the second derivative of 2*p**7/105 - 32*p**6/75 - 3*p**5/25 + 10*p**4/3 - 64*p**3/15 - 262*p - 1. What is z in a(z) = 0?
-2, 0, 1, 16
Let h(u) = -6*u**3 - 11*u**2 - 31*u + 1. Let c be h(-16). Solve 24637*l**2 + 484 - c*l**2 + 372*l**3 + 16*l**4 + 1310*l + 1198*l = 0 for l.
-11, -1, -1/4
Let z(m) be the first derivative of 1/28*m**4 - 2/7*m**2 + 0*m**3 + 80 + 0*m. Let z(r) = 0. What is r?
-2, 0, 2
Suppose -4*x - 29*x = -76*x + 86. What is i in -175/3*i - 5/6*i**x - 6125/6 = 0?
-35
Let z be -10 + 10 + (-11)/(-132). Let i(y) be the first derivative of -1/3*y**3 + z*y**4 - 5 + 1/3*y**2 + 0*y. Solve i(b) = 0 for b.
0, 1, 2
Suppose n = 6*u - 32, -5*u - 4*n - 1468 + 1427 = 0. Factor 3/2*q**5 + 36*q**u + 0 - 54*q**2 + 0*q + 33/2*q**4.
3*q**2*(q - 1)*(q + 6)**2/2
Suppose -2*f - 48*f = -29450. Let j = -2333/4 + f. Factor 5/4*t**3 - j*t**2 + 19/4*t + 3/4*t**4 - 1.
(t - 1)**2*(t + 4)*(3*t - 1)/4
Let l(r) = -9*r**3 + 174*r**2 + 979*r - 4. Let i(m) = -125*m**3 + 2435*m**2 + 13705*m - 55. Let u(n) = -4*i(n) + 55*l(n). Find o, given that u(o) = 0.
-5, 0, 39
Determine m, given that -525 + 1060 + 160*m - 4*m**2 - 535 = 0.
0, 40
Suppose -6 = 3*s + 3*l, -s - l + 3*l = -10. Let -67*k**2 + 5*k**3 + 65*k**s - k**4 - 2*k**4 = 0. Calculate k.
0, 2/3, 1
Suppose -i + 2*i = -3*h - 93, h + 3*i = -39. Let j = 33 + h. Factor -4*x - j - 4*x**2 - 1 + 4.
-4*x*(x + 1)
Let u be (-15*6/(-225))/(8 + 0). Let s(r) be the first derivative of -1/4*r**3 + 0*r**4 + 1/4*r**2 - 20 + u*r**5 + 0*r. Factor s(k).
k*(k - 1)**2*(k + 2)/4
Let u(w) be the third derivative of w**7/42 - w**6/4 - w**5/4 + 35*w**4/3 - 40*w**3 + 559*w**2. Factor u(q).
5*(q - 4)**2*(q - 1)*(q + 3)
Let d be 19/(57/(-2)) + (0 - -2). Let q(b) be the first derivative of d*b - 10/9*b**3 - b**2 - 2. Factor q(y).
-2*(y + 1)*(5*y - 2)/3
Let t(h) = -h**3 - 46*h**2 - 25*h - 16. Let x be t(-45). Let z = x + 916. Find c, given that -5/4*c**3 + 0 + 1/2*c**2 + z*c = 0.
0, 2/5
Suppose -2*b + 3*b - 20 = -4*o, 3*b - 2*o - 4 = 0. Solve -3*l**b - 291*l + 9*l**3 + 151*l + 8*l**2 - 3*l**5 + 146*l + 7*l**2 = 0 for l.
-1, 0, 2
Let m(d) be the second derivative of d**5 + 100*d**4 + 7995*d**3/2 + 159695*d**2/2 + 4304*d. Solve m(c) = 0 for c.
-41/2, -19
Let z(m) = 25*m - 696. Let y be z(28). Let n(g) be the second derivative of 4*g + 0 - 1/18*g**y + 4/3*g**2 + 1/3*g**3. Factor n(r).
-2*(r - 4)*(r + 1)/3
Suppose -1/3*o**2 - 2352 + 56*o = 0. Calculate o.
84
Suppose -269 + 274 = j. Determine l so that 5*l**j - 3*l**4 + 7*l**4 + 15*l**3 - 5*l**2 - 14*l**4 - 5*l**4 = 0.
0, 1
Let n be (-1 + 6)*74/185. Suppose -10 + 1639*f**2 - 1638*f**n - 16*f + 74 = 0. Calculate f.
8
Let j(f) be the third derivative of -11/36*f**4 - 228*f**2 + f - 1/18*f**5 + 1/720*f**6 + 0 + 0*f**3. Suppose j(h) = 0. What is h?
-2, 0, 22
Let l(a) = 2*a**2 + 1. Let j(x) = 2*x**3 - 96*x**2 + 1944*x - 11658. Let u(y) = -j(y) + 6*l(y). Factor u(p).
-2*(p - 18)**3
Let w = -11185/203 - -1602/29. Let b(r) be the third derivative of -19*r**2 + 1/280*r**6 + 3/140*r**5 + 0 + w*r**3 - 1/490*r**7 + 0*r - 5/56*r**4. Factor b(q).
-3*(q - 1)**3*(q + 2)/7
Suppose -o - 3*s + 25 = 0, -4*o = 2*s - 58 - 42. Determine u so that -124 - 89*u**5 + 60*u + 80*u**2 + 44 + 84*u**5 - 30*u**4 - o*u**3 = 0.
-4, -2, 1
Let w be (-14)/(392/12) - (-36)/35. Let l(d) be the first derivative of -w*d**5 + 0*d**4 + 2*d**3 - 9 - 3*d + 0*d**2. Factor l(g).
-3*(g - 1)**2*(g + 1)**2
Let h(b) = 5*b**3 - 13*b**2 - 16*b + 126. Let v(n) = -5*n**3 - 181*n + 377*n - 181*n + 15*n**2 - 125. Let x(p) = 5*h(p) + 6*v(p). Factor x(i).
-5*(i - 4)*(i - 3)*(i + 2)
Let o(w) = -10*w + 55. Let d be (19 + -9)*(-1)/(-2). Let q be o(d). Factor 5/2*l**3 + 0 + q*l - 15/2*l**2.
5*l*(l - 2)*(l - 1)/2
Let t(q) be the second derivative of 80/9*q**3 + 26/3*q**2 - 48*q + 1 + 1/3*q**4. Let t(k) = 0. What is k?
-13, -1/3
Let z(t) be the first derivative of -7*t**5/15 + 173*t**4/6 + 931*t**3/9 + 133*t**2/3 - 104*t - 3742. Let z(k) = 0. What is k?
-2, -1, 3/7, 52
Let j(i) be the first derivative of -1/20*i**2 + 0*i + 1/50*i**5 + 1/40*i**4 + 15 - 1/30*i**3. Let j(c) = 0. Calculate c.
-1, 0, 1
Let r(g) = g**3 - g**2 - 2*g - 1. Let q(w) = -74*w**3 + 26*w**2 + 2*w + 2. Let a(c) = -2*q(c) - 4*r(c). What is y in a(y) = 0?
0, 1/6
Let n(q) be the second derivative of -q**5/5 + 29*q**4/2 - 69*q**3 + 82*q**2 + 6395*q. Factor n(b).
-2*(b - 41)*(b - 2)*(2*b - 1)
Let h(z) = 5*z**4 - 59*z**3 + 128*z**2 + 8*z - 12. Let b(p) = -5*p**4 + 60*p**3 - 125*p**2 - 10*p + 15. Let q(t) = 4*b(t) + 5*h(t). Factor q(a).
5*a**2*(a - 7)*(a - 4)
Let z(m) be the third derivative of -m**7/1155 + 137*m**6/165 + 5*m**5 + 413*m**4/33 + 551*m**3/33 + 8*m**2 + 6*m + 16. Factor z(w).
-2*(w - 551)*(w + 1)**3/11
Let j(c) be the second derivative of -c**6/480 + c**5/80 - c**3/6 - 31*c**2 - 15*c. Let s(v) be the first derivative of j(v). Factor s(r).
-(r - 2)**2*(r + 1)/4
Let s(d) = 2945*d - 47117. Let r be s(16). Let o = 218 - 1960/9. Determine t so that 2/9*t**2 - o - 1/9*t + 1/9*t**r = 0.
-2, -1, 1
Let g(c) be the first derivative of c**4 + 20*c**3/3 + 12*c**2 - 1326. Factor g(w).
4*w*(w + 2)*(w + 3)
Let n be -15 + ((-4)/8)/((-38)/1254). Factor -3/2*h**5 + 0*h + n*h**3 - 3/2*h**4 + 3/2*h**2 + 0.
-3*h**2*(h - 1)*(h + 1)**2/2
Let v = -51673 + 671765/13. Factor 2/13*w**2 + v - 12/13*w.
2*(w - 4)*(w - 2)/13
Let x(k) be the second derivative of 0*k**5 - 53*k + 1/6*k**6 - 15/2*k**2 + 20/3*k**3 + 0 - 5/2*k**4. Let x(n) = 0. What is n?
-3, 1
Let r(g) be the second derivative of -3 + 0*g**2 - 200*g**4 + 0*g**3 - 6*g**5 - 1/20*g**6 + 12*g. Factor r(d).
-3*d**2*(d + 40)**2/2
Factor -303*a**2 + 22*a**4 - 115*a**2 + 111*a**3 - 19*a**4 + 609*a - 246 - 62*a**2 + 3*a**2.
3*(a - 2)*(a - 1)**2*(a + 41)
Let w(a) be the third derivative of -a**6/540 - a**5/36 - 7*a**3/2 + 3*a**2 - 10. Let j(b) be the first derivative of w(b). What is m in j(m) = 0?
-5, 0
Determine t, given that -1/3*t**3 - 3024 + 65/3*t**2 - 264*t = 0.
-7, 36
Let u be (-7250)/(-50) + 5/(1 - 0). Factor -u*m + 6*m**2 + 8*m**2 + 130*m + 6 + 4*m**2 - 4*m**3.
-2*(m - 3)*(m - 1)*(2*m - 1)
Let h(n) be the third derivative of -n**6/36 - 17*n**5/90 - 7*n**4/18 + 12*n**2 + 49. Let h(p) = 0. Calculate p.
-2, -7/5, 0
Suppose -453*m - 824*m = -408*m - 2607. Factor -1/2*n**4 + 0 + 0*n**m - 1/4*n + 1/2*n**2 + 1/4*n**5.
n*(n - 1)**3*(n + 1)/4
Let l(d) be the third derivative of d**7/840 + 13*d**6/480 - 19*d**5/240 - 73*d**4/96 - 7*d**3/4 - 112*d**2 + 3*d. What is h in l(h) = 0?
-14, -1, 3
Suppose -2*m + 7/4 + 1/4*m**2 = 0. What is m?
1, 7
Let w be 20/(-8)*544/(-85). Let g be 3/798*7*w. Factor -6/19 + g*x - 2/19*x**2.
-2*(x - 3)*(x - 1)/19
Suppose 47*r - 54*r = 0. Let p(