8)/(-6) - -4. Let j be ((-75)/18 + 4)/(2/(-219)). Solve -z*s**3 + 4 + j*s**2 - 14*s + 11/4*s**4 - 1/4*s**5 = 0 for s.
1, 4
Suppose 0 = 3*c + 5*y + 3, -2*c + 23 = 3*c - y. Factor 10*k**3 - 2*k**c + 1243 - 1243 - 3*k**4.
-5*k**3*(k - 2)
Let z(s) be the first derivative of s + 1/4*s**4 - 1/2*s**2 - 5 - 1/3*s**3. Find w, given that z(w) = 0.
-1, 1
Suppose -57*g - 33*g = -60*g - 60. Let b be 5/6*9/10. Factor -1/4*k**g - b - k.
-(k + 1)*(k + 3)/4
Let v(i) = 27*i + 111. Let j be v(-4). Suppose 0 + 3/5*m**j - 9/5*m**2 + 6/5*m = 0. What is m?
0, 1, 2
Let t(c) be the first derivative of 2*c**5/35 + 27*c**4/14 - 58*c**3/7 + 89*c**2/7 - 60*c/7 - 148. Suppose t(k) = 0. Calculate k.
-30, 1
Let t be (-1 - 27/(-6))/((-7)/42). Let n be 12/t*(-3)/6*7. Find w, given that -2/3*w + 2/3*w**4 - 2/3*w**n + 0 + 2/3*w**3 = 0.
-1, 0, 1
Let z(b) be the second derivative of -2*b**4/3 + 77*b**3/3 + 60*b**2 + 646*b. Suppose z(v) = 0. What is v?
-3/4, 20
Solve 13/2*p**2 + 0 - 5/2*p**3 - 3*p = 0.
0, 3/5, 2
Let d(s) be the third derivative of s**6/90 + 8*s**5/45 + 39*s**2. Factor d(g).
4*g**2*(g + 8)/3
Let o(u) be the second derivative of 3/5*u**5 + 0 + 0*u**3 - 3/10*u**6 - 1/3*u**4 + 16*u + 0*u**2. Solve o(d) = 0.
0, 2/3
Let p(v) = -v + 4. Let t be p(0). Factor -2 + u**4 + 7*u + 5*u**3 - 11*u**2 + 2*u**2 - 3*u**4 + u**t.
-(u - 2)*(u - 1)**3
Let z(k) be the first derivative of k**6/12 - k**5/10 - 33*k**4/8 - 21*k**3/2 + 8. Factor z(s).
s**2*(s - 7)*(s + 3)**2/2
Let w(p) be the first derivative of -5*p**3/3 + 20*p**2 - 35*p - 110. Factor w(a).
-5*(a - 7)*(a - 1)
Solve 363/4*o**3 - 21/4*o**4 - 45/2 + 501/4*o - 753/4*o**2 = 0.
2/7, 1, 15
Let a(f) = f**3 - 36*f**2 + 311*f - 153. Let r be a(13). Find d such that -16/9*d**2 + 2/9 - 2*d**4 - 4/9*d + 4*d**r = 0.
-1/3, 1/3, 1
Let z(c) = -c**2 + 19*c - 58. Let r be z(15). Let i(w) be the first derivative of 0*w**r + 8/13*w - 2/39*w**3 - 10. What is m in i(m) = 0?
-2, 2
Let x(w) be the first derivative of 5*w**6/24 - 13*w**5/20 + 9*w**4/16 + w**3/12 - w**2/4 - 70. Solve x(p) = 0 for p.
-2/5, 0, 1
Let r be ((-709)/1418)/((-2)/10). Factor 15/4 - 5/4*l**2 + r*l.
-5*(l - 3)*(l + 1)/4
Suppose -5*v + k = 5, -3*k = -5*v - 6*k + 15. Suppose 0 = -v*n - n + 2. Find a such that 0*a**n - 2/3*a**3 - 1/3 + 1/3*a**4 + 2/3*a = 0.
-1, 1
Let g = -51 - -54. Factor -7*u**3 - 15*u**2 - 8*u**3 + 10*u**g + 10 + 5*u + 5*u**4 + 0*u.
5*(u - 2)*(u - 1)*(u + 1)**2
Solve 1 + 1602*v**3 - 16*v**2 + 4*v**4 + 2*v**5 - 1 - 13*v + 5*v - 1608*v**3 = 0.
-2, -1, 0, 2
Let q(s) be the second derivative of -s**6/90 + 3*s**5/20 - 5*s**4/12 - 25*s**3/18 - 3*s + 10. Solve q(a) = 0.
-1, 0, 5
Let r(c) = c**3 + 17*c**2 + 16*c + 5. Let f be r(-16). Suppose 20 - 4 = 4*i. Let b**i - 3*b - 2*b**4 + 5*b**2 - f*b**3 - 12*b**2 = 0. What is b?
-3, -1, 0
Let c(p) be the second derivative of p**4/4 + 54*p**3 + 4374*p**2 - 342*p. Factor c(s).
3*(s + 54)**2
Let b(x) be the first derivative of x**9/13608 - x**8/3780 + x**6/810 - x**5/540 + x**3 + 13. Let s(n) be the third derivative of b(n). Factor s(t).
2*t*(t - 1)**3*(t + 1)/9
Let n(p) be the third derivative of 59*p**6/150 + p**5/75 - 275*p**2. Factor n(z).
4*z**2*(59*z + 1)/5
Let v(a) be the third derivative of -1/140*a**7 - 26*a**2 + 0 - 11/360*a**5 + 1/288*a**8 - 11/240*a**6 + 0*a**3 + a + 1/24*a**4. What is h in v(h) = 0?
-1, 0, 2/7, 3
Let x be ((-356)/3115)/(2/(-40)). Let 1/7*o**2 + x - 8/7*o = 0. What is o?
4
Let n(o) = -o**3 + 4*o**2 - 3*o + 1. Let r be n(2). Factor g**2 + 5*g**2 + 2*g**r + 3*g**2 - 11*g**2.
2*g**2*(g - 1)
Let i(a) be the second derivative of a**6/18 + 7*a**5/6 - 25*a**4/12 - 241*a. Suppose i(g) = 0. Calculate g.
-15, 0, 1
Let c = 272/525 - -4/75. Let i be (3 + -4)/2 + (-22)/(-28). Factor 2/7*b**5 - 2/7*b**4 + 4/7*b**2 + 2/7*b - i - c*b**3.
2*(b - 1)**3*(b + 1)**2/7
Let k(v) be the third derivative of -9*v**7/70 + 3*v**6/40 + 23*v**5/20 + 13*v**4/8 + v**3 + 11*v**2. Solve k(n) = 0.
-1, -1/3, 2
Let q(o) = o**3 + 12*o**2 + 8*o - 11. Let b be q(-12). Let p = b + 431/4. Factor 3/4 - 3/2*g**2 + p*g**4 + 0*g + 0*g**3.
3*(g - 1)**2*(g + 1)**2/4
Let c = 9028/7465 + -14/1493. Find g, given that 1/5*g**2 + c + 7/5*g = 0.
-6, -1
Let i(w) be the second derivative of 6*w + 0 - 8/7*w**2 - w**4 + 2*w**3 + 4/35*w**5. Factor i(p).
4*(p - 4)*(p - 1)*(4*p - 1)/7
Let n be (-92)/(-22) - -3*2/(-33). Factor -7*a**4 - 4*a**2 - 4*a**n + 2*a**2 + 13*a**4 + 2*a**3 - 2*a**5.
-2*a**2*(a - 1)**2*(a + 1)
Suppose 0 = 8*f + 3*o - 6, 6 = -5*o - 24. Solve 0 + 6/5*d**2 + 0*d - 27/5*d**4 + 21/5*d**f = 0 for d.
-2/9, 0, 1
Suppose 5*t = 1 + 14. Find i, given that 11*i**t + 3*i**2 + 4 - 12*i**3 + i - 7*i**2 = 0.
-4, -1, 1
Let s(u) be the first derivative of u**4/12 - 8*u**3/3 + 32*u**2 - 6*u - 11. Let y(j) be the first derivative of s(j). Factor y(v).
(v - 8)**2
Let w = -3607 - -3609. Let 7/4*x**5 - 11/4*x + 7/2*x**w + 1/2 - 4*x**4 + x**3 = 0. Calculate x.
-1, 2/7, 1
Let o(v) be the second derivative of 0 + 0*v**2 + 11*v + 0*v**3 + 1/20*v**5 - 1/15*v**6 + 1/12*v**4. Let o(i) = 0. What is i?
-1/2, 0, 1
Suppose 658 - 658 = 2*c. Determine z so that c - 2/5*z**2 - 2/5*z = 0.
-1, 0
Let y(b) = -b**4 - b**3 - b**2 - 1. Let z(a) = -13*a**4 - 16*a**3 - 6*a**2 + 5*a - 14. Let f(h) = 44*y(h) - 4*z(h). Determine p so that f(p) = 0.
-3, -1, 1/2, 1
Let a(g) be the second derivative of -g**2 - 1/12*g**4 + 5*g + 0 + 0*g**3 - 1/12*g**5. Let o(z) be the first derivative of a(z). Find p such that o(p) = 0.
-2/5, 0
Solve -609*w**2 + 607*w**2 + 1524 - 3580 - 3562 - 212*w = 0.
-53
Determine g, given that -1/9*g**3 + 1/9*g**2 + 0 + 0*g = 0.
0, 1
Let b(s) be the first derivative of 4*s**3/27 + 143*s**2/9 + 142*s/9 + 250. Factor b(r).
2*(r + 71)*(2*r + 1)/9
Let n(u) be the third derivative of 0*u**3 + 0*u**4 + 1/30*u**6 - 1/105*u**7 + 0*u + 14*u**2 + 0 - 1/168*u**8 + 0*u**5. Factor n(o).
-2*o**3*(o - 1)*(o + 2)
Let q(b) be the second derivative of 0*b**4 + 0*b**2 + 0*b**5 + 1/120*b**6 - 2*b + 0 + 2/3*b**3. Let w(a) be the second derivative of q(a). Solve w(t) = 0.
0
Let s(m) be the second derivative of m**6/360 - 13*m**5/40 + 27*m**4/2 - 729*m**3/4 - 19683*m**2/8 - 122*m. Factor s(g).
(g - 27)**3*(g + 3)/12
Factor 9/4*t + 0 + 15/8*t**2 + 3/8*t**3.
3*t*(t + 2)*(t + 3)/8
Let m(z) be the third derivative of -z**10/1285200 + z**8/85680 - z**6/6120 + z**5/20 - 19*z**2. Let j(d) be the third derivative of m(d). Solve j(u) = 0.
-1, 1
Let a(v) = -v**2 + 6*v + 5. Let t be a(6). Suppose 3*g - 18 = -0*g + 4*h, t*g - 4*h - 22 = 0. Factor 2*q - 4 + 2*q**g + 2*q**2 + 0*q**2 - 2*q**3.
-2*(q - 2)*(q - 1)*(q + 1)
Suppose -q - r + 4 = 3, 6 = 3*q + 2*r. Factor -27*c**q - 14 - 14*c**4 + c**4 - 6 + 5*c**5 - 140*c**2 + 110*c**3 + 85*c.
5*(c - 4)*(c - 1)**4
Let k(a) be the second derivative of 0 - 3*a - 1/90*a**4 - 1/9*a**3 - 2/5*a**2. Factor k(m).
-2*(m + 2)*(m + 3)/15
Let p = -5112 - -5116. Let f be (-4)/(-6) - (-1)/3. Solve z**p - z**3 + 1/2*z**5 + 1/2*z + f - 2*z**2 = 0.
-2, -1, 1
Let l(i) = -i**3 + 32*i**2 - 17*i + 2. Let h(b) = -b**3 + 21*b**2 - 11*b + 1. Let c = 14 + -6. Let g(a) = c*h(a) - 5*l(a). Factor g(u).
-(u - 2)*(u - 1)*(3*u + 1)
Find r such that 9/4*r**2 + 0*r - 3*r**3 + 0 + 3/4*r**4 = 0.
0, 1, 3
Let w(h) be the second derivative of 1/7*h**4 - 1/35*h**5 + 1/21*h**3 + 1/147*h**7 - 3/7*h**2 - 1/35*h**6 + 21*h + 0. Suppose w(j) = 0. Calculate j.
-1, 1, 3
Let g(c) be the third derivative of -2*c**7/105 + 3*c**6/2 - 45*c**5 + 1125*c**4/2 + 2*c**2 - 15*c. Determine b so that g(b) = 0.
0, 15
Let x(l) be the first derivative of -l**5 - 25*l**4/2 - 85*l**3/3 - 20*l**2 - 82. Determine j so that x(j) = 0.
-8, -1, 0
Find u such that -12*u + 12*u**3 + 71 + 111*u**4 - 107*u**4 + 1 - 101*u**2 + 25*u**2 = 0.
-6, -1, 1, 3
Let o = 5 + -1. Let v = -1 + o. Factor -4*u**4 - 2*u**4 + 8*u**5 - 5*u**5 - v*u**3 + 6*u**2.
3*u**2*(u - 2)*(u - 1)*(u + 1)
Let w(n) = -447*n**4 - 573*n**3 - 128*n**2 - 5*n + 3. Let v(r) = -448*r**4 - 572*r**3 - 128*r**2 - 6*r + 2. Let t(b) = -6*v(b) + 4*w(b). Factor t(z).
4*z*(z + 1)*(15*z + 2)**2
Factor -2/7*z**2 + 18/7 + 16/7*z.
-2*(z - 9)*(z + 1)/7
Let x be (-3)/(-15) - 27/(-315). Find z, given that 2/7*z - 2/7*z**3 - 2/7*z**2 + x = 0.
-1, 1
Let m(h) be the first derivative of 2*h**5/5 - 5*h**4/6 + h**3/3 + 27*h - 21. Let v(n) be the first derivative of m(n). Suppose v(w) = 0. Wha