Let p(b) be the third derivative of b**5/20 - 5*b**4/4 - 11*b**3/2 + 3*b**2 - 14. Determine r so that p(r) = 0.
-1, 11
Let d(c) be the first derivative of -c**6/3 - 14*c**5/5 + c**4/2 + 14*c**3/3 - 467. Solve d(a) = 0.
-7, -1, 0, 1
Let h(t) be the first derivative of t**5/20 + 9*t**4/16 + 7*t**3/4 - t**2/8 - 15*t/2 + 194. Let h(k) = 0. What is k?
-5, -3, -2, 1
Suppose -3*s = -2*s - 3. Solve 3*z + 6*z**3 - 11*z + s*z**2 - 6*z**4 + 4*z**3 + 5*z**2 = 0.
-1, 0, 2/3, 2
Let o(q) = -q**2 - 10*q - 13. Let a be o(-9). Let z be (a/3)/(22/(-33)). Factor 0*s**z + 0 - 1/4*s + 1/4*s**3.
s*(s - 1)*(s + 1)/4
Let r be 2/6*-1 - 342/27. Let d be ((-494)/60)/r - (-1)/6. Solve 0*t**3 + 2/5*t**5 + 0 - 2/5*t + d*t**2 - 4/5*t**4 = 0.
-1, 0, 1
Let t be 1/(-2)*10/(-4). Let q = 30440 + -30440. Determine m so that 5/4*m**4 + q - 1/4*m**3 + 3/4*m**5 - 1/2*m - t*m**2 = 0.
-1, -2/3, 0, 1
Let 138 - 40 - 4*z - 73*z + 5*z**3 + 16*z**2 - 6*z**3 = 0. Calculate z.
2, 7
Let f(c) be the second derivative of -c**7/126 - c**6/45 - c**5/60 - c + 10. Find s, given that f(s) = 0.
-1, 0
Let q(c) be the second derivative of c**6/6 - c**5 + 5*c**4/4 + 10*c**3/3 - 10*c**2 + 7*c + 4. Factor q(i).
5*(i - 2)**2*(i - 1)*(i + 1)
Factor 195112/7*n + 1414562/7 + 2/7*n**4 + 10092/7*n**2 + 232/7*n**3.
2*(n + 29)**4/7
Let m be (9 - 1)*(-2)/(-16)*2. Factor -c + 0 + 1/3*c**m.
c*(c - 3)/3
Factor 25*z**4 + 36*z + 27*z - 20*z**3 - 6*z**5 + z**5 - 63*z.
-5*z**3*(z - 4)*(z - 1)
Factor -10*m**3 - 506*m**4 - 502*m**4 + 15*m**2 + 1003*m**4.
-5*m**2*(m - 1)*(m + 3)
Let u(r) be the third derivative of -r**8/20160 - r**7/630 - r**6/45 + 13*r**5/60 + 8*r**2. Let b(i) be the third derivative of u(i). Find s such that b(s) = 0.
-4
Let c(t) = 2*t**3 + 19*t**2. Let j(d) = 5*d**3 + 55*d**2. Let w(v) = 10*c(v) - 3*j(v). What is i in w(i) = 0?
-5, 0
Let a(k) be the second derivative of -k**5/50 + k**4/15 + k**3/15 - 2*k**2/5 - 305*k. Factor a(x).
-2*(x - 2)*(x - 1)*(x + 1)/5
Factor 0*m**2 - 1 + 6 + 0 - 11*m + 8*m**2 - 2.
(m - 1)*(8*m - 3)
Factor 1/12*t**5 + 0 + 13/12*t**3 - 5*t**2 + 3*t + 5/6*t**4.
t*(t - 1)**2*(t + 6)**2/12
Suppose -62*s - 35 + 156 = -127. What is j in 2*j + 0 + 41/2*j**3 + 12*j**2 + 21/2*j**s = 0?
-1, -2/3, -2/7, 0
Let h(w) = -w**3 + w**2 + 2. Let k(u) = u**5 + 5*u**4 + 5*u**3 + u**2 - 8*u. Let l(j) = -2*h(j) + k(j). Factor l(y).
(y - 1)*(y + 1)**2*(y + 2)**2
Let f(w) be the third derivative of w**8/168 + w**7/15 - w**6/60 - 7*w**5/30 + w**2 - 6. Factor f(y).
2*y**2*(y - 1)*(y + 1)*(y + 7)
Let t(q) be the third derivative of 0*q + 4*q**3 - 5/6*q**4 + 0 + 21*q**2 + 1/15*q**5. Factor t(v).
4*(v - 3)*(v - 2)
Let q(y) = 172*y**2 - 144*y - 3. Let i(k) = -87*k**2 + 70*k + 2. Let j(x) = -5*i(x) - 3*q(x). What is o in j(o) = 0?
1/81, 1
Let a = 7/412 - -377/2060. Find d such that d - 1/5*d**3 - 3/5 - a*d**2 = 0.
-3, 1
Let g = 607 - 607. Factor 1/3*o**2 + 0 + g*o - 1/3*o**3.
-o**2*(o - 1)/3
Let l(z) = 3*z**4 - 3*z**2 - 3*z - 1. Let w(p) = -8*p**5 - p**3 - 1 + 0*p**3 + 2*p**5 + 5*p**5 - p. Let f(b) = -l(b) + w(b). Factor f(n).
-n*(n - 1)*(n + 1)**2*(n + 2)
Let v(s) be the third derivative of s**8/57120 - s**7/21420 + 25*s**4/24 - 35*s**2. Let o(h) be the second derivative of v(h). Let o(b) = 0. What is b?
0, 1
Let w(f) be the third derivative of 22*f**7/735 - 23*f**6/105 + 52*f**5/105 - 4*f**4/21 + 71*f**2. Factor w(l).
4*l*(l - 2)**2*(11*l - 2)/7
Let b(q) be the second derivative of q**8/560 + q**7/56 + q**6/15 + q**5/10 + 13*q**3/2 + 29*q. Let k(f) be the second derivative of b(f). Factor k(d).
3*d*(d + 1)*(d + 2)**2
Let d(l) be the third derivative of l**5/60 - 10*l**4/3 + 79*l**3/6 - 2*l**2 - 114. Let d(v) = 0. What is v?
1, 79
Let d(w) be the second derivative of -w**7/56 + w**6/8 - 9*w**5/40 - 100*w. Factor d(m).
-3*m**3*(m - 3)*(m - 2)/4
What is u in -4*u**4 - 55*u + 44*u**3 + 30 + 39*u**4 + 11*u**3 - 65*u**2 = 0?
-2, -1, 3/7, 1
Let a = 47 - 40. Suppose -4 = 5*l + 4*k, -5*k + 2 = -5*l + a. Factor l - t + t**3 - 1/2*t**2 + 1/2*t**4.
t*(t - 1)*(t + 1)*(t + 2)/2
Let m be (-1 - -1)*2/(-4). Let j = 1229 - 1224. Factor -1/2*c**4 - c**3 + 1/2*c**j + 0*c**2 + 0 + m*c.
c**3*(c - 2)*(c + 1)/2
Let s(r) be the first derivative of -2*r**3/9 - 2*r**2/3 - 66. Factor s(p).
-2*p*(p + 2)/3
Let n(i) = -i**3 - 1. Let h(z) = 18*z**5 + 31*z**4 - 20*z**3 - 24*z**2 - 4*z + 1. Let m(d) = -h(d) - n(d). What is b in m(b) = 0?
-2, -1/2, -2/9, 0, 1
Suppose -u - 50 + 44 = 0. Let b be 2 + -4 + 8/u + 4. Find m, given that -b - 1/3*m**2 + m = 0.
1, 2
Let y = 1322 + -7931/6. Factor 0*z + 1/3*z**3 - y*z**2 - 1/6*z**4 + 0.
-z**2*(z - 1)**2/6
Let c(b) = 9*b**5 + 4*b**3 - 4*b**4 + b**3 - 10*b**5 + 2*b**5 - 5*b**2. Let i(m) = -2*m**4 + 2*m**3 - 2*m**2. Let d(p) = 4*c(p) - 10*i(p). Factor d(l).
4*l**4*(l + 1)
Let f(y) = -2*y**2 - y - 5. Let n(w) = 5*w**2 + 2*w + 15. Let p(z) = -8*f(z) - 3*n(z). Let t be p(-4). Suppose -3 - d**2 + 4 - t*d**2 + 3*d = 0. Calculate d.
-1/4, 1
Let a(c) be the third derivative of 6*c**2 + 0 + 0*c**3 + 1/360*c**5 + 0*c + 0*c**4. Factor a(m).
m**2/6
Let y(n) be the second derivative of -2*n**6/75 + 2*n**5/5 + 4*n**4/15 - 308*n**3/15 - 294*n**2/5 - 81*n. Solve y(h) = 0 for h.
-3, -1, 7
Factor 5*o**4 - 3*o**3 + 134*o**2 - 120*o**2 - 52*o**2 - 52*o**2 - 12*o**3.
5*o**2*(o - 6)*(o + 3)
Let k(d) be the third derivative of -d**8/1512 + 44*d**7/945 - 113*d**6/108 + 901*d**5/135 - 520*d**4/27 + 800*d**3/27 - 675*d**2. What is r in k(r) = 0?
1, 2, 20
Let w(n) = 33*n**3 - 63*n**2 - 3*n. Let f(g) = -g**4 - g**3 + g. Let z(h) = -3*f(h) - w(h). Let z(a) = 0. What is a?
0, 3, 7
Suppose 2*k + 96 = -2*o + 270, -2*o = k - 171. Factor o + 4*s - 82 - s**2 + 3*s**2.
2*(s + 1)**2
Let o be (((-40)/154)/5)/((-4)/(-10)). Let w = o - -3/11. Factor -w*v - 2/7 + 1/7*v**2.
(v - 2)*(v + 1)/7
Let q(t) be the second derivative of t**4/9 - 22*t**3/9 + 14*t. Factor q(o).
4*o*(o - 11)/3
Suppose 16 = -3*b + 7*b. Let c = b - 0. Solve -2*q**2 + 2*q**5 - 4*q**c + 3*q**2 - q**2 = 0 for q.
0, 2
Let g = 1084288/7 - 154898. Let u = 610/77 - 84/11. Factor 0*b**2 + g*b**3 + 0*b + 0 - u*b**4.
-2*b**3*(b - 1)/7
Let v(n) be the first derivative of 3*n**5/25 + 3*n**4/4 + 6*n**3/5 + 318. Factor v(x).
3*x**2*(x + 2)*(x + 3)/5
Let j(u) be the first derivative of u**3/3 - 39*u**2 + 1521*u + 194. Solve j(k) = 0.
39
Let k(j) be the second derivative of j**8/16800 + j**7/1890 + j**6/600 + j**5/450 - 17*j**4/12 + 2*j + 1. Let n(s) be the third derivative of k(s). Factor n(f).
2*(f + 1)*(f + 2)*(3*f + 1)/15
Let h(o) = -55*o**2 - 562*o - 108. Let w(d) = 110*d**2 + 1125*d + 220. Let q(t) = -5*h(t) - 2*w(t). Factor q(l).
5*(l + 10)*(11*l + 2)
Suppose l - 4 = 1. Suppose -h - l*h = 0. Suppose 2/9*x**5 + 0*x**2 + 0 + 0*x**3 + h*x + 0*x**4 = 0. What is x?
0
Find v, given that 17/6*v - 1/6*v**3 + 5/2 + 1/6*v**2 = 0.
-3, -1, 5
Let q(t) be the first derivative of 0*t**2 - 16 + 1/9*t**3 + 0*t - 1/8*t**4 + 1/30*t**5. Factor q(w).
w**2*(w - 2)*(w - 1)/6
Let n(k) be the third derivative of k**5/20 + k**4 - 10*k**3 - 195*k**2. Solve n(u) = 0.
-10, 2
Let j be (-2)/(-4)*-6 - -7. Let d be (0 - j) + 21/3. Determine h so that -2*h - 4*h**4 + h**2 + 3*h**4 + h**d + 2*h - h**5 = 0.
-1, 0, 1
Let n(f) = 2*f**2 - 285*f + 2. Let d be n(0). Suppose 2/3*v + 0 + 8/3*v**d = 0. Calculate v.
-1/4, 0
Let y(b) = -3*b**2 + b**3 - 4*b - 23 + 0*b**2 + 13 + 12. Let g be y(4). Factor -1 - 1/2*h + 1/2*h**g.
(h - 2)*(h + 1)/2
Let p(r) be the third derivative of -r**6/80 + 3*r**5/40 + 9*r**4/16 - 27*r**3/4 + 2*r**2 - 5*r. Factor p(y).
-3*(y - 3)**2*(y + 3)/2
Factor -10 - 5292*h - 1 + 11 - 252*h**2 - 3*h**3.
-3*h*(h + 42)**2
What is i in 0*i**2 + 189*i**4 - i**3 - 2*i**2 - 188*i**4 - 10*i**2 = 0?
-3, 0, 4
Factor 1659 - 16*b + 10*b**2 - 2*b**3 - 1683 + 4*b**3.
2*(b - 2)*(b + 1)*(b + 6)
Let a(g) = -g**2 - 161*g - 778. Let t be a(-5). Solve 2/3*u**3 - 8/3 - 14/3*u - 4/3*u**t = 0 for u.
-1, 4
Determine h, given that -35*h**2 - 136*h**3 - 34*h + 133*h**3 + 13*h + 11 = 0.
-11, -1, 1/3
Let d(i) be the second derivative of i**4/12 - 11*i**3/3 + 20*i**2 - 47*i. Find n such that d(n) = 0.
2, 20
Let m be 2/((-24)/(-2))*45/10. Let u(k) be the second derivative of m*k**2 + 0 - 1/8*k**4 + 0*k**3 - 4*k. Factor u(b).
-3*(b - 1)*(b + 1)/2
Let x(d) = d**3 + 11*d**2 - 24*d. Let a(z) = z**2. Let m(j) = 4*a(j) - 4*x(j). Let m(v) = 0.