0)/9*(-5)/(-10)*-3. Find k, given that 0 + 7/4*k**4 - 15/4*k**3 - 1/4*k**a + 9/4*k**2 + 0*k = 0.
0, 1, 3
Let o = 15/1787 + 23171/7148. Factor -3*z + 1 + 21/4*z**3 - o*z**2.
(z - 1)*(3*z + 2)*(7*z - 2)/4
Let j(o) be the third derivative of o**8/1008 - o**7/21 - o**6/360 + o**5/6 + 35*o**2 - 2*o. Suppose j(t) = 0. What is t?
-1, 0, 1, 30
Let t(z) be the third derivative of z**5/12 + 15*z**4/2 + 270*z**3 + 104*z**2 - 1. Find p, given that t(p) = 0.
-18
Let m(u) be the first derivative of -u**5/5 - 11*u**4/2 - 52*u**3 - 189*u**2 - 243*u + 194. Let m(n) = 0. Calculate n.
-9, -3, -1
Determine u so that 0 + 1/2*u**4 - 1/2*u**2 + u**3 - 1/4*u**5 - 3/4*u = 0.
-1, 0, 1, 3
Let w(j) = -22*j**2 - 149*j - 100. Let t be w(-6). Solve -6/5 + 1/5*x + 1/5*x**t = 0.
-3, 2
Let y(b) be the second derivative of -b**8/1344 + b**7/120 - 11*b**6/480 + b**5/48 - 27*b**2/2 + 3*b - 7. Let n(l) be the first derivative of y(l). Factor n(x).
-x**2*(x - 5)*(x - 1)**2/4
Suppose -3/5*b**3 - 129/5*b + 69/5*b**2 + 63/5 = 0. What is b?
1, 21
Let c be (2 - (-81)/(-39)) + 1. Let s = 86/65 - c. Suppose -8/5*f**2 + 0 - 2/5*f - 12/5*f**3 - 8/5*f**4 - s*f**5 = 0. Calculate f.
-1, 0
Let w(b) be the first derivative of -b**4/12 + 10*b**3/9 + b**2/6 - 10*b/3 - 4. Factor w(q).
-(q - 10)*(q - 1)*(q + 1)/3
Let q = -454 + 34. Let i be 48/q*(-5)/2. Let i - 2/7*r**3 - 6/7*r + 6/7*r**2 = 0. What is r?
1
Let r(s) = 12*s**4 - 31*s**3 + 49*s**2 - 53*s + 23. Let f(p) = 10*p**4 - 28*p**3 + 48*p**2 - 52*p + 22. Let c(x) = 5*f(x) - 4*r(x). Factor c(k).
2*(k - 3)**2*(k - 1)**2
Let i(k) = -2*k - 1. Let b(y) = -11*y + 1. Let m(d) = -b(d) + 2*i(d). Let x be m(1). Find z such that -6/19*z**3 + 6/19*z + 2/19*z**x + 2/19*z**2 - 4/19 = 0.
-1, 1, 2
Let f(y) be the second derivative of -9*y**2 - 8*y + 0 + 1/10*y**5 + y**3 + 5/6*y**4. Determine x so that f(x) = 0.
-3, 1
Let m(w) = -w**4 + 8*w**3 + 9*w**2 - 8*w - 5. Let u(p) = -3*p**4 + 16*p**3 + 19*p**2 - 16*p - 9. Let s(r) = -14*m(r) + 6*u(r). Let s(j) = 0. Calculate j.
-2, -1, 1
Let i = 130 + -77. Let o = 56 - i. Let -7/5*m**o + 3/5*m**4 - 2/5 + 3/5*m**2 + 3/5*m = 0. Calculate m.
-2/3, 1
Let t(w) be the first derivative of -2*w**3/3 + 9*w**2/2 - 2*w + 58. Let b be t(4). Factor 1/3*r - 1/3*r**3 + 2/3*r**b - 2/3.
-(r - 2)*(r - 1)*(r + 1)/3
Let j(g) = g**3 - 7*g**2 + g + 1. Let q be j(7). Suppose 7 = 2*m + t, -2*m - 2*t = -0*t - q. Factor 1 + 5 + v + m*v + 5*v + 3*v**2.
3*(v + 1)*(v + 2)
Suppose 15 = -0*a + 5*a. Factor 0*w + 60*w**a - 4*w - 52*w**3 - 4*w**5.
-4*w*(w - 1)**2*(w + 1)**2
Let n(p) be the second derivative of 3*p**7/280 - p**6/30 + p**5/40 - p**3/3 + p. Let x(w) be the second derivative of n(w). Determine s so that x(s) = 0.
0, 1/3, 1
Suppose 25 = -41*y + 25. Let d(f) be the second derivative of y*f**3 + 1/15*f**6 - 1/3*f**4 + 4*f + 0*f**5 + f**2 + 0. Determine s, given that d(s) = 0.
-1, 1
Factor 1/3*y**3 - 4/3*y**2 + 10/3 - 7/3*y.
(y - 5)*(y - 1)*(y + 2)/3
Let y be 108/30*10/6. Let j(g) = -9*g**2. Let b(u) = -3*u - 2*u**2 + u**2 + 3*u. Let s(q) = y*b(q) - j(q). Suppose s(o) = 0. Calculate o.
0
Determine r, given that 13964*r**4 - 254*r**2 + 514*r**3 - 14158*r**4 + 18*r**5 - 63*r - 21*r = 0.
-2/9, 0, 1, 3, 7
Factor -5*d**3 + 6*d**4 + 12*d + 3*d**5 - 2*d**5 + 22*d**2 - 34*d**2 + 2*d**5 - 4*d**3.
3*d*(d - 1)**2*(d + 2)**2
Let f(i) be the first derivative of 7*i**2/2 - 40*i + 21. Let v be f(6). Factor -1/2*x**2 + 0*x + v.
-(x - 2)*(x + 2)/2
Let s = 29 + -24. Let 3*q**s + q**3 - 2*q**5 + 0 + 0 + 2*q**4 = 0. Calculate q.
-1, 0
Let q(n) = -n**3 + 2*n**2 + n + 6. Let z be q(3). Let 4*i**4 + 8*i**2 - 5*i**2 + i**2 + z*i**2 + 8*i**3 = 0. Calculate i.
-1, 0
Factor -7/5*p**2 + 1/5*p**3 + 0 + 0*p.
p**2*(p - 7)/5
Determine v, given that -2/19*v**3 + 22/19*v**2 - 40/19*v - 64/19 = 0.
-1, 4, 8
Let 62*p - 3*p**2 - 192*p - 5*p = 0. What is p?
-45, 0
Let s(o) be the second derivative of 5*o - 10/21*o**3 + 0 - 1/7*o**4 - 4/7*o**2 + 1/35*o**5 + 2/105*o**6. Factor s(y).
4*(y - 2)*(y + 1)**3/7
Let l be (4/(-3))/(62/(-186)). Find y such that -3*y**l + 1/4*y**5 + 57/4*y**3 - 67/2*y**2 + 39*y - 18 = 0.
2, 3
Let m(s) be the second derivative of s**7/315 - 2*s**6/225 - 4*s**5/75 - 107*s. Factor m(d).
2*d**3*(d - 4)*(d + 2)/15
Find h such that -242/5 - 2/5*h**2 - 44/5*h = 0.
-11
Let p = 116 - 73. Let n = 44 - p. What is z in z**4 + n + 7/2*z**5 - 2*z**2 + 7/2*z - 7*z**3 = 0?
-1, -2/7, 1
Let x = 26662/20001 + 2/6667. Find w, given that -8 - x*w**2 - 20/3*w = 0.
-3, -2
Suppose 2*m + 6 = 10. Factor -6*a**3 + 36 - 31 + 20*a - 55*a**m + 36*a**3.
5*(a - 1)**2*(6*a + 1)
Let h(u) be the third derivative of u**8/1680 + u**7/525 - u**6/75 - 3*u**5/50 - 3*u**4/40 + 182*u**2. Factor h(n).
n*(n - 3)*(n + 1)**2*(n + 3)/5
Let y(j) be the first derivative of 0*j**2 + 0*j**3 - 1/4*j**4 + 2/5*j**5 + 0*j - 1/6*j**6 + 2. Find n, given that y(n) = 0.
0, 1
Suppose -7 = -27*y + 20. Let k(l) be the first derivative of y + 1/2*l**4 + 0*l + l**2 - 4/3*l**3. Suppose k(c) = 0. Calculate c.
0, 1
Suppose 5*z = 13*z. Solve 2*f + 3*f + 8*f**2 - 4*f**3 + z*f - f - 8 = 0 for f.
-1, 1, 2
Let g(k) be the first derivative of k**5 + 5*k**4/2 - 25*k**3 + 779. Factor g(y).
5*y**2*(y - 3)*(y + 5)
Let p be -6 - (-7 - 234/42)/2. Solve p*l**2 + 4/7*l + 2/7 = 0.
-1
Suppose 0*n + 4*n - 12 = 0. What is r in -n*r - 12 - 9*r + 12*r**2 - 3*r**2 = 0?
-2/3, 2
Let t(l) be the third derivative of -l**8/1512 - 2*l**7/945 + 4*l**6/135 + l**5/135 - 5*l**4/36 + 459*l**2. What is o in t(o) = 0?
-5, -1, 0, 1, 3
Let r(j) be the first derivative of -j**5/5 + 2*j**4/3 + 2*j**3/3 - 4*j**2 + 12*j + 15. Let u(w) be the first derivative of r(w). Factor u(h).
-4*(h - 2)*(h - 1)*(h + 1)
Let m(g) be the third derivative of -g**5/12 + 155*g**4/2 - 28830*g**3 - 3*g**2 - 21*g. Suppose m(u) = 0. Calculate u.
186
Suppose 112*w**3 - 8*w**4 - 54*w**3 - 47*w**3 - 37*w**3 = 0. What is w?
-13/4, 0
Suppose -104 = -38*r + 10. Factor 0*n + 1/2*n**r + 0 + 0*n**2.
n**3/2
Let d = 2065/3 + -687. Let g(a) be the third derivative of 1/120*a**5 - 1/6*a**4 + 0 + d*a**3 + 0*a + 11*a**2. Determine z, given that g(z) = 0.
4
Let a(m) be the first derivative of -m**6/220 - m**5/330 + m**4/66 - 10*m**2 + 15. Let u(q) be the second derivative of a(q). Factor u(o).
-2*o*(o + 1)*(3*o - 2)/11
Let z = -2/27 + 43/216. Let s be 4*((-24)/(-84) - 9/56). Suppose z*p**2 + 0*p - s = 0. What is p?
-2, 2
Let d(j) be the first derivative of -5*j**4/42 + 2*j**3/7 - j**2/7 + 14*j - 2. Let a(t) be the first derivative of d(t). Factor a(r).
-2*(r - 1)*(5*r - 1)/7
Let v(d) be the second derivative of -5*d**4/72 - 17*d**3/18 + 13*d**2/4 - 175*d. Factor v(j).
-(j - 1)*(5*j + 39)/6
Suppose -21*c = 14 - 28 - 49. Factor 0 - 4/3*y**c + 2*y**2 + 0*y - 2/3*y**4.
-2*y**2*(y - 1)*(y + 3)/3
Let j(l) = 52*l**2 - 288*l + 864. Let b(t) = -8*t**2 + 44*t - 133. Let x(y) = 32*b(y) + 5*j(y). Factor x(o).
4*(o - 4)**2
Let m = -73475/14 + 5245. Let v = -19/7 - m. Suppose -v*x - 1/4*x**2 + 0 = 0. What is x?
-2, 0
Let j(u) = 2*u**2 + 13*u - 10. Let w be j(-7). Let g be (-3 + 13/5)/(w/15). Factor -1/2*x**g - 3/2 + 2*x.
-(x - 3)*(x - 1)/2
Find p, given that -95*p - p**3 + 192 + 21*p**2 + 151 - 52*p = 0.
7
Solve -3/2*x**2 + 0*x + 0 + 1/4*x**4 + 5/4*x**3 = 0.
-6, 0, 1
Let g(z) = z**3 + z**2 + z + 3. Let u be g(0). Let n be (-13 - -15) + u/(3/34). Determine w so that -81/2*w**2 - 3/2 - 14*w - 8*w**4 - n*w**3 = 0.
-3, -1, -1/4
Let u be -4 + 4 + 6/(-9)*-6. Suppose -u*k = -4*t, -4*k + 2*t = 7*t. Factor k*r + 0*r**2 + 1/5*r**3 + 0.
r**3/5
Let d(l) be the first derivative of l**5/10 - 7*l**3/6 + 3*l**2/2 + 120. Find k, given that d(k) = 0.
-3, 0, 1, 2
Let z = 1874 - 1870. Let m be (2/(-25))/(2/(-10)). Factor 2/5*d**z + 0 - m*d - 2/5*d**2 + 2/5*d**3.
2*d*(d - 1)*(d + 1)**2/5
Let u(i) be the third derivative of -2/105*i**7 - 3/20*i**5 - 5*i**2 + 0 + 1/6*i**3 + 1/24*i**4 + 11/120*i**6 + 0*i. Factor u(l).
-(l - 1)**3*(4*l + 1)
Factor -35/2*w - 20*w**2 + 5*w**4 - 5 + 5/2*w**5 - 5*w**3.
5*(w - 2)*(w + 1)**4/2
Let g = 584/3 + -1165/6. Factor -5/4*h**3 - 1/2 + 5/4*h + g*h**2.
-(h - 1)*(h + 1)*(5*h - 2)/4
Let r(p) be the first derivative of 5*p**3/3 - 750*p**2 + 112500*p - 58. Solve r(c) = 0.
150
Let i(c) = c**3 - 7*c**2 + c - 4. Let g be i(7). Determine p so that 0*p**g + 4*p - p**3 + 5*p**3 - 8 - 16*p = 0.
-1, 2
Suppose -63*o**