 Find r, given that 23*r**3 - 15*r**5 - 27*r**4 + 31*r**4 - z*r - 4*r**2 - 3*r**3 + 3*r**5 = 0.
-1, -2/3, 0, 1
Let h = -2600/3 + 1124. Let s(p) be the first derivative of 36*p - 156*p**2 + h*p**3 + 64/5*p**5 - 7 - 104*p**4. Factor s(n).
4*(n - 3)**2*(4*n - 1)**2
Let t = 20 + -12. Let -x**4 - 8 + 17*x**2 - 5*x**2 + t*x**3 - 4*x**3 - 3*x**4 - 4*x = 0. Calculate x.
-1, 1, 2
Let j = 637/4 - 159. Let w(v) be the first derivative of j*v**2 - 1/4*v**3 + 1/16*v**4 + 4 + 0*v. Factor w(m).
m*(m - 2)*(m - 1)/4
Let d(v) be the third derivative of -v**5/120 - 25*v**4/48 + 13*v**3/6 - 623*v**2. Factor d(a).
-(a - 1)*(a + 26)/2
Let l(m) be the third derivative of m**8/1008 + m**7/315 - m**6/360 - m**5/90 - 55*m**2. Let l(s) = 0. What is s?
-2, -1, 0, 1
Let m(d) = 30*d**2 + 24*d + 3. Let z(o) = -o**3 - 60*o**2 - 49*o - 5. Let t(b) = 5*m(b) + 3*z(b). Factor t(q).
-3*q*(q + 1)*(q + 9)
Let h(x) be the third derivative of -x**8/1344 + 19*x**7/840 + 21*x**6/160 + 13*x**5/48 + 11*x**4/48 - 518*x**2. Factor h(a).
-a*(a - 22)*(a + 1)**3/4
Let j(f) be the third derivative of 1/1260*f**7 + 0*f - 1/16*f**4 + 21*f**2 + 0 + 1/120*f**5 + 0*f**3 + 1/144*f**6. Factor j(y).
y*(y - 1)*(y + 3)**2/6
Solve 338*a - 26*a**2 + 2/3*a**3 - 4394/3 = 0.
13
Let a = -75/16 - -241/48. What is h in 1/3*h + a*h**2 - 2 = 0?
-3, 2
Let h(p) be the third derivative of -p**6/24 - 3*p**5/2 - 20*p**4 - 320*p**3/3 - 3*p**2 - 11. Find f such that h(f) = 0.
-8, -2
Suppose w + 5 = -2*t, -5*t - w - 2*w = 15. Suppose -60*f + 54*f = -124*f + 236. Determine s, given that 0*s**3 + 16/9*s**f - 2/9*s**4 - 32/9 + t*s = 0.
-2, 2
Factor 72/5 - 68/5*w + 14/5*w**2 + 1/5*w**3.
(w - 2)**2*(w + 18)/5
Solve 2/13*g**3 - 2/13*g - 28/13*g**2 + 28/13 = 0 for g.
-1, 1, 14
Solve 10/9*k**2 + 16/9 - 52/9*k + 2/3*k**3 = 0 for k.
-4, 1/3, 2
Suppose -y + 3*u = 18, 76*u = -4*y + 78*u - 12. Factor -10*a + 10*a**2 + y - 5/2*a**3.
-5*a*(a - 2)**2/2
Let j(q) = -q**4 + 5*q**3 + 34*q**2 + 8*q - 48. Let w(d) = 12*d**4 - 66*d**3 - 441*d**2 - 102*d + 624. Let p(k) = 27*j(k) + 2*w(k). Factor p(z).
-3*(z - 4)*(z - 1)*(z + 2)**2
Let n(y) be the third derivative of -14*y**2 + 8/3*y**4 + 2197/105*y**7 + 0 + 338/15*y**6 + 52/5*y**5 + 0*y + 16/39*y**3. Let n(c) = 0. Calculate c.
-2/13
Let n be (-10)/45 + 0 - 936/(-567). Suppose 12/7 - n*m - 2/7*m**2 = 0. Calculate m.
-6, 1
Let h be (9135/84)/(-5) + 22. Factor 1/2*y + h*y**2 + 0 - 1/4*y**3.
-y*(y - 2)*(y + 1)/4
Let c(r) be the second derivative of 0 - 2/15*r**3 + 2/5*r**2 - 1/15*r**4 + 6*r + 1/25*r**5. Factor c(v).
4*(v - 1)**2*(v + 1)/5
Let x(v) = -v. Let j(l) be the second derivative of l**4/6 - 7*l**3/6 + 2*l**2 - 12*l. Let m(f) = -j(f) + x(f). Solve m(c) = 0 for c.
1, 2
Let v = 15831/31666 + 1/15833. Find h such that -v*h**4 - 3/2*h + 5/2*h**2 - 1/2*h**3 + 0 = 0.
-3, 0, 1
Let f(w) be the second derivative of -1/4*w**4 + 7*w - 3/20*w**5 + 0 + 1/10*w**6 + 1/2*w**3 + 0*w**2. Suppose f(l) = 0. Calculate l.
-1, 0, 1
Let i be (-3 - (-20)/6)*(-6)/(-20). Let n(b) be the second derivative of 0 + i*b**4 - 2*b + 0*b**2 + 1/10*b**3 + 3/100*b**5. Determine y, given that n(y) = 0.
-1, 0
Let o(r) be the second derivative of -r**5/10 + 4*r**3 - 16*r**2 - 3*r - 19. Determine v so that o(v) = 0.
-4, 2
Factor 13/3*a - 22/3 - 1/3*a**2.
-(a - 11)*(a - 2)/3
Let l(f) = -2*f - 12. Let i be l(-7). Suppose -i*a + 2*m + 4 = 0, -m = 4*m. Factor -5*c - 10 + 13*c - a*c**2 + 2.
-2*(c - 2)**2
Let o(j) be the first derivative of 6*j**4/7 - 22*j**3/7 - 9*j**2/7 + 105. Let o(k) = 0. What is k?
-1/4, 0, 3
Let y(q) be the third derivative of q**8/112 + 5*q**7/168 + q**6/36 + 7*q**3/2 - 14*q**2. Let s(m) be the first derivative of y(m). Solve s(z) = 0.
-1, -2/3, 0
Suppose -5*s = p - 5 - 1, -2*s - 2*p = 4. Factor 8*m + 1 - 9 - 2 + 4 - s*m**2.
-2*(m - 3)*(m - 1)
Let p(z) be the second derivative of 1/540*z**6 - 1/108*z**4 + 1/270*z**5 + 0 + 2*z - 2/3*z**3 + 0*z**2. Let d(f) be the second derivative of p(f). Factor d(r).
2*(r + 1)*(3*r - 1)/9
Let d = 1168/959 - 72/959. What is r in 0 + d*r + 44/7*r**2 + 48/7*r**3 - 4/7*r**4 - 16/7*r**5 = 0?
-1, -1/4, 0, 2
Let i be ((-2)/(-2))/((-2)/(-8)). Let u be -5 - (30/(-75) - 23/5). Factor -2*q**2 + 2/3*q**i - 4/3*q + u + 0*q**3.
2*q*(q - 2)*(q + 1)**2/3
Let z(k) be the first derivative of -k**6/8 - 3*k**5/4 - 21*k**4/16 + k**3/4 + 3*k**2 + 3*k - 158. Solve z(c) = 0.
-2, -1, 1
Let u = 8/21 + -62/273. Factor u*d**2 + 0*d - 2/13*d**3 + 0.
-2*d**2*(d - 1)/13
Let s = 287 - 283. Let a(x) be the second derivative of 0 + 1/12*x**s + 3*x - 2/3*x**2 + 1/60*x**5 + 0*x**3. Factor a(i).
(i - 1)*(i + 2)**2/3
Let n = -2565/154 + 184/11. Let i(o) be the third derivative of 0*o - 1/210*o**5 + n*o**4 - 9*o**2 - 3/7*o**3 + 0. Factor i(v).
-2*(v - 3)**2/7
Let 434*d + 5*d**5 + 157*d - 679*d**2 - 23*d**4 + d - 33*d**2 - 54*d**4 + 360*d**3 - 144 = 0. What is d?
2/5, 2, 9
Factor 1 - 60*i**5 + 33*i**5 - 67*i**3 + 25*i**3 - 195*i**4 - 1.
-3*i**3*(i + 7)*(9*i + 2)
Let p(h) be the first derivative of 15*h**4/4 + 6*h**3 - 27*h**2/2 - 6*h - 51. Factor p(f).
3*(f - 1)*(f + 2)*(5*f + 1)
Let z(b) be the first derivative of 7*b**4 - 176*b**3/3 + 94*b**2 - 40*b + 31. Factor z(u).
4*(u - 5)*(u - 1)*(7*u - 2)
Let z(n) be the first derivative of -2*n**3/33 + 6*n**2/11 - 16*n/11 + 41. Factor z(t).
-2*(t - 4)*(t - 2)/11
Let v(h) = -3*h**5 + 11*h**4 - 9*h**3 + 4*h - 1. Let y(u) = u**4 + u**3 - u + 1. Let p(g) = -2*v(g) + 2*y(g). Factor p(q).
2*(q - 1)**4*(3*q + 2)
Solve -12/5 - 2/5*a**3 + 14/5*a + 0*a**2 = 0.
-3, 1, 2
Let a(d) be the third derivative of -3*d**2 + 1/180*d**6 + 0 + 0*d + 1/18*d**5 - d**3 + 1/12*d**4. Suppose a(g) = 0. Calculate g.
-3, 1
Let x(i) = 2*i**2 - 4*i - 22. Let k be x(7). Let p = k - 526/11. Factor 0 + 2/11*j + p*j**5 + 0*j**2 + 0*j**4 - 4/11*j**3.
2*j*(j - 1)**2*(j + 1)**2/11
Let g = 1149 + -1147. Suppose 0*w**g + 1/6*w + 0 - 1/6*w**3 = 0. What is w?
-1, 0, 1
Let c(r) = -r + 15. Let m be c(3). Suppose -40*q**2 - 308 + 142 - 4*q**5 - 84*q + 24*q**3 + m*q**4 + 130 = 0. What is q?
-1, 3
Let t(j) be the third derivative of j**7/210 + j**6/90 - 3*j**3/2 - 11*j**2. Let v(p) be the first derivative of t(p). Factor v(c).
4*c**2*(c + 1)
Let m(k) be the third derivative of -1/120*k**6 + 1/24*k**4 + 0*k - 1/15*k**3 + 11*k**2 + 0 + 1/350*k**7 - 1/300*k**5. Factor m(l).
(l - 1)**2*(l + 1)*(3*l - 2)/5
Let l be (-362)/(-180) + (-7)/(21/6). Let q(p) be the second derivative of 1/54*p**4 - 2*p + l*p**5 - 5/27*p**3 + 0 + 1/3*p**2. What is k in q(k) = 0?
-3, 1
Let i(m) be the first derivative of -m**6/24 - m**5/5 + 13*m**4/8 - 11*m**3/3 + 31*m**2/8 - 2*m - 16. Factor i(z).
-(z - 1)**4*(z + 8)/4
Suppose -l + 1 = -3*b, 5*b = 9*b + 8. Let g be (-3)/l - (-5)/25. Factor -8/5*y + 4/5*y**2 + g.
4*(y - 1)**2/5
Let j be ((-44)/417)/(54/(-675)). Let x = 2/139 + j. What is q in 4/3*q**2 - 4/3*q**4 + x*q + 0 - 7/3*q**3 + q**5 = 0?
-1, -2/3, 0, 1, 2
Let p be -3 - (0 - 1)/((-9)/(-33)). Let x = 28/51 - -2/17. Factor 0 - 1/3*s + 0*s**3 - x*s**2 + p*s**4 + 1/3*s**5.
s*(s - 1)*(s + 1)**3/3
Factor 8*s**3 + 1012*s + 242 + 75*s**2 + 103*s**2 + 0*s**3.
2*(s + 11)**2*(4*s + 1)
Solve 0 - 2/13*h**2 + 16/13*h = 0 for h.
0, 8
Factor 1/4*j**4 - 3/4 - j**3 + 1/2*j**2 + j.
(j - 3)*(j - 1)**2*(j + 1)/4
Suppose 4*k = 2*m - 20, -k + 3*k + 6 = 0. Factor 0*o**m + 3*o**4 - 6*o**3 - 4*o**5 + 0*o**3 + 7*o**5.
3*o**3*(o - 1)*(o + 2)
Suppose 22 = 11*l - 0*l. Let 28*k**3 - l*k**2 + k**2 - 27*k**3 - 2*k**2 = 0. What is k?
0, 3
Let f(j) = 3*j. Let i be f(1). Factor 2 - 3*v + i + 2*v**2 + 11*v + 1.
2*(v + 1)*(v + 3)
Factor 8 + 15 - 8*b + 4*b**2 - 8 - 27.
4*(b - 3)*(b + 1)
Let v(o) be the third derivative of -o**8/1848 - 4*o**7/1155 + 80*o**2 - o. Determine f so that v(f) = 0.
-4, 0
Suppose 0 = 3*h - x, 0 = 6*h - 10*h - x + 14. Factor h*b - 2 - 1/2*b**2.
-(b - 2)**2/2
Let n = -698 - -701. Factor j + 13*j**2 + 0 + 169/4*j**n.
j*(13*j + 2)**2/4
Solve 39/2*n**2 + 33/2*n**4 + 30*n**3 + 0 + 15/4*n + 9/4*n**5 = 0.
-5, -1, -1/3, 0
Let t(u) be the second derivative of -2*u**7/525 + u**6/150 + 2*u**5/75 - 12*u**2 + 10*u. Let f(r) be the first derivative of t(r). Factor f(k).
-4*k**2*(k - 2)*(k + 1)/5
Solve -6561/2*a + 41/3*a**4 + 0 - 378*a**3 - 1/6*a**5 + 3645*a**2 = 0.
0, 1, 27
Let d(g) be the third derivative of -g**6/120 - g**5/8 - 3*g**4/4 - 31*g**3/6 + 7*g**2. Let n(u) b