 k, given that 15/2*k - 2*k**2 + 2 = 0.
-1/4, 4
Let g = 50 - 39. Let y be -2 - ((-24)/g - 10/(-55)). Factor y*o + 0 + 1/6*o**2 + 1/6*o**5 - 1/6*o**4 - 1/6*o**3.
o**2*(o - 1)**2*(o + 1)/6
Let z = -73/12 - -19/3. Suppose 1132*m = 1141*m - 18. Factor 0 - z*h - 1/4*h**m.
-h*(h + 1)/4
Suppose t - 10 = -6*y + 3*y, -14 = -4*y - 2*t. Let m(u) be the second derivative of 0 - 1/4*u**4 - 8*u + 2*u**y - 6*u**2. Suppose m(a) = 0. What is a?
2
Let o = -105/53 + 631/265. Solve 2/5*t**2 + 6/5*t**3 - 4/5*t**4 + o - 6/5*t = 0.
-1, 1/2, 1
Let i(p) be the first derivative of p**7/630 - p**5/45 - p**2/2 - 53. Let l(y) be the second derivative of i(y). Factor l(v).
v**2*(v - 2)*(v + 2)/3
Let k(m) be the first derivative of m**5/35 + 3*m**4/28 - 16*m**3/21 + 6*m**2/7 - 121. Let k(j) = 0. Calculate j.
-6, 0, 1, 2
Suppose 12*a - 33*a = 0. Let y(c) be the first derivative of a*c - 1/8*c**3 + 7 - 1/40*c**5 + 0*c**2 + 1/8*c**4. Let y(w) = 0. Calculate w.
0, 1, 3
Let x(b) be the first derivative of b**3/2 - 93*b**2/2 + 2883*b/2 + 57. Factor x(i).
3*(i - 31)**2/2
Let l(y) be the second derivative of -y**5/60 + 2*y**4/9 - 7*y**3/18 + y - 12. Factor l(r).
-r*(r - 7)*(r - 1)/3
Suppose 4*x + 20 = 0, x = -43*p + 38*p + 10. Factor 2/3*k**p - 3 + 4*k + 11/3*k**2.
(k + 3)**2*(2*k - 1)/3
Let s(f) = f**5 - f**4 + f**2 - 1. Let l(v) = 4*v**5 - 20*v**4 + 46*v**3 - 4*v**2 - 72*v - 2. Let w(i) = -l(i) + 2*s(i). Suppose w(o) = 0. Calculate o.
-1, 0, 3, 4
Factor -625*m - 1/3*m**3 - 25*m**2 - 15625/3.
-(m + 25)**3/3
Let d = 47/211 + 281/633. What is u in 0*u + 8/3*u**2 + 8/3*u**3 + d*u**4 + 0 = 0?
-2, 0
Let x(b) be the third derivative of b**10/30240 - b**8/3360 + b**6/720 - b**4/12 - 5*b**2. Let q(s) be the second derivative of x(s). What is j in q(j) = 0?
-1, 0, 1
Suppose 5*w + 5*h - 5 = 0, 0*h + 2 = -2*w + 2*h. Let j(s) be the second derivative of w*s**2 - 1/9*s**3 + 1/36*s**4 + 0 + s. Factor j(q).
q*(q - 2)/3
Let g(o) be the second derivative of -o**7/84 + o**6/12 - o**5/5 + o**4/6 - 2*o - 11. Factor g(d).
-d**2*(d - 2)**2*(d - 1)/2
Let r = 444874/11 - 40414. Let 2*u**4 - 256/11 - 16/11*u**2 + 2/11*u**5 - r*u + 68/11*u**3 = 0. Calculate u.
-4, -1, 2
Let c be ((-26)/(-40) + 3/5)/((-10)/(-24)). Find b such that -b**2 + 0*b + 1/5*b**c + 0 = 0.
0, 5
Let c(x) = -x**5 - 2*x**3. Let w = 11 - 9. Let d(k) = 7*k**3 - k**5 - 4*k**3 - w*k**5 + 4*k**5. Let f(u) = 4*c(u) + 3*d(u). Determine v, given that f(v) = 0.
-1, 0, 1
Let m(x) be the third derivative of 0*x**3 + 0 + 1/60*x**6 + 0*x + x**2 - 1/5*x**5 + 2/3*x**4. Determine v so that m(v) = 0.
0, 2, 4
Let f(s) be the third derivative of s**7/70 - s**6/20 - 19*s**5/20 + 5*s**4/2 + 428*s**2. Factor f(h).
3*h*(h - 5)*(h - 1)*(h + 4)
Let h(c) be the second derivative of -c**6/45 + c**5/15 + 2*c**4/9 - 2*c**3/9 - c**2 + 51*c - 1. Solve h(f) = 0.
-1, 1, 3
Let p(d) = -7*d**2 + 18*d + 25. Let q be p(-1). Suppose 9/2*w**5 - 7/2*w**3 + q + 11/2*w**4 - 11/2*w**2 - w = 0. What is w?
-1, -2/9, 0, 1
Find o such that 7/5*o + 0 + 1/10*o**2 = 0.
-14, 0
Factor 29*d - 8*d**2 - 28 + 1/4*d**3.
(d - 28)*(d - 2)**2/4
Let w = 130 - 60. Find p, given that w*p**3 + p**2 - 4*p**4 - 68*p**3 + 5*p**4 = 0.
-1, 0
Let p(z) be the first derivative of -z**4/14 - 16*z**3/7 + 81*z**2/7 + 744. Factor p(t).
-2*t*(t - 3)*(t + 27)/7
Let t be ((-48)/140)/(-7 + 402/60). Factor -1/7*y**4 - 22/7*y**2 - t*y**3 - 24/7*y - 9/7.
-(y + 1)**2*(y + 3)**2/7
Let l be 3/(-9) - (-5060)/15270. Let y = 2029/3563 - l. Determine c, given that 10/7*c**2 + y*c + 0 + 2/7*c**4 + 8/7*c**3 = 0.
-2, -1, 0
Suppose -7*l = -11*l + 28. Let h = 10 - l. Suppose h*m - 2*m**3 - 3*m**3 + 12*m**2 + 0*m**2 - 7*m = 0. Calculate m.
0, 2/5, 2
Suppose -5*p = 2*t - 10, 5*p - 3*t = t + 10. Let -40*s + 40*s - 2*s**3 - 2*s**p = 0. What is s?
-1, 0
Suppose 2/5*z**3 + 88/5*z + 56/5 + 34/5*z**2 = 0. What is z?
-14, -2, -1
Let v(s) be the first derivative of -1/3*s**3 + 0*s + 3/10*s**4 - 6 - 1/10*s**2. Factor v(t).
t*(t - 1)*(6*t + 1)/5
Let n(m) be the second derivative of -m**7/630 - m**6/45 - 2*m**5/15 + m**4/4 + 6*m. Let c(p) be the third derivative of n(p). Factor c(q).
-4*(q + 2)**2
Let n be 37/10 + -3 + (-12)/60. Let a(p) be the first derivative of 0*p**3 - 1/16*p**4 + 3/8*p**2 - 5 + n*p. Factor a(c).
-(c - 2)*(c + 1)**2/4
Let u(h) = -2*h**3 - 3*h**2 + h - 6. Let m be u(-5). Let f be -2 + (-1 - m/(-52)). Factor -2/13*y**3 + 4/13*y**2 - f*y + 0.
-2*y*(y - 1)**2/13
Suppose -3*n + 3*z + 15 = -2*n, n = -3*z + 3. Suppose -2*q + 44 = n*q. Factor -q*u + 2 - 5/2*u**2.
-(u + 2)*(5*u - 2)/2
Let w(y) = 16*y**2 - 4*y + 4. Let z be w(2). Let k be (-7)/(-4) - (-15)/z. Factor -8 + 0*p**k + 3*p**2 + 12*p + 20.
3*(p + 2)**2
Let z be ((-4)/3)/(44/(-33)). Suppose -4*m + z = -15. Determine w, given that -3/2*w**5 + 3/2*w**m + 3/2*w**3 - 3/2*w**2 + 0*w + 0 = 0.
-1, 0, 1
Let m be ((-285)/(-114))/(5/36)*1/4. Let -27/2*j + 3/2*j**3 + m*j**2 + 15/2 = 0. Calculate j.
-5, 1
Let z(o) = 13720 - o + o**2 - 13720 - o**3. Let u(k) = -10*k**3 - 5*k. Let b(w) = -u(w) + 15*z(w). Factor b(q).
-5*q*(q - 2)*(q - 1)
Let r(m) = -2*m - m - 28*m**2 - 2*m + 3*m**2 + 65*m**3. Let a(b) = 33*b**3 - 12*b**2 - 2*b. Let n(l) = -5*a(l) + 2*r(l). Factor n(x).
-5*x**2*(7*x - 2)
Suppose 0*h - 4*h - 4*s - 184 = 0, -s = -3*h - 150. Let a = 149/3 + h. Factor a*j + 1/3*j**2 + 0.
j*(j + 2)/3
Suppose 1/3*r**4 + 0 - 50/3*r + 8/3*r**3 + 5/3*r**2 = 0. Calculate r.
-5, 0, 2
Find j such that -4*j - 96/11 + 2/11*j**2 = 0.
-2, 24
Factor -550*t**3 - 60*t + 278*t**3 - 5*t**2 + 277*t**3.
5*t*(t - 4)*(t + 3)
Solve -2/9*y**4 + 8/9*y**3 + 0 + 4/9*y - 10/9*y**2 = 0 for y.
0, 1, 2
Let i = 89 - 56. Let p = 35 - i. Solve 9*y + 15*y**p - 17*y**2 - 8 - y = 0 for y.
2
Suppose -10*a + 18 = -7*a. Suppose d + 1 = -3*f, 3*d + f - a*f - 11 = 0. Let 2*h - 4*h**3 + 0*h**2 + 2*h + 3*h**d + h**2 - 4*h**4 = 0. Calculate h.
-1, 0, 1
Let w = -61274291/1563 - -39203. Let h = 39071/3126 - w. Let 0 + 45/2*p**3 + 2*p - 12*p**2 - h*p**4 = 0. What is p?
0, 2/5, 1
Determine f, given that 133*f**3 + 3/2*f**5 + 371/2*f + 25*f**4 + 49 + 246*f**2 = 0.
-7, -1, -2/3
Let t(f) be the second derivative of f**4/15 - 52*f**3/15 - 54*f**2/5 - 2*f + 82. Let t(b) = 0. Calculate b.
-1, 27
Let p = -212 + 214. Let m be 107/22 + -5 - (-1)/p. Factor -2/11*y**4 - 2/11*y**5 + 10/11*y**2 + 6/11*y**3 + m*y + 0.
-2*y*(y - 2)*(y + 1)**3/11
Let a(w) be the first derivative of -w**6/30 - 3*w**5/25 + 11*w**4/10 - 38*w**3/15 + 27*w**2/10 - 7*w/5 + 164. Factor a(z).
-(z - 1)**4*(z + 7)/5
Suppose -19 = 3*z + 2*y - 38, -z - 17 = -4*y. Find x, given that 0 + 1/3*x**z + 1/3*x**4 + 0*x**2 + 0*x = 0.
-1, 0
Let -4*r**2 - 200*r + 161 - 1067 - 487 - 1107 = 0. Calculate r.
-25
Let d(p) = -2*p**2 - 5*p + 4. Let b be d(-4). Let w(f) = f + 11. Let v be w(b). Find z, given that 4*z**v + 6*z - 24*z**2 - 32 + 8*z + 10*z + 24*z = 0.
2
Let t(j) = 2*j**4 + 12*j**3 + 14*j**2 + 4*j. Let h(x) = -3*x + 11. Let s be h(5). Let f(d) = d**4 + d**3. Let z(o) = s*f(o) - t(o). Find w such that z(w) = 0.
-1, -2/3, 0
Let i(u) be the first derivative of 5*u**4/12 - 25*u**3/6 + 15*u**2 - 24*u - 16. Let q(v) be the first derivative of i(v). Factor q(y).
5*(y - 3)*(y - 2)
Factor 27/5*v**2 + 2*v + 6/5*v**4 + 23/5*v**3 + 0.
v*(v + 1)*(v + 2)*(6*v + 5)/5
Solve 2/3*m + 0*m**2 + 0 - 4/3*m**3 + 2/3*m**5 + 0*m**4 = 0.
-1, 0, 1
Let b be (-1 - 5/(-2))*(-92)/(-3). Factor -13*c - 7*c - b*c**3 + 16*c**2 + 50*c**3.
4*c*(c - 1)*(c + 5)
Let x be 462/3465 - (-16)/30. Suppose 2*n**2 + 4/3*n + x*n**3 + 0 = 0. What is n?
-2, -1, 0
Let h(x) be the first derivative of 15/28*x**4 + 0*x - 4/7*x**3 + 14 - 3/35*x**5 + 0*x**2. Suppose h(r) = 0. Calculate r.
0, 1, 4
Let a(s) = -s**2 - 10*s + 16. Let n be a(-12). Let y(v) = -2*v - 7. Let z be y(n). Factor -p + 3*p**2 + 0*p**2 - 4*p**2 + 7*p - z.
-(p - 3)**2
Let r(n) = -24*n**2 - 24*n + 8. Let z(q) = 49*q**2 + 47*q - 16. Let m(y) = 2*y + 2. Let u be m(-3). Let l(j) = u*z(j) - 7*r(j). Let l(t) = 0. Calculate t.
-1, 2/7
Factor -5/2*s - 3*s**2 + 0 - 1/2*s**3.
-s*(s + 1)*(s + 5)/2
Let v = 165/292 - 23/73. Suppose 0*u + 3/2*u**5 - 3/2*u**3 + 0 + v*u**4 - 1/4*u**2 = 0. Calculate u.
-1, -1/6, 0, 1
Let h(t) be the first derivative of t**4/2 + 6*t**3 + 15*t**2 + 14*t - 88. Factor h(b).
2*(b + 1)**2*(b + 7)
Let v = 12 - 9. What is z in 4*z - 23 + 38 - 8*z**v - 14 + 4*z**5 