Let o be (6/(-4))/((-31)/124). Let z be 7*(-2)/o - -5. Factor 2/3*n**2 + 0*n - z.
2*(n - 2)*(n + 2)/3
Let p(g) be the first derivative of -2*g**5/75 - g**4/15 + 2*g**3/15 + 4*g**2/15 - 8*g/15 - 12. Factor p(l).
-2*(l - 1)**2*(l + 2)**2/15
Let h(q) be the third derivative of q**8/840 + q**7/140 + q**6/90 - 3*q**3/2 + 9*q**2. Let y(l) be the first derivative of h(l). Factor y(w).
2*w**2*(w + 1)*(w + 2)
Let k(d) = d + 15. Let q(s) = -2*s - 30. Let u(v) = 5*k(v) + 2*q(v). Let n be u(-12). What is j in 6*j**2 - 2*j**n - 18*j**2 - 2*j**3 = 0?
-3, 0
Let n(t) be the first derivative of 5*t**4/4 - 31*t**3/9 + 17*t**2/6 - t/3 + 63. Solve n(q) = 0.
1/15, 1
Suppose 3*t = -3*i, -24*t + 5*i = -23*t. Let o(m) be the second derivative of -8*m + t + 0*m**2 + 1/4*m**3 + 1/16*m**4. Factor o(v).
3*v*(v + 2)/4
Find k such that 94/3*k - 70/3 - 26/3*k**2 + 2/3*k**3 = 0.
1, 5, 7
Let b(n) = 10*n + 12. Let l(t) = -3*t + 10. Let c be l(5). Let d(k) = k**2 - 19*k - 25. Let f(p) = c*b(p) - 2*d(p). Let f(i) = 0. Calculate i.
-5, -1
Let z be 4/(-7) - (-4056)/42. Let y = -670/7 + z. Factor -4/7*b - y - 2/7*b**2.
-2*(b + 1)**2/7
Let b(j) be the third derivative of -j**5/80 + 5*j**4/32 - 3*j**3/4 - 334*j**2. Factor b(i).
-3*(i - 3)*(i - 2)/4
Let q(b) be the second derivative of -b**7/252 - b**6/36 + b**5/60 + 7*b**4/18 + 2*b**3/9 - 8*b**2/3 - 3*b + 36. Suppose q(j) = 0. Calculate j.
-4, -2, 1, 2
Let n(b) = -292*b - 2041. Let i be n(-7). Factor -1/3*g**4 + 1/3*g**i + 3*g**2 + 4/3 + 11/3*g.
-(g - 4)*(g + 1)**3/3
Let h = 254/5 - 253/5. Determine j so that 0*j**4 + 0*j**2 + h*j + 0 - 2/5*j**3 + 1/5*j**5 = 0.
-1, 0, 1
Let q be (-13 - (-16)/12 - -11)/((-5)/1). Factor 8/15*y**2 - 4/5 - q*y - 2/15*y**3.
-2*(y - 3)*(y - 2)*(y + 1)/15
Factor -15*i**3 + 0 - 12/5*i + 12*i**2.
-3*i*(5*i - 2)**2/5
Let a = 58/91 + -804/1547. Factor -a*n**2 - 18/17 - 12/17*n.
-2*(n + 3)**2/17
Let u(p) be the first derivative of -p**4 - 172*p**3/3 - 966*p**2 - 1764*p + 90. Find v, given that u(v) = 0.
-21, -1
Let v(x) = -117*x**4 + 3300*x**3 + 90771*x**2 + 21*x - 21. Let f(o) = 11*o**4 - 330*o**3 - 9077*o**2 - 2*o + 2. Let k(d) = 21*f(d) + 2*v(d). Factor k(z).
-3*z**2*(z + 55)**2
Let w(y) be the second derivative of y**5/20 - 5*y**4/3 + 50*y**3/3 + 6*y - 2. Factor w(v).
v*(v - 10)**2
Let b = 146/27 + -104/27. Determine v so that b*v**2 - 4/9 - 2*v**3 - 10/9*v**4 + 2*v = 0.
-2, -1, 1/5, 1
Let d(u) be the third derivative of -5/72*u**4 + 0 - 1/72*u**6 - 1/18*u**5 + 0*u**3 + 0*u + u**2. Let d(y) = 0. What is y?
-1, 0
Let h(u) be the second derivative of u**6/1080 - u**4/72 - u**3/3 + 39*u. Let d(w) be the second derivative of h(w). Factor d(g).
(g - 1)*(g + 1)/3
Let i(c) be the first derivative of 2*c**5/25 - 3*c**4/10 + 2*c**3/15 + 3*c**2/5 - 4*c/5 + 71. Factor i(m).
2*(m - 2)*(m - 1)**2*(m + 1)/5
Let x be 6/21 - 104/(-28). Let k(j) = -j**2 + 6*j. Let t be k(5). Factor 2*b**x + b**4 + b**4 + 0*b**t - 4*b**5.
-4*b**4*(b - 1)
Let y(t) be the second derivative of t**4/24 + 71*t**3/12 + 69*t**2/2 + 3*t + 70. Factor y(s).
(s + 2)*(s + 69)/2
Let z(w) be the second derivative of 0 + 14*w**2 + 1/3*w**4 - 3*w - 16/3*w**3. Factor z(x).
4*(x - 7)*(x - 1)
Let u(n) be the third derivative of -n**7/70 + 3*n**6/20 - 11*n**5/20 + 3*n**4/4 + 3*n**2 - 46*n. Factor u(z).
-3*z*(z - 3)*(z - 2)*(z - 1)
Let n(p) be the second derivative of p**5/80 - 11*p**4/48 - 31*p**3/8 - 153*p**2/8 + 162*p. Factor n(w).
(w - 17)*(w + 3)**2/4
Let k = 191 + -187. Let x(z) be the third derivative of -1/96*z**k + 5*z**2 - 1/120*z**5 + 0*z**3 - 1/480*z**6 + 0 + 0*z. Suppose x(f) = 0. What is f?
-1, 0
Let w be ((-3757)/170)/(-17) + (-1)/2. Let q(d) be the first derivative of -16*d - 4*d**4 + w*d**5 + 8*d**2 + 4*d**3 - 8. Factor q(v).
4*(v - 2)**2*(v - 1)*(v + 1)
Let q(w) be the second derivative of -w**7/14 + w**6/10 + 9*w**5/20 - w**4/4 - w**3 + 351*w. What is r in q(r) = 0?
-1, 0, 1, 2
Suppose -8*j + 45 = 21. Suppose 9/4*t**4 + 1/2*t**5 + 0 + 1/2*t + 9/4*t**2 + 7/2*t**j = 0. Calculate t.
-2, -1, -1/2, 0
Let w(y) be the first derivative of -y**5/3 + 25*y**4/12 + 20*y**3/9 - 50*y**2/3 + 79. Determine a, given that w(a) = 0.
-2, 0, 2, 5
Let o = -32436/7 - -4634. Let 0*h**2 + 1/7 + 2/7*h**3 - o*h - 1/7*h**4 = 0. What is h?
-1, 1
Let x be ((-130)/4)/((-5)/10). Let x*p**3 + 12*p - 5*p**4 + 8*p - 80*p**3 = 0. What is p?
-2, 0, 1
Let o(n) be the third derivative of -n**5/180 - 11*n**4/72 - 5*n**3/9 + 47*n**2. Factor o(p).
-(p + 1)*(p + 10)/3
Let b(q) = -10*q**2 + 4*q + 14. Let c(w) be the second derivative of -w**4/12 + w**2/2 - 7*w. Let a(v) = b(v) - 6*c(v). Factor a(g).
-4*(g - 2)*(g + 1)
Let s(u) = 2*u**2. Let d(k) = 8*k**2 - k - 4*k**2 + 4*k**2 + 0*k. Let l(q) = -4*d(q) + 18*s(q). Determine z, given that l(z) = 0.
-1, 0
Let a(f) be the first derivative of -3*f**5/5 + 99*f**4/4 - 30*f**3 - 96*f**2 + 508. Suppose a(v) = 0. Calculate v.
-1, 0, 2, 32
Let s(o) be the third derivative of -o**8/141120 - o**7/8820 - o**5/10 + 16*o**2. Let z(g) be the third derivative of s(g). Suppose z(j) = 0. What is j?
-4, 0
Let -22*w - 5 + 17 + w**2 + 9 = 0. Calculate w.
1, 21
Let u(h) be the first derivative of -1/6*h**5 - 18 - 5/8*h**4 - 5/12*h**2 + 0*h - 5/6*h**3. Factor u(m).
-5*m*(m + 1)**3/6
Let l = -1 + 9. Suppose 2*v + 2*v - l = 0. What is y in -y**2 + y + 8 + y**2 - 4*y**v + 3*y = 0?
-1, 2
Let c = 12/29 + -91/290. What is y in 3/10*y**2 + 0 + c*y**3 + 1/5*y = 0?
-2, -1, 0
Suppose 34*i - 87*i = -48 - 164. Let 6/5*g**2 + 0*g - 21/5*g**3 - 12/5*g**i + 0 = 0. What is g?
-2, 0, 1/4
Factor -2*b**2 + 321*b**4 + 2*b**2 - 317*b**4 - 4*b**5.
-4*b**4*(b - 1)
Suppose 0*s - 3*s + 34 = -5*l, 4*s - 27 = 3*l. Let 2*c**3 + 4*c**s - c**3 - 4 - 2*c**2 - 7*c - 4*c**3 = 0. Calculate c.
-1, 4
Factor -26/3*p**2 + 98/3 - 2/3*p**3 - 70/3*p.
-2*(p - 1)*(p + 7)**2/3
Let r = 82 - 79. Factor 4*v**3 - 16*v**r - 2*v + 6 - 6*v**2 + 14*v**3.
2*(v - 3)*(v - 1)*(v + 1)
Let i(z) be the third derivative of 1/20*z**5 + 25/2*z**3 + 0 - 5/4*z**4 + 14*z**2 + 0*z. Solve i(t) = 0.
5
Let z = -2200 - -2202. Determine v, given that 0 + 0*v - 16/15*v**z - 8/3*v**3 - 28/15*v**4 - 2/5*v**5 = 0.
-2, -2/3, 0
Let x(a) be the third derivative of 0 + 10*a**2 + 0*a**3 + 1/48*a**4 + 0*a - 1/240*a**5 + 1/840*a**7 - 1/16*a**6 + 1/48*a**8. Find k, given that x(k) = 0.
-1, -2/7, 0, 1/4, 1
Let x = -497 - -503. Let s(z) be the third derivative of 1/540*z**x + 0*z**3 + 3*z**2 - 1/270*z**5 + 0*z + 0*z**4 + 0. Factor s(o).
2*o**2*(o - 1)/9
Let k = 12 + 1. Suppose 3 - 9*l**3 - 3*l**3 - k + 12*l + 22 - 3*l**4 - 9*l**2 = 0. What is l?
-2, -1, 1
Suppose -2*x + 2 = -x. Let a = 14 - 11. Solve -a*y - 3/2 - 3/2*y**x = 0 for y.
-1
Let c(g) be the third derivative of -g**6/15 - g**5/5 + 2*g**3/3 - 11*g**2 + g. Let c(l) = 0. What is l?
-1, 1/2
Let o(d) = d**2 + 3*d - 12. Let h be o(-6). Let p be h/(-4)*24/(-54). Factor -1/3*x + 8/3*x**2 - 5/3*x**3 - p.
-(x - 1)**2*(5*x + 2)/3
Let r(w) be the second derivative of -w**5/450 - w**4/18 - 5*w**3/9 + 15*w**2/2 + 2*w. Let j(y) be the first derivative of r(y). Factor j(k).
-2*(k + 5)**2/15
Let j(s) = -2*s - 5. Let r be j(-4). Let 16*b**3 + b**4 - 7*b**r - 3*b - 5*b**2 - 10*b**3 = 0. Calculate b.
-1, 0, 3
Let l(a) be the first derivative of -16 + 1/2*a**2 + 2/3*a**3 + 1/4*a**4 + 0*a. Suppose l(v) = 0. Calculate v.
-1, 0
Let j(r) be the third derivative of 1/300*r**6 + 49/20*r**4 - r**2 + 0 + 343/15*r**3 + 7/50*r**5 + 0*r. Factor j(a).
2*(a + 7)**3/5
Let z(b) be the first derivative of b**4/66 + b**3/33 + 8*b - 11. Let a(s) be the first derivative of z(s). Suppose a(j) = 0. Calculate j.
-1, 0
Let j(y) = 2*y**2 - 41*y - 21. Let s be j(21). Let z(v) be the second derivative of 1/30*v**4 + 9/5*v**2 + s - 5*v - 2/5*v**3. Suppose z(c) = 0. What is c?
3
Let u(d) be the second derivative of 1/360*d**5 + 2*d + 0 - 1/144*d**4 + 5/2*d**2 - 1/18*d**3. Let b(f) be the first derivative of u(f). Factor b(m).
(m - 2)*(m + 1)/6
Let x = -35 + 40. Let n(j) = -2*j**5 + 8*j**4 - 3*j**3 + 2*j**2 + 5. Let z(q) = -q**5 + q**4 + q**2 + 1. Let w(p) = x*z(p) - n(p). Let w(f) = 0. Calculate f.
-1, 0, 1
Let p(f) be the third derivative of f**8/3864 - 8*f**7/2415 + f**6/92 + 11*f**2. What is b in p(b) = 0?
0, 3, 5
Let p(c) = 15*c**2 - 21*c - 30. Let a(h) = -43*h**2 + 63*h + 89. Suppose 0 = -2*y - 4*n - 29 - 5, 0 = -n. Let t(z)