v = 0. Let f(x) be the first derivative of 9/22*x**p - 6/11*x + 10/11*x**3 + 3/11*x**2 - 23. Determine r so that f(r) = 0.
-1, 1/3
Suppose -19*g + 17*g + 6 = 0. Suppose 15 + 100*v - 7*v**3 + 45 + 12*v**g + 45*v**2 = 0. Calculate v.
-6, -2, -1
Suppose 957*h = 699*h. Let x be 2/(-9) + (-224)/(-441). Let 0*t**3 - 2/7*t**4 + h*t + x*t**2 + 0 = 0. Calculate t.
-1, 0, 1
Factor -1/4*s**4 + 0 + 9/4*s + 7/4*s**3 + 17/4*s**2.
-s*(s - 9)*(s + 1)**2/4
Suppose 9*t - 331 = 29. Let b = -38 + t. Factor y**4 + 57*y**2 - 6 - 4*y - 4*y**3 - 63*y**2 - b*y**4 + 5.
-(y + 1)**4
Let z be (-5)/(-110) + 4*(-3664)/(-2816). Factor -z*w + 3/4*w**2 + 15/2.
3*(w - 5)*(w - 2)/4
Let s(v) = -3*v**2 + 3*v + 2. Let o be s(3). Let z = -14 - o. What is g in -10*g**z - 3 + 0*g + 9*g**2 - 4*g = 0?
-3, -1
Let f = 425 + -424. Let q be f + -4 - 170/(-50). Factor -8/5*s + 2/5 + 12/5*s**2 - 8/5*s**3 + q*s**4.
2*(s - 1)**4/5
Let r(p) be the third derivative of p**5/330 - 151*p**4/66 + 4*p**2 - 131*p - 3. Factor r(x).
2*x*(x - 302)/11
Let d = 3390913/4 + -847728. Factor -d*i**3 + 55/4*i + 7 + 13/2*i**2.
-(i - 28)*(i + 1)**2/4
Factor -10006*f - 1378742 + 1561*f + 12*f**2 + 1376630.
3*(f - 704)*(4*f + 1)
Let z be (136/(-10) - 3/(-5))*-5. Let p = z - 65. Solve -5*k + 10*k**3 - 9*k**4 + 4*k**4 - 5*k**5 + p*k**4 - 5 + 10*k**2 = 0 for k.
-1, 1
Let o(w) be the second derivative of w**4/48 - 67*w**3/6 + 267*w**2/8 + 1343*w. Factor o(l).
(l - 267)*(l - 1)/4
Let r(q) be the second derivative of -3/14*q**3 + 2/21*q**4 + 0 + 1/140*q**5 - 80*q + 0*q**2. Factor r(s).
s*(s - 1)*(s + 9)/7
Let a(z) be the third derivative of -1/30*z**5 + 0*z + 1/3*z**4 - 1/60*z**6 + 19 + 2*z**2 + 4/3*z**3. Suppose a(w) = 0. Calculate w.
-2, -1, 2
Solve 70/17*s**2 + 2/17*s**3 - 656/17*s + 1376/17 = 0 for s.
-43, 4
Let f(u) be the first derivative of -130 + 0*u**2 + 0*u + 10/9*u**3 - 4/15*u**5 + 3/2*u**4. Factor f(j).
-2*j**2*(j - 5)*(2*j + 1)/3
Let z(w) be the third derivative of 0*w + 0 - 18*w**3 + 7/4*w**5 + 1/70*w**7 + 3/2*w**4 + 81*w**2 - 3/10*w**6. Factor z(d).
3*(d - 6)**2*(d - 1)*(d + 1)
Let t(f) = 2*f**3 + f - 2*f**2 + f**2 - 20 - 16 + 35. Let w(o) = -12*o**3 + 6*o**2 + 2. Let l(a) = -4*t(a) - w(a). Determine m, given that l(m) = 0.
-1, 1/2, 1
Suppose -40*d + 2559 = 2559. Let c(i) be the second derivative of d*i**2 - 1 + 1/4*i**4 - 3*i - 9/2*i**3. Suppose c(f) = 0. What is f?
0, 9
Let f(w) = -w**2 + 53*w + 56. Let k(c) = c**2 + c + 2. Let m = 506 - 504. Let l(b) = m*k(b) - 2*f(b). Find r, given that l(r) = 0.
-1, 27
Let n(f) be the first derivative of f**4 - 4316*f**3/3 - 2*f**2 + 4316*f + 3720. Find c such that n(c) = 0.
-1, 1, 1079
Let u(j) be the third derivative of j**7/1050 + j**6/600 - 11*j**5/150 + 11*j**4/30 - 4*j**3/5 + 140*j**2 + 15. Factor u(d).
(d - 2)**2*(d - 1)*(d + 6)/5
Factor 42 + 90*y + 6*y**4 + 3966*y**3 - 142 + 126*y**2 - 4024*y**3.
2*(y - 5)**2*(y + 1)*(3*y - 2)
Let w = 290 + -298. Let n(o) = -o**3 - 8*o**2 + 4*o + 32. Let a be n(w). Factor 3/4*t**4 - 9/8*t**3 + 0 + a*t**2 + 0*t + 3/8*t**5.
3*t**3*(t - 1)*(t + 3)/8
Let m(p) be the first derivative of 14*p**5/25 - 8*p**4/5 - 272*p**3/15 - 128*p**2/5 + 96*p/5 + 473. What is s in m(s) = 0?
-2, 2/7, 6
Determine y so that -151*y**2 - 3902 + 306*y**2 + 3*y**3 - 3933*y - 43750 - 173*y**2 = 0.
-19, 44
Let h(d) be the first derivative of 23*d**5/7 + 86*d**4/7 - d**3/7 + 4359. Find q such that h(q) = 0.
-3, 0, 1/115
Let r(z) be the third derivative of -z**6/180 - 5*z**5/18 - 23*z**4/18 - 132*z**2. Factor r(v).
-2*v*(v + 2)*(v + 23)/3
Let t(l) be the third derivative of -l**7/1575 + 7*l**6/900 + 2*l**5/75 - 7*l**4/45 - 32*l**3/45 - 4369*l**2. Find r such that t(r) = 0.
-2, -1, 2, 8
Let a(v) be the first derivative of -v**4/14 + 18*v**3/7 - 179*v**2/7 + 306*v/7 - 419. Suppose a(g) = 0. Calculate g.
1, 9, 17
Let y(r) be the first derivative of 113 - 3/4*r**4 - 3*r**2 - 5*r**3 + 24*r. Factor y(d).
-3*(d - 1)*(d + 2)*(d + 4)
Let f(x) be the first derivative of -7*x**4/16 - 10*x**3/3 - 51*x**2/8 + 9*x/2 + 517. Factor f(g).
-(g + 3)**2*(7*g - 2)/4
Let p(f) be the first derivative of 0*f - 6 + 0*f**4 + 1/270*f**5 + 14*f**2 - 4/27*f**3. Let v(u) be the second derivative of p(u). Suppose v(j) = 0. What is j?
-2, 2
Suppose 5*j + 31 = -2*v - 10, -5*j - 44 = 3*v. Let p = j - -9. Let -24*a**p + 129*a + 52*a**3 + 31*a - 4*a**4 - 84*a**3 - 100 = 0. Calculate a.
-5, 1
Factor 849430*p**2 - 849429*p**2 - 9*p - 240 + 31*p.
(p - 8)*(p + 30)
Let t(y) = 1135*y**2 + 6555*y - 6565. Let x(c) = -101*c**2 - 596*c + 597. Let v(o) = 4*t(o) + 45*x(o). Factor v(b).
-5*(b - 1)*(b + 121)
Let y = 986 - 990. Let n be (-14)/((-98)/(-1)) - y/14. Let -n*t**2 - 8/7 - 6/7*t = 0. What is t?
-4, -2
Suppose -32 = -4*r + 4*x, 6*x - 8*x = -8. Suppose 5*u - 51 = -n, 0*n + 4 = -n. Factor -4*c**2 + 7*c**3 - 12*c**2 + u*c**4 - 4*c + 16*c - r*c**4.
-c*(c - 3)*(c - 2)**2
Let o(m) be the second derivative of -m**5/4 + 55*m**4/12 + 5*m**3/6 - 55*m**2/2 + 772*m + 1. Factor o(f).
-5*(f - 11)*(f - 1)*(f + 1)
Let n = 1 + -11/12. Let g(y) be the first derivative of 14 + 1/4*y**2 + n*y**3 + 0*y. Factor g(f).
f*(f + 2)/4
Let j = -44 - -47. Suppose 37 = 8*l - j. Suppose -2*h**2 + 9*h**3 + 27*h + l*h**2 - 3 - 36*h = 0. Calculate h.
-1, -1/3, 1
Let m(r) be the third derivative of r**7/126 + r**6/72 - 3*r**5/4 - 125*r**4/72 + 125*r**3/9 - 28*r**2 + 7*r. Find c, given that m(c) = 0.
-5, -2, 1, 5
Let w = 10583 + -10581. Let d(v) be the second derivative of 0 + 1/3*v**4 - 4/3*v**3 + 36*v - 6*v**w. Find o, given that d(o) = 0.
-1, 3
Let t = -14/3 - -73/6. Suppose 1796*s - 982*s = 906*s - 184. Factor 9 + 3/2*j**s + t*j.
3*(j + 2)*(j + 3)/2
Suppose 5*z - 11*m + 6*m + 15 = 0, -m + 1 = -2*z. Let o be z*8/(64/2). Factor 7/2 + 3*h - o*h**2.
-(h - 7)*(h + 1)/2
Let t be (0/(-42))/(3 - 5). Let r(n) be the second derivative of 1/45*n**5 + 0*n**3 + t*n**2 - 21*n + 0 + 2/27*n**4 - 2/135*n**6. Let r(l) = 0. Calculate l.
-1, 0, 2
Let j(l) be the first derivative of -2*l**5/25 + 39*l**4/20 + 22*l**3/5 - 61*l**2/10 - 42*l/5 - 1085. Let j(h) = 0. What is h?
-2, -1/2, 1, 21
Let q(r) = 2*r - 41. Let t(b) = 2. Let k(x) = -q(x) + 3*t(x). Let h be k(22). Factor -1/6*v**h - 1/3*v - 4/3 + 5/6*v**2.
-(v - 4)*(v - 2)*(v + 1)/6
Let q = -738 + 504. Let b = q + 237. Factor 4/5*d**2 - 4/5 - 2/5*d + 2/5*d**b.
2*(d - 1)*(d + 1)*(d + 2)/5
Factor 387 + 787*j + 68*j**3 + 1106 + 1086*j**2 - 268 - 275*j + j**4 - 2892*j.
(j - 1)**2*(j + 35)**2
Let n(d) be the second derivative of 19*d**7/42 + 41*d**6/90 - 17*d**5/60 - d**4/36 - 158*d. Suppose n(v) = 0. Calculate v.
-1, -1/19, 0, 1/3
Factor 144*x**3 + 1053/2*x - 405*x**2 - 24*x**4 + 3/2*x**5 - 243.
3*(x - 6)*(x - 3)**3*(x - 1)/2
Solve -48/5 - 578/5*y - 24/5*y**2 = 0.
-24, -1/12
Factor -1225449/7 + 3/7*s**5 - 765/7*s**4 + 1245375/7*s - 428490/7*s**2 + 52110/7*s**3.
3*(s - 123)**2*(s - 3)**3/7
Let f(b) be the third derivative of 0 + 1/336*b**8 + 55*b**2 + 1/90*b**7 - 1/45*b**5 + 0*b + 0*b**4 + 0*b**6 + 0*b**3. What is n in f(n) = 0?
-2, -1, 0, 2/3
Let -78*b**3 + 218*b**3 - 142*b**3 = 0. What is b?
0
Let 2960*h - 400*h**2 + 187*h**3 - 408*h**3 - 1389 - 3635 - 736 + 226*h**3 = 0. What is h?
4, 72
Factor -299*l**2 - 344*l**2 + 84*l**3 + 31*l**3 - 4 + 592*l**2 - 25*l**4 - 35*l.
-(l - 4)*(l - 1)*(5*l + 1)**2
Let o = -72967 + 656761/9. Factor -2/9*t**5 - 162 - 378*t - o*t**4 - 596/9*t**3 - 276*t**2.
-2*(t + 1)**2*(t + 9)**3/9
Let m(q) be the first derivative of -1/8*q**4 + 0*q - 24 + 0*q**3 + q**2. Suppose m(v) = 0. What is v?
-2, 0, 2
Suppose 130*n - 3 = 127*n. Let g(r) be the first derivative of -n + 2/15*r**3 + 3/10*r**2 + 1/30*r**6 + 0*r**5 - 2/5*r - 1/5*r**4. Solve g(b) = 0.
-2, -1, 1
Let y(o) be the second derivative of -o**4/108 - 124*o**3/3 - 69192*o**2 + 1705*o. Solve y(r) = 0.
-1116
Factor -4*k**4 + 4217*k + 2410*k - 3600 + 188*k**3 - 1487*k - 1724*k**2.
-4*(k - 36)*(k - 5)**2*(k - 1)
Find f such that 2/9*f**2 - 46/9*f - 2/9*f**4 + 0 + 46/9*f**3 = 0.
-1, 0, 1, 23
Let g(o) be the first derivative of -o**6/1800 - o**5/50 - o**3 + 20*o + 38. Let l(u) be the third derivative of g(u). Factor l(c).
-c*(c + 12)/5
Let d be (-72)/1548 - 528/(-258). Let -2/9*j**d + 4/9*j - 4/9*j**3 + 1/3*j**4 - 1/9 = 0. What is j?
-1, 1/3, 1
Let t(j) = 3*j**2 - 2*j - 2. Let z = -28 - -27. Let a be t(z). Let 3*r**3 - 24*r**2 - 23 - 