 + 3)
Let c(u) be the first derivative of 7/5*u**3 - 3/10*u**2 + 27/25*u**5 - 9/4*u**4 + 0*u - 3. Factor c(r).
3*r*(r - 1)*(3*r - 1)**2/5
Let p = -10445 - -10445. What is g in p - 2/5*g + 2/5*g**2 = 0?
0, 1
Suppose 5*n = 15, -5*q + 7*n - 2*n + 185 = 0. Factor q*i - 79*i - 1 - i**2 + 41*i.
-(i - 1)**2
Let n(l) = -9*l**2 + 55*l - 39. Let u(q) = 5*q**2 - 30*q + 20. Let t(f) = -4*n(f) - 7*u(f). Determine i, given that t(i) = 0.
2, 8
Let z(c) be the first derivative of c**6/2 - 58*c**5/5 + 259*c**4/4 + 220*c**3/3 - 50*c**2 + 57. Solve z(m) = 0 for m.
-1, 0, 1/3, 10
Let z(a) be the first derivative of 0*a - 9 + 1/4*a**2 + 1/12*a**3 - 1/16*a**4. Solve z(b) = 0.
-1, 0, 2
Let w(d) be the third derivative of -d**7/420 - d**6/240 + 7*d**5/60 + d**4/2 - 113*d**2. Factor w(u).
-u*(u - 4)*(u + 2)*(u + 3)/2
Let n = 46379/17656 + -4/2207. Suppose -3/8*u**4 + 0 + n*u**2 - 3/4*u**3 - 3/2*u = 0. Calculate u.
-4, 0, 1
Let x(w) be the third derivative of -w**5/150 - 11*w**4/60 + 4*w**3/5 + 166*w**2. What is s in x(s) = 0?
-12, 1
Let n be 40/(-36)*87*(-12)/(-10). Let v = -340/3 - n. Suppose 4/3*y**3 - v*y**2 + 8/3 - 4/3*y = 0. What is y?
-1, 1, 2
Let i(t) be the first derivative of t**5/200 + t**4/24 + t**3/15 - 27*t - 42. Let z(d) be the first derivative of i(d). Factor z(s).
s*(s + 1)*(s + 4)/10
Let v(b) be the first derivative of 20*b**3/3 - 464*b**2 + 368*b + 459. What is o in v(o) = 0?
2/5, 46
Let b(i) be the third derivative of i**7/350 + 3*i**6/200 - i**5/100 - 3*i**4/40 + 21*i**2. Factor b(m).
3*m*(m - 1)*(m + 1)*(m + 3)/5
Let t be (172/48 - (-56)/(-24))/((-18)/(-24)). Factor -1/3*b**3 - 4/3*b**2 - t*b - 2/3.
-(b + 1)**2*(b + 2)/3
Factor 0 - 1/4*h**5 + 0*h - 1/4*h**2 - 3/4*h**4 - 3/4*h**3.
-h**2*(h + 1)**3/4
Let w(y) = -164*y**3 + 2*y**2 - 1. Let r be w(1). Let x = r - -165. Let 1/3*p - 2/3 + p**x = 0. What is p?
-1, 2/3
Let s(z) be the second derivative of -3/5*z**5 + 0*z**4 + 0*z**2 + 0 + 0*z**3 + 25*z + 1/2*z**7 - 6/5*z**6. Let s(r) = 0. What is r?
-2/7, 0, 2
Let m(w) = w**3 - 4*w**2 + 66*w - 262. Let c be m(4). Factor -7/5*r + 7/5*r**3 - 2/5*r**c + 2/5.
(r - 1)*(r + 1)*(7*r - 2)/5
Let b(w) = -9*w**3 + 15*w**2 + 33*w + 19. Let r(j) = -32*j**3 + 54*j**2 + 116*j + 66. Let h(p) = -18*b(p) + 5*r(p). Let h(u) = 0. Calculate u.
-2, -1, 3
Let g(u) be the second derivative of 3*u**7/56 - u**6/5 + 9*u**5/40 - u**3/8 - 2*u + 45. Factor g(h).
3*h*(h - 1)**3*(3*h + 1)/4
What is p in -15*p - 29/2*p**3 - 4 - 1/2*p**5 - 43/2*p**2 - 9/2*p**4 = 0?
-4, -2, -1
Let a(p) = -13*p**2 - 515*p - 10. Let g(v) = 84*v**2 + 3348*v + 64. Let w(y) = 32*a(y) + 5*g(y). Factor w(r).
4*r*(r + 65)
Let x(z) = -14*z - 712. Let r be x(-51). Factor -1/8*g**r - 1/8 + 1/4*g.
-(g - 1)**2/8
Let w = 359/3 - 119. Let t(n) be the third derivative of n**2 + 0*n + w*n**3 - 7/6*n**4 + 0 + 31/60*n**5 + 21/40*n**6. Solve t(m) = 0.
-1, 2/9, 2/7
Let x = 5 - 3. Let r = -25 + 73. What is g in r*g + 0*g**2 + 45*g - 9*g**3 - 90*g + 6*g**x = 0?
-1/3, 0, 1
Let k(z) = z - 10. Let h be k(13). Suppose -h*y - i = 2*y - 11, -y = -i - 1. Suppose 2/3*o**y - 8/3 - 2*o = 0. Calculate o.
-1, 4
Let x(u) be the second derivative of -1/200*u**5 - 1/40*u**4 + 13*u - 1/30*u**3 + 0*u**2 + 0. Factor x(a).
-a*(a + 1)*(a + 2)/10
Let n(o) be the second derivative of 3*o**5/20 + 3*o**4 - 27*o**3/2 - 729*o**2 - 154*o. Solve n(x) = 0.
-9, 6
What is g in -2/9 + 4/9*g - 2/9*g**2 = 0?
1
Let t(j) be the second derivative of j**5/50 - j**4/6 - 12*j**3/5 + 871*j. Find h such that t(h) = 0.
-4, 0, 9
Suppose -2*w - 2*b = 10, 36*w - 34*w - 4*b = 20. Let u(s) be the first derivative of w*s**2 - 6 + 0*s**4 + 0*s + 1/33*s**6 + 0*s**3 + 4/55*s**5. Factor u(r).
2*r**4*(r + 2)/11
Let l(t) be the first derivative of -t**3/12 - 33*t**2 - 4356*t - 200. Find w, given that l(w) = 0.
-132
Let a(n) = -n**3 - 74*n**2 + 227*n - 305. Let x be a(-77). Find o such that 0 + 3/7*o**x + 15/7*o - 18/7*o**2 = 0.
0, 1, 5
Let o(y) be the first derivative of -70*y**3/3 - 325*y**2/2 - 45*y - 422. Determine k, given that o(k) = 0.
-9/2, -1/7
Suppose -3*f - 1 = 5*a - 0, -f + a = -13. Suppose 4*o = f + 24. Determine b so that 4*b**2 + b**3 + 28*b - 20*b**3 + o - 9*b**4 - 3*b**4 - 9*b**3 = 0.
-2, -1, -1/3, 1
Factor -24 + 3/2*h**3 + 21/2*h**2 + 12*h.
3*(h - 1)*(h + 4)**2/2
Let k(v) be the first derivative of v**6/135 - v**5/15 + 13*v**4/54 - 4*v**3/9 + 4*v**2/9 - 14*v - 24. Let d(w) be the first derivative of k(w). Factor d(r).
2*(r - 2)**2*(r - 1)**2/9
Solve 0 + 130*s + 24*s - 235*s + 81 + 12*s**3 = 0 for s.
-3, 3/2
Suppose -4*s + 0*s + 4 = 0. Let m be (2/s)/(1/2). Factor 7*d**m + 8*d - 14*d**3 + 8*d**2 - 3*d**4 + 0*d.
2*d*(d - 2)**2*(2*d + 1)
Suppose 0 = -5*q - 0*q + 20. Suppose -c + 0*c + 4 = 0. Factor 67*y**3 + 2*y**q - 3*y**2 - 61*y**3 - 5*y**c.
-3*y**2*(y - 1)**2
Let v be 966/294 + (-2)/7 + 0. Let g be -3 - (11*v/(-6) + 2). Solve 0*n + 0*n**3 + 0*n**4 - g*n**5 + 0 + 0*n**2 = 0.
0
Let u(p) be the third derivative of 1/12*p**4 - 1/150*p**5 + 0 - 17*p**2 + 2/5*p**3 + 2*p. Find s, given that u(s) = 0.
-1, 6
Let l(m) = -m**3 - 6*m**2 - m - 4. Suppose -2*i - 20 - 4 = 4*t, -2*i = -t - 6. Let k be l(t). Suppose r**4 + 5*r**2 + k*r**2 - 4*r**2 - 4*r**4 = 0. What is r?
-1, 0, 1
Suppose 396/5*m + 3/5*m**2 + 13068/5 = 0. What is m?
-66
Factor 26/15*u**2 - 14/3*u - 2/15*u**3 - 98/15.
-2*(u - 7)**2*(u + 1)/15
Find n such that -10597 + 7*n + 10609 + n - 4*n**2 = 0.
-1, 3
Suppose -5*s = -3*s - 8. Suppose -4*t = -4 - s. Factor 3*g - 3*g**3 + 18*g**3 - g**2 + 3*g - 20*g**t.
3*g*(g - 1)*(5*g - 2)
Let k = 3792 + -11375/3. Factor y**3 + 0 - k*y**4 + 1/3*y - y**2.
-y*(y - 1)**3/3
Let r(m) = m**2 - m - 1. Let x(p) = p**3 + 3*p**2 + 2*p - 1. Let h be x(-2). Let n(b) = 3*b**2 + 2*b - 3. Let q(o) = h*n(o) - 2*r(o). Factor q(k).
-5*(k - 1)*(k + 1)
Let y(t) be the second derivative of -25*t - 5/12*t**4 + 5/2*t**3 + 0 - 5*t**2. Find m, given that y(m) = 0.
1, 2
Let x be 1*(1 - 38) + 4. Let r be 2 - (-60)/x - 14/(-44). Factor 0 + 0*f + 0*f**2 - r*f**3.
-f**3/2
Factor 15129/7 - 246/7*x + 1/7*x**2.
(x - 123)**2/7
Let y = -651665/33 - -59515/3. Let y + 2*r**4 + 38/11*r**3 - 400/11*r + 2/11*r**5 - 230/11*r**2 = 0. Calculate r.
-5, 2
Let g(c) be the second derivative of c**7/504 + c**6/72 + c**5/24 - 2*c**4/3 + 9*c. Let u(h) be the third derivative of g(h). Suppose u(x) = 0. What is x?
-1
Let c(y) be the third derivative of -2*y**6/5 + 58*y**5/5 - 113*y**4/8 + 7*y**3 + 403*y**2. Let c(h) = 0. Calculate h.
1/4, 14
Let y(x) be the first derivative of -9 - 5/3*x**3 - 5*x - 5*x**2. Factor y(b).
-5*(b + 1)**2
Let q = -805/2 - -403. Let s(a) be the second derivative of 6*a - q*a**4 + 0 + 1/2*a**3 + 3/20*a**5 + 0*a**2. Factor s(k).
3*k*(k - 1)**2
Suppose 15*s + 8 = -c + 20*s, -5*c - s = -12. Let q(f) be the second derivative of -1/20*f**4 + 0*f**c + 0 + 0*f**3 + 12*f. Let q(n) = 0. What is n?
0
Let j(m) be the first derivative of 4*m**5/5 - 4*m**3/3 - 60. Suppose j(t) = 0. Calculate t.
-1, 0, 1
Let n(g) be the first derivative of 1/120*g**6 - 3 + 1/16*g**5 + 7/24*g**3 + 1/4*g**2 + 3/16*g**4 + 4*g. Let z(h) be the first derivative of n(h). Factor z(j).
(j + 1)**3*(j + 2)/4
Factor -8 + 12*u + 2*u**2 + 2*u**2 + 19 - 3*u**2.
(u + 1)*(u + 11)
Let b(n) be the second derivative of n**7/21 - 9*n**6/10 + 23*n**5/4 - 185*n**4/12 + 41*n**3/2 - 14*n**2 + 2*n - 173. What is v in b(v) = 0?
1/2, 1, 4, 7
Let i = 5/14 - 1/14. Suppose 52*g - 738*g = 0. Factor g + i*x**3 + 0*x - 2/7*x**2.
2*x**2*(x - 1)/7
Let t(b) be the first derivative of -b**5/20 + 2*b**4/3 - 7*b**3/2 + 9*b**2 + 7*b + 32. Let r(p) be the first derivative of t(p). Factor r(y).
-(y - 3)**2*(y - 2)
Suppose 102 = 8*r - 2*r. Suppose -i**2 + 24*i - 7*i**2 - 35*i + 2*i**3 + r*i = 0. Calculate i.
0, 1, 3
Let t(m) be the first derivative of -m**3/18 + 14*m**2/3 - 394. Factor t(x).
-x*(x - 56)/6
Let d(h) = 7*h**4 + 3*h**3 - h**2 - 3*h. Let x = -3 - 4. Let s(r) = -15*r**4 - 7*r**3 + r**2 + 7*r. Let j(y) = x*d(y) - 3*s(y). Factor j(i).
-4*i**2*(i - 1)*(i + 1)
Let z be 8/2 + 11*(-26)/143. Find d, given that 4 + 2/3*d**z + 10/3*d = 0.
-3, -2
Let g = 2 - -3. Let v(t) = -t + 7. Let y be v(g). Factor -4*q**4 + 293*q**y - 4*q**5 - 293*q**2.
-4*q**4*(q + 1)
Let n(x) = -2*x**2 + 70*x - 12 - 14 - 12. Let w(v) = v**2 - 23*v + 13. Let t(d) = 3*n(d) + 10*w(d). What is s in t(s) 